罗斯公司理财答案第六版(英文)

公司理财习题答案第二十八章Chapter 28: Cash Management28.1 Firms need to hold cash to:a. Satisfy the transaction needs. For example, cash is collected from sales and newfinancing and disbursed as wages, salaries, trade debts, taxes and dividends.b. Maintain compensating balances. A minimum required compensating balance atbanks providing credit service to the firm may impose a lower limit on the level ofcash a firm holds.28.2 a. Decrease. Examine the Baumol model. As the interest rate (k) increases, the optimalcash balance must also rise.b. Increase. Examine the Baumol model. As brokerage costs (F, the per transactioncosts) rise, the optimal balance increases.c. Decrease. Clearly, if the bank lowers its compensating balance requirement, a firmwill not be required to hold as much of its assets as cash.d. Decrease. If the cost of borrowing falls, a firm need not hold as much of its assets ascash because the cost of running short, i.e. the cost to borrow to fill cash needs, islower.e. Increase. As a firm’s credit rating falls, its cost to borrow increases. Thus, the firmcannot as easily afford to run short of cash and its cash balance must be higher.f. Decrease. Introduction of direct banking fees would increase the fixed costsassociated with holding cash. As fixed costs rise, the optimal balance must also rise.28.3 The average weekly cash balance is $20,750 [ ($24,000 + $34,000 + $10,000 +$15,000)/ 4].With monthly compounding, the return that the firm can earn on its average balance is$20,750 [[( 1 + 0.12/12)12 - 1] = $2,631.62Your answer may differ if you made different assumptions about the interest payments.28.4 a. The total amount of cash that will be disbursed during the year is:$345,000 * 12 = $4,140,000 Using the optimal cash balance formula,193,243$07.0)000,140,4)(500($2K 2FT*C ===$243,193 should be kept as cash. The balance, $556,807 (=$800,000-$243,193),should be invested in marketable securities.b. The number of times marketable securities will be sold during the next twelvemonths is $4,140,000 / $243,193 = 17 times28.5C*2FT K T KC *2F 7.5%(20mil)25,0007.5%200.01$3,000(mil)Average w eekly disbursement 3,00052$57.69mil222===⨯⨯=⨯===28.6 Use the Miller-Orr formula. The target cash balance = Z*3F 4K L 23=+σ The upper limit = H*=3Z*-2LThe daily opportunity cost = K= 1.0836510.000211-=Z*3($600)($1,440,00)4(0.000211)3$20,000$34,536H *$63,608=+== The average cash balance:C *4Z *L34($34,536)$20,0003$39,381=-=-=28.7 a.Z g*Hg 2L g 3200,0002100,0003$133,333Z s *Hs 2L s 3300,0002150,0003$200,000=+=+⨯==+=+⨯=b. Gold Star:()()s Z *L 4K /3F 133,333100,00040.00026132,0006,444,251K 1.1010.000261g 2g g3g g 3g 365=-=-⨯⨯⨯≈=-=Silver Star:()()s Z *L 4K /3F 200,000150,00040.00023632,000K 1.0910.000236g 2g g3g g 3g 365=-=-⨯⨯⨯≈=-=15733333,,So, Silver Star Co. has a more volatile daily cash flow.28.8 Garden Groves float = 150 ($15,000) = $2,250,000Increase in collected cash balance if a 3 day lockbox is installed = 3($2,250,000)= $6,750,000Annual earnings from this amount = $6,750,000 x 0.075 = $506,250The system should be installed if its cost is below this amount.Variable cost $ 0.5 x 150 x 365 = $27,375 Fixed cost = 80,000Total cost =$107,375The lockbox system should be installed. The net earnings from the use of the system are $398,875 (= $506,250 - $107,375)公司理财习题答案第二十八章28.9 To make the system profitable, the net earnings of installing the lockbox system must benon-negative. The lower limit for acceptability is zero profits.Let N be the number of customers per day.Earnings = ($4,500) (N) (2) (0.06) = $540 x NCosts:Variable cost: N (365) ($0.25) = $91.25 x NFixed cost: $15,000Equate Earnings to total costs:N = 33.43Salisbury Stakes needs at least 34 customers per day for the lockbox system to beprofitable.28.10 Disbursement float = $12,000 x 5 = $60,000Collection float = -$15,000 x 3 = -$45,000Net float = $60,000 - $45,000 = $15,000If funds are collected in four days rather than three, disbursement float will not change.Collection float will change to -$60,000. This change makes the net float equal to zero.28.11 a. Reduction in outstanding cash balances = $100,000 x 3 days = $300,000b. Return on savings = $300,000 (0.12) = $360,000c. Maximum monthly charge = $36,000 / 12 = $3,000Note: The calculation in part b assumes annual compounding. The answer in part cdoes not account for the time value of money. With monthly compounding of theinterest earned, the return on savings at the end of the year is$300,000 [(1.01)12 - 1] = $38,047.51The present value of this amount is $38,047.51 / (1.01) 12 = $33,765.23Compute the monthly payment as an annuity with a discount rate of 1% per periodfor twelve periods. That annuity factor is 11.2551. Thus, the payment is$33,765.23 = (Payment) (11.2551)Payment = $3,000Notice, as long as the treatment of the cash flows is the same, the payment is thesame.28.12 The cash savings are the earnings from the interest bearing account. Assuming dailycompounding, the three-day return to the delayed payment is($200,000)[(1.0004)3-1] = $240.096The interest rate for two weeks is 0.5615% (=(1.0004)14-1).Therefore, the present value of this annuity is($240.096)11(1.005615)260.005615$5,793.12 -=⎡⎣⎢⎢⎢⎢⎤⎦⎥⎥⎥⎥The Walter Company will save $5,793.12 per year.28.13 If the Miller Company divides the eastern region, collections will be accelerated by oneday freeing up $4 million per day. Compensating balances will be increased by $100,000 [=2($300,000)-$500,000]. The net effect is to have $3,900,000 to invest. If T-bills pay 7%per year, the annual net savings from the division of the eastern region is $3,900,000 x 0.07 = $273,000.28.14 Lockbox: interest saved = 7,500 x 250 x 1.5 x0.0003 = $843.75Annual saving (Annual charge) = 843.75 x 365 - 30,000 - 0.3 x 250 x 365= $250,593.75Annual saving (Concentration Banking) = 7,500 x 250 x1 x 0.0003 x 365= 562.5 x 365 = $205,312.5So the lockbox system is recommended.28.15 The important characteristics of short-term marketable securities are:i. maturityii. default riskiii. marketabilityiv. taxability。

Chapter 18: Dividend Policy: Why Does It Matter?18.1 February 16: Declaration date - the board of directors declares a dividend payment thatwill be made on March 14.February 24: Ex-dividend date - the shares trade ex dividend on and after this date.Sellers before this date receive the dividend. Purchasers on or after thisdate do not receive the dividend.February 26: Record date - the declared dividends are distributable to shareholders of record on this date.March 14: Payable date - the checks are mailed.18.2Based on Miller and Modigliani reasoning, the stock will sell for $8.75. This is the same priceyoupurchased the stock. When the stock goes ex-dividend the stock is expected to fall $0.75 a share.18.3 a. If the dividend is declared, the price of the stock will drop on the ex-dividenddate by the value of the dividend, $5. It will then trade for $95.b. If it is not declared, the price will remain at $100.c. Mann’s outflows for investments are $2,000,000. These outflows occ urimmediately. One year from now, the firm will realize $1,000,000 in netincome and it will pay $500,000 in dividends. Since the only immediatefinancing need is for the investments, Mann must finance $2,000,000 throughthe sale of shares worth $100. It must sell $2,000,000 / $100 = 20,000 shares.d. The MM model is not realistic since it does not account for taxes, brokeragefees, uncertainty over future cash flows, investors’ preferences, signaling effects,and agency costs.18.4 a. The ex-dividend date is Feb. 27, which is two business days before the record date.b. The stock price should drop by $1.25 on the ex-dividend date.18.5 Knowing that share price can be expressed as the present value of expected futuredividends does not make dividend policy relevant. Under the growing perpetuitymodel, if overall corporate cash flows are unchanged, then a change in dividend policy only changes the timing of the dividends. The PV of those dividends is the same. This is true because, given that future earnings are held constant, dividend policy simplyrepresents a transfer between current and future stockholders.In a more realistic context and assuming a finite holding period, the value of the shares should represent the future stock price as well as the dividends. Any cash flow not paid as a dividend will be reflected in the future stock price. As such the PV of the flowswill not change with shifts in dividend policy; dividend policy is still irrelevant.18.6 a. The price is the PV of the dividends,$2 .$17..$1511553751152+=b. The current value of your shares is ($15)(500) = $7,500. The annuity youreceive must solve$7,500X1.15X1.152 =+;You desire $4,613.3721 each year. You will receive $1,000 in dividends in the first year, so you must sell enough shares to generate $3,613.3721. The end-of-year price at which you will sell your shares is the PV of the liquidating dividend, $17.5375 / 1.15 = $15.25, so you must sell 236.942 shares. The173 / 6remaining shares will each earn the liquidating dividend. At the end of thesecond year, you will receive $4,613.38 [= (500 - 236.942) x $17.5375].(Rounding causes the discrepancies).18.7 a. The value is the PV of the cash flows.Value = $32,000 + $1,545,600 / 1.12 = $1,412,000b. The current price of $141.20 per share will fall by the value of the dividend to $138.c. i. According to MM, it cannot be true that the low dividend is depressing theprice. Since dividend policy is irrelevant, the level of the dividend shouldnot matter. Any funds not distributed as dividends add to the value of thefirm hence the stock price. These directors merely want to change the timingof the dividends (more now, less in the future). As the calculations belowindicate, the value of the firm is unchanged by their proposal. Therefore,share price will be unchanged.To pay the $4.25 dividend, new shares, which total $10,500 (-$42,500 -$32,000) in value, must be sold. Those shares must also earn 12% so thevalue of the old shareholders’ interest one year hence will fall $11,760(=10,500 x 1.12). Under this scenario, the current value of the firm is Value= $42,500 + $1,533,840 / 1.12 = $1,412,000ii. The new shareholders are not entitled to receive the current dividend. They will receive only the value of the equity one year hence. The PV of thoseflows is $1,533,840 / 1.12 = $1,369,500, so the share price will be $136.95and 76.67 shares will be sold.18.8 a. (1.2 + 15) / 1 = $16.2Expected share price is $16.2.b. He can invest the dividends into the Gibson stock.Dividends that he gets = $1.2 million x 50% x 1,000 / 1,000,000 = $600Expected share price after dividend = (0.6 + 15) / 1 =$15.6Number of shares that Jeff needs to buy = 600 / 15.6 = 3818.9 Alternative 1: Dividends are paid out to the shareholders now.2 (1-31%) (1+7% (1-31%))3 = $1.59 millionAlternative 2: NBM invests cash in the financial assets:i. T-bill2 (1+7% (1-35%))3 (1-31%) = $1.58 millionii. Preferred stock2 {1+11% [1-(1-30%) x 35%]3} (1-31%) = $1.75 millionThe after-tax cash flow for the shareholders is maximized when the firm invests thecash in the preferred stocks.18.10 You should not expect to find either low dividend, high growth stocks or tax-freemunicipal bonds in the University of Pennsylvania’s portfolio. Since the universitydoes not pay taxes on investment income, it will want to invest in securities, whichprovide the highest pre-tax return. Since tax-free municipal bonds generally providelower returns than taxable securities, there is no reason for the university to holdmunicipal bonds.The Litzenberger-Ramaswamy research (discussed in the section on empirical evidence) found that high dividend stocks pay higher pre-tax returns than risk comparable lowdividend stocks because of the taxes on dividend income. Since the University ofPennsylvania does not pay taxes, it would be wise to invest in high dividend stocksrather than low dividend stocks in the same risk class.18.11 a. If T C = T0 then (P e - P b) / D =1. The stock price will fall by the amount of thedividend.b. If T C = 0 and T0 0 then (P e - P b) / D =1 - T0. The stock price will fall by theafter-tax proceeds from the dividend.c. In a, there was no tax disadvantage to dividends. Thus, investors are indifferentbetween buying the stock at P b and receiving the dividend or waiting, buying thestock at P e and receiving a subsequent capital gain. When only the dividend istaxed, after-tax proceeds must be equated for investors to be indifferent. Sincethe after-tax proceeds from the dividend are D (1 - T0), the price will fall by thatamount.d. No, Elton and Gruber’s paper is not a prescription for dividend policy. In aworld with taxes, a firm should never issue stock to pay a dividend, but thepresence of taxes does not imply that firms should not pay dividends fromexcess cash. The prudent firm, when faced with other financial considerationsand legal constraints may choose to pay dividends.18.12 a. Let x be the ordinary income tax rate. The individual receives an after-taxdividend of $1,000(1-x) which she invests in Treasury bonds. The T-bond willgenerate after-tax cash flows to the investor of $1,000 (1 - x)[1+0.08(1-x)].If the firm invests the money, its proceeds are $1,000 [1 + 0.08 (1-0.35)]To be indifferent, the investor’s proceeds must be the same whether she investsthe after-tax dividend or receives the proceeds from the firm’s investment andpays taxes on that amount.1,000 (1 - x) [1 + 0.08 (1 - x)] = (1 - x) {1,000 [1 + 0.08 (1 - 0.35)]}x = 0.35Note: This argument does not depend upon the length of time the investment isheld.b.Yes, this is a reasonable answer. She is only indifferent if the after-tax proceedsfrom the $1,000 investment in identical securities are identical; that occurs onlywhen the tax rates are identical.c. Since both investors will receive the same pre-tax return, you would expect thesame answer as in part a. Yet, because Carlson enjoys a tax benefit frominvesting in stock, the tax rate on ordinary income, which induces indifference,is much lower.1,000 (1 - x) [1 + 0.12(1 - x)] = (1 - x) {1,000 [1 + 0.12 (1 – 0.3) (0.35)]}x = 24.5%d. It is a compelling argument, but there are legal constraints, which deter firmsfrom investing large sums in stock of other companies.18.13 The fallacy behind both groups’ arguments is that they are considering dividends theonly return on a stock. They ignored capital gains. If dividends are controlled, firmsare likely to decrease their dividends. When dividends are reduced, the companiesretain more income, which causes share price to increase. That increase in share price will add to the investors’ capital gains. Sin ce dividends and capital gains are both ways of compensating investors, if transaction costs are negligible and there are no taxes,investors will be indifferent between the two forms of compensation.175 / 618.14 a. The after-tax expected return on Grebe stock is 4 / 20 = 0.2. Since Deaton stockis in the same risk class, it will be priced to yield the same after-tax expectedreturn.0.2(20P)(1T g)4(0.75)P;T g0P$19.170=--+= =b. If T g = 25%, the after-tax expected return on Grebe stock is (4) (1-0.25) / 20 =0.15. Deaton’s price will be0.15(20P)(0.75)4(0.75)PP$200=-+ =c. In this MM world, when the tax rates are identical, there is no tax disadvantageto the dividend. Investors are indifferent between $1 in capital gains and $1 individends. Hence, Deaton’s price will also be $20.18.15 P (Payall) = [100 + 25 (1-25%)] / (1 + 25%) = $95P (Payless) = [100 + 25 (50%) + 25 (50%) (1 - 25%)] / (1 + 25%) = $97.5P (Paynone) = $10018.16 a. Dividend yield: 4.5 / 50.50 = 0.0891b. The pricing of bonds was discussed in an earlier chapter. Whenever a bond isselling at par, the yield to maturity is the coupon rate. So, the yield on theDuPont bonds is 11%.c. After-tax shield = (Pre-tax yield) (1 - T)Preferred stock Debti. GM’s pension fund; T=0 8.91% 11.00%ii. GM; T=.34 8.00% 7.26%iii Roger Smith; T = 0.28 6.42% 7.92% *GM is exempt from 70% of taxes on dividend income, therefore, its effectivetax rate is (0.3) (0.34) = 0.102.d. Corporations, which are exempt from 70% of taxes on dividend income, wouldhold the preferred stock.18.17 The bird-in-the-hand argument is based upon the erroneous assumption that increaseddividends make a firm less risky. If capital spending and investment spending areunchanged, the firm’s overall c ash flows are not affected by the dividend policy.18.18 This argument is theoretically correct. In the real world with transaction costs ofsecurity trading, home-made dividends can be more expensive than dividends directlypaid out by the firms. However, the existence of financial intermediaries such asmutual funds reduces the transaction costs for individuals greatly. Thus, as a whole,the desire for current income shouldn’t be a major factor favoring high-current-dividend policy.18.19 To minimize her tax burden, your aunt should divest herself of high dividend yieldstocks and invest in low dividend yield stock. Or, if possible, she should keep her highdividend stocks, borrow an equivalent amount of money and invest that money in a taxdeferred account.18.20 This is not evidence on investor preferences. A rise in stock price when the currentdividend is increased may reflect expectations that future earnings, cash flows, etc. will rise. The better performance of the 115 companies, which raised their payouts, mayalso reflect a signal by management through the dividends that the firms were expected to do well in the future.18.21 Virginia Power’s investors probably were not aware of the cash flow crunch. Thus, theprice drop was due to the negative information about the cost overruns. Even if they were suspicious that there were overruns, the announcement would still cause a drop in price because it removed all uncertainty about overruns and indicated their magnitude.18.22 As the firm has been paying out regular dividends for more than 10 years, the currentsevere cut in dividends can cause the shareholders to lower their expectations oncurrent and future cash flows of the firm. It then results in the drop in the stock price.18.23 a. Cap’s past behavior suggests a preference for capital gains while Widow Jonesexhibits a preference for current income.b. Cap could show the widow how to construct homemade dividends through thesale of stock. Of course, Cap will also have to convince her that she lives in anMM world. Remember that homemade dividends can only be constructed underthe MM assumptions.c.Widow Jones may still not invest in Neotech because of the transaction costsinvolved in constructing homemade dividends. Also the Widow may desire theuncertainty resolution which comes with high dividend stocks.18.24 The capital investment needs of small, growing companies are very high. Therefore,payment of dividends could curtail their investment opportunities. Their other option is to issue stock to pay the dividend thereby incurring issuance costs. In either case, the companies and thus their investors are better off with a zero dividend policy during the firms’ rapid growth phases. This fact makes these firms attract ive only to low dividend clienteles.This example demonstrates that dividend policy is relevant when there are issuancecosts. Indeed, it may be relevant whenever the assumptions behind the MM model are not met.18.25 Unless there is an unsatisfied high dividend clientele, a firm cannot improve its shareprice by switching policies. If the market is in equilibrium, the number of people who desire high dividend payout stocks should exactly equal the number of such stocksavailable. The supplies and demands of each clientele will be exactly met inequilibrium. If the market is not in equilibrium, the supply of high dividend payoutstocks may be less than the demand. Only in such a situation could a firm benefit froma policy shift.18.26 a. Div1 = Div0 + s (t EPS1 - Div0)= 1.25 + 0.3 (0.4 x 4.5 -1.25)= 1.415b. Div1 = Div0 + s (t EPS1 - Div0)= 1.25 + 0.6 (0.4 x 4.5 - 1.25)= 1.58Note: Part “a” is more conservative since the adjustment rate is lower.18.27 This finding implies that firms use initial dividends to “signal” their potentialgrowth and positive NPV prospects to the stock market. The initiation of177 / 6regular cash dividends also serves to convince the market that their high currentearnings are not temporary.[文档可能无法思考全面，请浏览后下载，另外祝您生活愉快，工作顺利，万事如意!]。

CHAPTER 20INTERNATIONAL CORPORATE FINANCEAnswers to Concepts Review and Critical Thinking Questions1. a.The dollar is selling at a premium because it is more expensive in the forward market than inthe spot market (SFr 1.53 versus SFr 1.50).b.The franc is expected to depreciate relative to the dollar because it will take more francs to buyone dollar in the future than it does today.c.Inflation in Switzerland is higher than in the United States, as are nominal interest rates.2.The exchange rate will increase, as it will take progressively more pesos to purchase a dollar. This isthe relative PPP relationship.3. a.The Australian dollar is expected to weaken relative to the dollar, because it will take moreA$ in the future to buy one dollar than it does today.b.The inflation rate in Australia is higher.c.Nominal interest rates in Australia are higher; relative real rates in the two countries are thesame.4. A Yankee bond is most accurately described by d.5. No. For example, if a country’s currency strengthens, imports become cheaper (good), but its exportsbecome more expensive for others to buy (bad). The reverse is true for currency depreciation.6.Additional advantages include being closer to the final consumer and, thereby, saving ontransportation, significantly lower wages, and less exposure to exchange rate risk. Disadvantages include political risk and costs of supervising distant operations.7.One key thing to remember is that dividend payments are made in the home currency. Moregenerally, it may be that the owners of the multinational are primarily domestic and are ultimately concerned about their wealth denominated in their home currency because, unlike a multinational, they are not internationally diversified.8. a.False. If prices are rising faster in Great Britain, it will take more pounds to buy the sameamount of goods that one dollar can buy; the pound will depreciate relative to the dollar.b.False. The forward market would already reflect the projected deterioration of the euro relativeto the dollar. Only if you feel that there might be additional, unanticipated weakening of the euro that isn’t reflected in forward rates today, will the forward hedge protect you against additional declines.c.True. The market would only be correct on average, while you would be correct all the time.9. a.American exporters: their situation in general improves because a sale of the exported goods fora fixed number of euros will be worth more dollars.American importers: their situation in general worsens because the purchase of the imported goods for a fixed number of euros will cost more in dollars.b.American exporters: they would generally be better off if the British government’s intentionsresult in a strengthened pound.American importers: they would generally be worse off if the pound strengthens.c.American exporters: they would generally be much worse off, because an extreme case of fiscalexpansion like this one will make American goods prohibitively expensive to buy, or else Brazilian sales, if fixed in cruzeiros, would become worth an unacceptably low number of dollars.American importers: they would generally be much better off, because Brazilian goods will become much cheaper to purchase in dollars.10.IRP is the most likely to hold because it presents the easiest and least costly means to exploit anyarbitrage opportunities. Relative PPP is least likely to hold since it depends on the absence of market imperfections and frictions in order to hold strictly.11.It all depends on whether the forward market expects the same appreciation over the period andwhether the expectation is accurate. Assuming that the expectation is correct and that other traders do not have the same information, there will be value to hedging the currency exposure.12.One possible reason investment in the foreign subsidiary might be preferred is if this investmentprovides direct diversification that shareholders could not attain by investing on their own. Another reason could be if the political climate in the foreign country was more stable than in the home country. Increased political risk can also be a reason you might prefer the home subsidiary investment. Indonesia can serve as a great example of political risk. If it cannot be diversified away, investing in this type of foreign country will increase the systematic risk. As a result, it will raise the cost of the capital, and could actually decrease the NPV of the investment.13.Yes, the firm should undertake the foreign investment. If, after taking into consideration all risks, aproject in a foreign country has a positive NPV, the firm should undertake it. Note that in practice, the stated assumption (that the adjustment to the discount rate has taken into consideration all political and diversification issues) is a huge task. But once that has been addressed, the net present value principle holds for foreign operations, just as for domestic.14.If the foreign currency depreciates, the U.S. parent will experience an exchange rate loss when theforeign cash flow is remitted to the U.S. This problem could be overcome by selling forward contracts. Another way of overcoming this problem would be to borrow in the country where the project is located.15.False. If the financial markets are perfectly competitive, the difference between the Eurodollar rateand the U.S. rate will be due to differences in risk and government regulation. Therefore, speculating in those markets will not be beneficial.16.The difference between a Eurobond and a foreign bond is that the foreign bond is denominated in thecurrency of the country of origin of the issuing company. Eurobonds are more popular than foreign bonds because of registration differences. Eurobonds are unregistered securities.Solutions to Questions and ProblemsNOTE: All end-of-chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to space and readability constraints, when these intermediate steps are included in this solutions manual, rounding may appear to have occurred. However, the final answer for each problem is found without rounding during any step in the problem.Basicing the quotes from the table, we get:a.$50(€0.7870/$1) = €39.35b.$1.2706c.€5M($1.2706/€) = $6,353,240d.New Zealand dollare.Mexican pesof.(P11.0023/$1)($1.2186/€1) = P13.9801/€This is a cross rate.g.The most valuable is the Kuwait dinar. The least valuable is the Indonesian rupiah.2. a.You would prefer £100, since:(£100)($.5359/£1) = $53.59b.You would still prefer £100. Using the $/£ exchange rate and the SF/£ exchange rate to find theamount of Swiss francs £100 will buy, we get:(£100)($1.8660/£1)(SF .8233) = SF 226.6489ing the quotes in the book to find the SF/£ cross rate, we find:(SF 1.2146/$1)($0.5359/£1) = SF 2.2665/£1The £/SF exchange rate is the inverse of the SF/£ exchange rate, so:£1/SF .4412 = £0.4412/SF 13. a.F180= ¥104.93 (per $). The yen is selling at a premium because it is more expensive in theforward market than in the spot market ($0.0093659 versus $0.009530).b.F90 = $1.8587/£. The pound is selling at a discount because it is less expensive in the forwardmarket than in the spot market ($0.5380 versus $0.5359).c.The value of the dollar will fall relative to the yen, since it takes more dollars to buy one yen inthe future than it does today. The value of the dollar will rise relative to the pound, because it will take fewer dollars to buy one pound in the future than it does today.4. a.The U.S. dollar, since one Canadian dollar will buy:(Can$1)/(Can$1.26/$1) = $0.7937b.The cost in U.S. dollars is:(Can$2.19)/(Can$1.26/$1) = $1.74Among the reasons that absolute PPP doe sn’t hold are tariffs and other barriers to trade, transactions costs, taxes, and different tastes.c.The U.S. dollar is selling at a discount, because it is less expensive in the forward market thanin the spot market (Can$1.22 versus Can$1.26).d.The Canadian dollar is expected to appreciate in value relative to the dollar, because it takesfewer Canadian dollars to buy one U.S. dollar in the future than it does today.e.Interest rates in the United States are probably higher than they are in Canada.5. a.The cross rate in ¥/£ terms is:(¥115/$1)($1.70/£1) = ¥195.5/£1b.The yen is quoted too low relative to the pound. Take out a loan for $1 and buy ¥115. Use the¥115 to purchase pounds at the cross-rate, which will give you:¥115(£1/¥185) = £0.6216Use the pounds to buy back dollars and repay the loan. The cost to repay the loan will be:£0.6216($1.70/£1) = $1.0568You arbitrage profit is $0.0568 per dollar used.6.We can rearrange the interest rate parity condition to answer this question. The equation we will useis:R FC = (F T– S0)/S0 + R USUsing this relationship, we find:Great Britain: R FC = (£0.5394 – £0.5359)/£0.5359 + .038 = 4.45%Japan: R FC = (¥104.93 – ¥106.77)/¥106.77 + .038 = 2.08%Switzerland: R FC = (SFr 1.1980 – SFr 1.2146)/SFr 1.2146 + .038 = 2.43%7.If we invest in the U.S. for the next three months, we will have:$30M(1.0045)3 = $30,406,825.23If we invest in Great Britain, we must exchange the dollars today for pounds, and exchange the pounds for dollars in three months. After making these transactions, the dollar amount we would have in three months would be:($30M)(£0.56/$1)(1.0060)3/(£0.59/$1) = $28,990,200.05We should invest in U.S.ing the relative purchasing power parity equation:F t = S0 × [1 + (h FC– h US)]tWe find:Z3.92 = Z3.84[1 + (h FC– h US)]3h FC– h US = (Z3.92/Z3.84)1/3– 1h FC– h US = .0069Inflation in Poland is expected to exceed that in the U.S. by 0.69% over this period.9.The profit will be the quantity sold, times the sales price minus the cost of production. Theproduction cost is in Singapore dollars, so we must convert this to U.S. dollars. Doing so, we find that if the exchange rates stay the same, the profit will be:Profit = 30,000[$145 – {(S$168.50)/(S$1.6548/$1)}]Profit = $1,295,250.18If the exchange rate rises, we must adjust the cost by the increased exchange rate, so:Profit = 30,000[$145 – {(S$168.50)/1.1(S$1.6548/$1)}]Profit = $1,572,954.71If the exchange rate falls, we must adjust the cost by the decreased exchange rate, so:Profit = 30,000[$145 – {(S$168.50)/0.9(S$1.6548/$1)}]Profit = $955,833.53To calculate the breakeven change in the exchange rate, we need to find the exchange rate that make the cost in Singapore dollars equal to the selling price in U.S. dollars, so:$145 = S$168.50/S TS T = S$1.1621/$1S T = –.2978 or –29.78% decline10. a.If IRP holds, then:F180 = (Kr 6.43)[1 + (.08 – .05)]1/2F180 = Kr 6.5257Since given F180 is Kr6.56, an arbitrage opportunity exists; the forward premium is too high.Borrow Kr1 today at 8% interest. Agree to a 180-day forward contract at Kr 6.56. Convert the loan proceeds into dollars:Kr 1 ($1/Kr 6.43) = $0.15552Invest these dollars at 5%, ending up with $0.15931. Convert the dollars back into krone as$0.15931(Kr 6.56/$1) = Kr 1.04506Repay the Kr 1 loan, ending with a profit of:Kr1.04506 – Kr1.03868 = Kr 0.00638b.To find the forward rate that eliminates arbitrage, we use the interest rate parity condition, so:F180 = (Kr 6.43)[1 + (.08 – .05)]1/2F180 = Kr 6.525711.The international Fisher effect states that the real interest rate across countries is equal. We canrearrange the international Fisher effect as follows to answer this question:R US– h US = R FC– h FCh FC = R FC + h US– R USa.h AUS = .05 + .035 – .039h AUS = .046 or 4.6%b.h CAN = .07 + .035 – .039h CAN = .066 or 6.6%c.h TAI = .10 + .035 – .039h TAI = .096 or 9.6%12. a.The yen is expected to get stronger, since it will take fewer yen to buy one dollar in the futurethan it does today.b.h US– h JAP (¥129.76 – ¥131.30)/¥131.30h US– h JAP = – .0117 or –1.17%(1 – .0117)4– 1 = –.0461 or –4.61%The approximate inflation differential between the U.S. and Japan is – 4.61% annually.13. We need to find the change in the exchange rate over time, so we need to use the relative purchasingpower parity relationship:F t = S0 × [1 + (h FC– h US)]TUsing this relationship, we find the exchange rate in one year should be:F1 = 215[1 + (.086 – .035)]1F1 = HUF 225.97The exchange rate in two years should be:F2 = 215[1 + (.086 – .035)]2F2 = HUF 237.49And the exchange rate in five years should be:F5 = 215[1 + (.086 – .035)]5F5 = HUF 275.71ing the interest-rate parity theorem:(1 + R US) / (1 + R FC) = F(0,1) / S0We can find the forward rate as:F(0,1) = [(1 + R US) / (1 + R FC)] S0F(0,1) = (1.13 / 1.08)$1.50/£F(0,1) = $1.57/£Intermediate15.First, we need to forecast the future spot rate for each of the next three years. From interest rate andpurchasing power parity, the expected exchange rate is:E(S T) = [(1 + R US) / (1 + R FC)]T S0So:E(S1) = (1.0480 / 1.0410)1 $1.22/€ = $1.2282/€E(S2) = (1.0480 / 1.0410)2 $1.22/€ = $1.2365/€E(S3) = (1.0480 / 1.0410)3 $1.22/€ = $1.2448/€Now we can use these future spot rates to find the dollar cash flows. The dollar cash flow each year will be:Year 0 cash flow = –€$12,000,000($1.22/€) = –$14,640,000.00Year 1 cash flow = €$2,700,000($1.2282/€) = $3,316,149.86Year 2 cash flow = €$3,500,000($1.2365/€) = $4,327,618.63Year 3 cash flow = (€3,300,000 + 7,400,000)($1.2448/€) = $13,319,111.90And the NPV of the project will be:NPV = –$14,640,000 + $3,316,149.86/1.13 + $4,4327,618.63/1.132 + $13,319,111.90/1.133NPV = $914,618.7316. a.Implicitly, it is assumed that interest rates won’t change over the life of the project, but theexchange rate is projected to decline because the Euroswiss rate is lower than the Eurodollar rate.b.We can use relative purchasing power parity to calculate the dollar cash flows at each time. Theequation is:E[S T] = (SFr 1.72)[1 + (.07 – .08)]TE[S T] = 1.72(.99)TSo, the cash flows each year in U.S. dollar terms will be:t SFr E[S T] US$0 –27.0M –$15,697,674.421 +7.5M 1.7028 $4,404,510.222 +7.5M 1.6858 $4,449,000.223 +7.5M 1.6689 $4,493,939.624 +7.5M 1.6522 $4,539,332.955 +7.5M 1.6357 $4,585,184.79And the NPV is:NPV = –$15,697,674.42 + $4,404,510.22/1.13 + $4,449,000.22/1.132 + $4,493,939.62/1.133 + $4,539,332.95/1.134 + $4,585,184.79/1.135NPV = $71,580.10c.Rearranging the relative purchasing power parity equation to find the required return in Swissfrancs, we get:R SFr = 1.13[1 + (.07 – .08)] – 1R SFr = 11.87%So, the NPV in Swiss francs is:NPV = –SFr 27.0M + SFr 7.5M(PVIFA11.87%,5)NPV = SFr 123,117.76Converting the NPV to dollars at the spot rate, we get the NPV in U.S. dollars as:NPV = (SFr 123,117.76)($1/SFr 1.72)NPV = $71,580.10Challenge17. a.The domestic Fisher effect is:1 + R US = (1 + r US)(1 + h US)1 + r US = (1 + R US)/(1 + h US)This relationship must hold for any country, that is:1 + r FC = (1 + R FC)/(1 + h FC)The international Fisher effect states that real rates are equal across countries, so:1 + r US = (1 + R US)/(1 + h US) = (1 + R FC)/(1 + h FC) = 1 + r FCb.The exact form of unbiased interest rate parity is:E[S t] = F t = S0 [(1 + R FC)/(1 + R US)]tc.The exact form for relative PPP is:E[S t] = S0 [(1 + h FC)/(1 + h US)]td.For the home currency approach, we calculate the expected currency spot rate at time t as:E[S t] = (€0.5)[1.07/1.05]t= (€0.5)(1.019)tWe then convert the euro cash flows using this equation at every time, and find the present value. Doing so, we find:NPV = –[€2M/(€0.5)] + {€0.9M/[1.019(€0.5)]}/1.1 + {€0.9M/[1.0192(€0.5)]}/1.12 + {€0.9M/[1.0193(€0.5/$1)]}/1.13NPV = $316,230.72For the foreign currency approach, we first find the return in the euros as:R FC = 1.10(1.07/1.05) – 1 = 0.121Next, we find the NPV in euros as:NPV = –€2M + (€0.9M)/1.121 + (€0.9M)/1.1212+ (€0.9M)/1.1213= €158,115.36And finally, we convert the euros to dollars at the current exchange rate, which is:NPV ($) = €158,115.36 /(€0.5/$1) = $316,230.72。

Concept Questions◆Define pure discount bonds, level-coupon bonds, and consols.A pure discount bond is one that makes no intervening interest payments. One receives a single lump sum payment at maturity. A level-coupon bond is a combination of an annuity and a lump sum at maturity. A consol is a bond that makes interest payments forever.◆Contrast the state interest rate and the effective annual interest rate for bonds paying semi-annual interest. Effective annual interest rate on a bond takes into account two periods of compounding per year received on the coupon payments. The state rate does not take this into account.◆What is the relationship between interest rates and bond prices?There is an inverse relationship. When one goes up, the other goes down.◆How does one calculate the yield to maturity on a bond?One finds the discount rate that equates the promised future cash flows with the price of the bond.◆What are the three factors determining a firm's P/E ratio?Today's expectations of future growth opportunities.The discount rate.The accounting method.◆What is the closing price of General Data?The closing price of General Data is 6 3/16.◆What is the PE of General House?The PE of General House is 29.◆What is the annual dividend of General Host?The annual dividend of General Host is zero.Concept Questions - Appendix To Chapter 5◆What is the difference between a spot interest rate and the yield to maturity?The yield to maturity is the geometric average of the spot rates during the life of the bond.◆Define the forward rate.Given a one-year bond and a two-year bond, one knows the spot rates for both. The forward rate is the rate of return implicit on a one-year bond purchased in the second year that would equate the terminal wealth of purchasing the one-year bond today and another in one year with that of the two-year bond.◆What is the relationship between the one-year spot rate, the two-year spot rate and the forward rate over the second year?The forward rate f2 = [(1+r2)2 /(1+r1 )] - 1◆What is the expectation hypothesis?Investors set interest rates such that the forward rate over a given period equals the spot rate for that period.◆What is the liquidity-preference hypothesis?This hypothesis maintains that investors require a risk premium for holding longer-term bonds (i.e. they prefer to be liquid or short-term investors). This implies that the market sets the forward rate for a given period above the expected spot rate for that period.Questions And ProblemsHow to Value Bonds5.1 What is the present value of a 10-year, pure discount bond that pays $1,000 at maturity and is priced to yield the following rates?a. 5 percentb. 10 percentc. 15 percentSolutions a. $1,000 / 1.0510 = $613.91b. $1,000 / 1.1010 = $385.54c. $1,000 / 1.1510 = $247.185.2 Microhard has issued a bond with the following characteristics:Principal: $1,000Term to maturity: 20 yearsCoupon rate: 8 percentSemiannual paymentsCalculate the price of the Microhard bond if the stated annual interest rate is:a. 8 percentb. 10 percentc. 6 percentSolutions The amount of the semi-annual interest payment is $40 (=$1,000 ⨯ 0.08 / 2). There are a total of 40 periods; i.e., two half years in each of the twenty years in the term to maturity.The annuity factor tables can be used to price these bonds. The appropriate discount rate touse is the semi-annual rate. That rate is simply the annual rate divided by two. Thus, for part b the rate to be used is 5% and for part c is it 3%.a. $40 (19.7928) + $1,000 / 1.0440 = $1,000Notice that whenever the coupon rate and the market rate are the same, the bond ispriced at par.b. $40 (17.1591) + $1,000 / 1.0540 = $828.41Notice that whenever the coupon rate is below the market rate, the bond is pricedbelow par.c. $40 (23.1148) + $1,000 / 1.0340 = $1,231.15Notice that whenever the coupon rate is above the market rate, the bond is pricedabove par.5.3 Consider a bond with a face value of $1,000. The coupon is paid semiannually and the market interest rate (effective annual interest rate) is 12 percent. How much would you pay for the bond if a. the coupon rate is 8 percent and the remaining time to maturity is 20 years?b. the coupon rate is 10 percent and the remaining time to maturity is 15 years?Solutions Semi-annual discount factor = (1.12)1/2 - 1 = 0.05830 = 5.83%a. Price = $40400583.0A+ $1,000 / 1.058340= $614.98 + $103.67= $718.65b. Price = $50300583.0A+ $1,000 / 1.058330= $700.94 + $182.70 = $883.645.4 Pettit Trucking has issued an 8-percent, 20-year bond that pays interest semiannually. If the market prices the bond to yield an effective annual rate of 10 percent, what is the price of the bond? Solutions Effective annual rate of 10%:Semi-annual discount factor = (1.1)0.5 - 1 = 0.04881 = 4.881%Price = $404004881.0A+ $1,000 / 1.0488140= $846.335.5 A bond is sold at $923.14 (below its par value of $1,000). The bond has 15 years to maturity and investors require a 10-percent yield on the bond. What is the coupon rate for the bond if the coupon is paid semiannually?Solutions $923.14 = C3005.0A+ $1,000 / 1.0530= (15.37245) C + $231.38C = $45The annual coupon rate = $45 ⨯ 2 / $1,000 = 0.09 = 9%5.6 You have just purchased a newly issued $1,000 five-year Vanguard Company bond at par. This five-year bond pays $60 in interest semiannually. You are also considering the purchase of another Vanguard Company bond that returns $30 in semiannual interest payments and has six years remaining before it matures. This bond has a face value of $1,000.a. What is effective annual return on the five-year bond?b. Assume that the rate you calculated in part (a) is the correct rate for the bond with six years remaining before it matures. What should you be willing to pay for that bond?c. How will your answer to part (b) change if the five-year bond pays $40 in semiannual interest? Solutionsa. The semi-annual interest rate is $60 / $1,000 = 0.06. Thus, the effective annual rate is 1.062 - 1 =0.1236 = 12.36%.b. Price = $301206.0A+ $1,000 / 1.0612= $748.48c. Price = $301204.0A+ $1,000 / 1.0412= $906.15Note: In parts b and c we are implicitly assuming that the yield curve is flat. That is, the yield in year 5 applies for year 6 as well.Bond Concepts5.7 Consider two bonds, bond A and bond B, with equal rates of 10 percent and the same face values of $1,000. The coupons are paid annually for both bonds. Bond A has 20 years to maturity while bond B has10 years to maturity.a. What are the prices of the two bonds if the relevant market interest rate is 10 percent?b. If the market interest rate increases to 12 percent, what will be the prices of the two bonds?c. If the market interest rate decreases to 8 percent, what will be the prices of the two bonds?Solutionsa. PA = $1002010.0A+ $1,000 / 1.1020 = $1,000PB = $1001010.0A+ $1,000 / 1.1010 = $1,000b. PA = $1002012.0A+ $1,000 / 1.1220 = $850.61PB = $1001012.0A+ $1,000 / 1.1210 = $887.00c. PA = $1002008.0A+ $1,000 / 1.0820 = $1,196.36PB = $1001008.0A+ $1,000 / 1.0810 = $1,134.205.8 a. If the market interest rate (the required rate of return that investors demand) unexpectedly increases, what effect would you expect this increase to have on the prices of long-term bonds? Why?b. What would be the effect of the rise in the interest rate on the general level of stock prices? Why? Solutionsa. The price of long-term bonds should fall. The price is the PV of the cash flowsassociated with the bond. As the interest rate rises, the PV of those flows falls.This can be easily seen by looking at a one-year, pure discount bond.Price = $1,000 / (1 + i)As i. increases, the denominator rises. This increase causes the price to fall.b. The effect upon stocks is not as certain as that upon the bonds. The nominalinterest rate is a function of both the real interest rate and the inflation rate; i.e.,(1 + i) = (1 + r) (1 + inflation)From this relationship it is easy to conclude that as inflation rises, the nominalinterest rate rises. Stock prices are a function of dividends and future prices aswell as the interest rate. Those dividends and future prices are determined by theearning power of the firm. When inflation occurs, it may increase or decreasefirm earnings. Thus, the effect of a rise in the level of general prices upon thelevel of stock prices is uncertain.5.9 Consider a bond that pays an $80 coupon annually and has a face value of $1,000. Calculate the yield to maturity if the bond hasa. 20 years remaining to maturity and it is sold at $1,200.b. 10 years remaining to maturity and it is sold at $950.Solutions a. $1,200 = $8020rA+ $1,000 / (1 + r)20r = 0.0622 = 6.22%b. $950 = $8010rA+ $1,000 / (1 + r)10r = 0.0877 = 8.77%5.10 The Sue Fleming Corporation has two different bonds currently outstanding. Bond A has a face value of $40,000 and matures in 20 years. The bond makes no payments for the first six years and then pays $2,000 semiannually for the subsequent eight years, and finally pays $2,500 semiannually for the last six years. Bond B also has a face value of $40,000 and a maturity of 20 years; it makes no coupon payments over the life of the bond. If the required rate of return is 12 percent compounded semiannually, what is the current price of Bond A? of Bond B?Solutions PA = ($2,0001606.0A) / (1.06)12 + ($2,5001206.0A) / (1.06)28 + $40,000 / (1.06)40= $18,033.86PB = $ 40,000 / (1.06)40 = $3,888.89The Present Value of Common Stocks5.11 Use the following February 11, 2000, WSJ quotation for AT&T Corp. Which of the following statements is false?a. The closing price of the bond with the shortest time to maturity was $1,000.b. The annual coupon for the bond maturing in year 2016 is $90.00.c. The price on the day before this quotation (i.e., February 9) for the ATT bond maturing in year 2022 was $1.075 per bond contract.d. The current yield on the ATT bond maturing in year 2002 was 7.125%e. The ATT bond maturing in year 2002 has a yield to maturity less than 7.125%.Bonds Cur Yld Vol Close Net ChgATT 9s 16 ? 10 117 _ 1/4ATT 5 1/8 01 ? 5 100 _ 3/4ATT 7 1/8 02 ? 193 104 1/8 _ 1/4ATT 8 1/8 22 ? 39 107 3/8 _ 1/8Solutions a. TrueTrueFalseFalseTrue5.12 Following are selected quotations for New York Exchange Bonds from the Wall Street Journal. Which of the following statements about Wilson’s bond is false?a. The bond maturing in year 2000 has a yield to maturity greater th an 63⁄8%.b. The closing price of the bond with the shortest time to maturity on the day before this quotation was $1,003.25.c. This annual coupon for the bond maturing in year 2013 is $75.00.d. The current yield on the Wilson’s bond with the longest time to maturity was 7.29%.e. None of the above.Quotations as of 4 P.M. Eastern TimeFriday, April 23, 1999Bonds Current Yield Vol Close NetWILSON 6 3/8 99 ? 76 100 3/8 _ 1/8WILSON 6 3/8 00 ? 9 98 1/2WILSON 7 1/4 02 ? 39 103 5/8 1/8WILSON 7 1/2 13 ? 225 102 7/8 _ 1/8Solutions a. TrueFalseTrueTrueFalse5.13 A common stock pays a current dividend of $2. The dividend is expected to grow at an 8-percent annual rate for the next three years; then it will grow at 4 percent in perpetuity.The appropriate discount rate is 12 percent. What is the price of this stock?Solutions Price = $2 (1.08) / 1.12 + $2 (1.082) / 1.122 + $2 (1.083) / 1.123+ {$2 (1.083) (1.04) / (0.12 - 0.04)} / 1.123= $28.895.14 Use the following February 12, 1998, WSJ quotation for Merck & Co. to answer the next question. 52 Weeks Yld Vol NetHi Lo Stock Sym Div % PE 100s Hi Lo Close Chg120. 80.19 Merck MRK 1.80 ? 30 195111 115.9 114.5 115 _1.25Which of the following statements is false?a. The dividend yield was about 1.6%.b. The 52 weeks’ trading range was $39.81.c. The closing price per share on February 10, 1998, was $113.75.d. The closing price per share on February 11, 1998, was $115.e. The earnings per share were about $3.83.Solutions a. FalseTrueFalseFalseTrue5.15 Use the following stock quote.52 Weeks Yld Vol NetHi Lo Stock Sym Div % PE 100s Hi Lo Close Chg126.25 72.50 Citigroup CCI 1.30 1.32 16 20925 98.4 97.8 98.13 _.13The expected growth rate in Citigroup’s dividends is 7% a year. Suppose you use the discounted dividend model to price Citigroup’s shares. The constant growth dividend model would suggest that the required return on the Citigroup’s stock is what?98.125 = 1.30 ( 1.07) / r - 0.07r = 8.4175 %5.16 You own $100,000 worth of Smart Money stock. At the end of the first year you receive a dividend of $2 per share; at the end of year 2 you receive a $4 dividend. At the end of year 3 you sell the stock for $50 per share. Only ordinary (dividend) income is taxed at the rate of 28 percent. Taxes are paid at the time dividends are received. The required rate of return is 15 percent. How many shares of stock do you own? Solutions Price = $2 (0.72) / 1.15 + $4 (0.72) / 1.152 + $50 / 1.153= $36.31The number of shares you own = $100,000 / $36.31 = 2,754 shares5.17 Consider the stock of Davidson Company that will pay an annual dividend of $2 in the coming year. The dividend is expected to grow at a constant rate of 5 percent permanently.The market requires a 12-percent return on the company.a. What is the current price of a share of the stock?b. What will the stock price be 10 years from today?Solutionsa. P = $2 / (0.12 - 0.05) = $28.57b. P10 = D11 / (r - g)= $2 (1.0510) / (0.12 - 0.05) = $46.545.18 Easy Type, Inc., is one of a myriad of companies selling word processor programs. Their newest program will cost $5 million to develop. First-year net cash flows will be $2 million. As a result of competition, profits will fall by 2 percent each year thereafter.All cash inflows will occur at year-end. If the market discount rate is 14 percent, what is the value of this new program?SolutionsValue = -$5,000,000 + $2,000,000 / {0.14 - (-0.02)}= $7,500,0005.19 Whizzkids, Inc., is experiencing a period of rapid growth. Earnings and dividends per share are expected to grow at a rate of 18 percent during the next two years, 15 percent in the third year, and at a constant rate of 6 percent thereafter. Whizzkids’ last dividend, which has just been paid, was $1.15. If the required rate of return on the stock is 12 percent, what is the price of a share of the stock today? SolutionsPrice = $1.15 (1.18) / 1.12 + $1.15 (1.182) / 1.122 + $1.152 (1.182) / 1.123+ {$1.152 (1.182) (1.06) / (0.12 - 0.06)} / 1.123= $26.955.20 Allen, Inc., is expected to pay an equal amount of dividends at the end of the first two years. Thereafter, the dividend will grow at a constant rate of 4 percent indefinitely. The stock is currently traded at $30. What is the expected dividend per share for the next year if the required rate of return is 12 percent? Solutions$30 = D / 1.12 + D / 1.122 + {D (1 + 0.04) / (0.12 - 0.04)} / 1.122= 12.053571 DD = $2.495.21 Calamity Mining Company’s reserves of ore are being depleted, and its costs of recovering a declining quantity of ore are rising each year. As a result, the company’s earnings are declining at the rate of 10 percent per year. If the dividend per share that is about to be paid is $5 and the required rate of return is 14 percent, what is the value of the firm’s stock?SolutionsDividend one year from now = $5 (1 - 0.10) = $4.50Price = $5 + $4.50 / {0.14 - (-0.10)} = $23.75Since the current $5 dividend has not yet been paid, it is still included in the stock price.5.22 The Highest Potential, Inc., will pay a quarterly dividend per share of $1 at the end of each of the next 12 quarters. Subsequently, the dividend will grow at a quarterly rate of 0.5 percent indefinitely. The appropriate rate of return on the stock is 10 percent. What is the current stock price?Estimates of Parameters in the Dividend-Discount ModelSolutionsPrice = $112025.0A+ {$1 (1 + 0.005) / (0.025 - 0.005)} / 1.02512= $10.26 + $37.36= $47.625.23 The newspaper reported last week that Bradley Enterprises earned $20 million. The report also stated that the firm’s return on equity remains on its historical trend of 14 percent. Bradley retains 60 percent of its earnings. What is the firm’s growth rate of earnings? What will next year’s earnings be? SolutionsGrowth rate g = 0.6 ⨯ 0.14 = 0.084 = 8.4%Next year earnings = $20 million ⨯ 1.084 = $21.68 million5.24 Von Neumann Enterprises has just reported earnings of $10 million, and it plans to retain 75 percent of its earnings. The company has 1.25 million shares of common stock outstanding. The stock is selling at $30. The historical return on equity (ROE) of 12 percent is expected to continue in the future. What is the required rate of return on the stock?Growth Opportunitiesg = retention ratio ⨯ ROE = 0.75 ⨯ 0.12= 0.09 = 9%Dividend per share = $10 million ⨯ (1 - 0.75) / 1.25 million= $2The required rate of return = $2 (1.09) / $30 + 0.09= 0.1627 = 16.27%5.25 Rite Bite Enterprises sells toothpicks. Gross revenues last year were $3 million, and total costs were $1.5 million. Rite Bite has 1 million shares of common stock outstanding. Gross revenues and costs are expected to grow at 5 percent per year. Rite Bite pays no income taxes, and all earnings are paid out as dividends.a. If the appropriate discount rate is 15 percent and all cash flows are received at year’s end, what is the price per share of Rite Bite stock?b. The president of Rite Bite decided to begin a program to produce toothbrushes. The project requires an immediate outlay of $15 million. In one year, another outlay of $5 million will be needed. The year after that, net cash inflows will be $6 million. This profit level will be maintained in perpetuity. What effect will undertaking this project have on the price per share of the stock?Solutionsa. Price = ($3 - $1.5) ⨯ 1.05 / (0.15 - 0.05)= $15.75b. NPVGO = -$15,000,000 - $5,000,000 / 1.15 + ($6,000,000 / 0.15) / 1.15= $15,434,783The price increases by $15.43 per share.5.26 California Electronics, Inc., expects to earn $100 million per year in perpetuity if it does not undertake any new projects. The firm has an opportunity that requires an investment of $15 million today and $5 million in one year. The new investment will begin to generate additional annual earnings of $10 million two years from today in perpetuity. The firm has 20 million shares of common stock outstanding, and the required rate of return on the stock is 15 percent.a. What is the price of a share of the stock if the firm does not undertake the new project?b. What is the value of the growth opportunities resulting from the new project?c. What is the price of a share of the stock if the firm undertakes the new project?Solutionsa. Price = EPS / r = {$100 million / 20 million} / 0.15= $33.33b. NPV = -$15 million - $5 million / 1.15 + ($10 million / 0.15) / 1.15= $38,623,188c. Price = $33.33 + $38,623,188 / 20,000,000= $35.265.27 Suppose Smithfield Foods, Inc., has just paid a dividend of $1.40 per share. Sales and profits for Smithfield Foods are expected to grow at a rate of 5% per year. Its dividend is expected to grow by the same rate. If the required return is 10%, what is the value of a share of Smithfield Foods?SolutionsPrice = 1.40 (1.05) / 0.10 - 0.05Price = $29.405.28 In order to buy back its own shares, Pennzoil Co. has decided to suspend its dividends for the next two years. It will resume its annual cash dividend of $2.00 a share 3 years from now. This level of dividends will be maintained for one more year. Thereafter, Pennzoil is expected to increase its cash dividend payments by an annual growth rate of 6% per year forever. The required rate of return on Pennzoil’s stock is 16%. According to the discounted dividend model, what should Pennzoil’s current share price be? SolutionsPrice = 2 / (1.16) 3 + 2 / (1.16)4 + 2.12 / 0.16 - 0.06= 1.28 + 1.10 + 21.20= $23.585.29 Four years ago, Ultramar Diamond Inc. paid a dividend of $0.80 per share. This year Ultramar paid a dividend of $1.66 per share. It is expected that the company will pay dividends growing at the same rate for the next 5 years. Thereafter, the growth rate will level at 8% per year. The required return on this stock is 18%. According to the discounted dividend model, what would Ultramar’s cash dividend be in 7 years? a. $2.86c. $3.68d. $4.30e. $4.82Solutionsa. g = 0.4 ⨯ 0.15 = 0.06 = 6%b. Dividend per share = $1.5 million ⨯ 0.6 / 300,000= $3Price = $3 (1.06) / (0.13 - 0.06)= $45.43c. Assuming the additional earnings generated are all paid out as cash dividends.NPV = -$1.2 million + $0.3 million {1 / (0.13 - 0.10)} {1 - (1.10 / 1.13)10}= $1,159,136.93d. Price = $45.43 + $1,159,136.93 / 300,000= $49.295.30 The Webster Co. has just paid a dividend of $5.25 per share. The company will increase its dividendby 15 percent next year and will then reduce its dividend growth by 3 percent each year until it reaches the industry average of 5 percent growth, after which the company will keep a constant growth, forever. The required rate of return for the Webster Co. is 14 percent. What will a share of stock sell for?SolutionsPrice = 3 / 1.15 + 4.5 / ( 1.15)2 + 4.725 / 0.15- 0.05= 2.61 + 3.40 + 47.52= $53.535.31 Consider Pacific Energy Company and U.S. Bluechips, Inc., both of which reported recent earnings of $800,000 and have 500,000 shares of common stock outstanding. Assume both firms have the same required rate of return of 15 percent a year.a. Pacific Energy Company has a new project that will generate cash flows of $100,000 each year in perpetuity. Calculate the P/E ratio of the company.Chapter 5 How to Value Bonds and Stocks 129b. U.S. Bluechips has a new project that will increase earnings by $200,000 in the coming year. The increased earnings will grow at 10 percent a year in perpetuity. Calculate the P/E ratio of the firm. Solutionsa. P/E of Pacific Energy Company:EPS = ($800,000 / 500,000) = $1.6NPVGO = {$100,000 / 500,000} / 0.15 = $1.33P/E = 1 / 0.15 + 1.33 / 1.6 = 7.50b. P/E of U. S. Bluechips, Inc.:NPVGO = {$200,000 / 500,000} / (0.15 - 0.10) = $8P/E = 1 / 0.15 + 8 / 1.6 = 11.675.32 (Challenge Question) Lewin Skis Inc. (today) expects to earn $4.00 per share for each of the future operating periods (beginning at time 1) if the firm makes no new investments (and returns the earnings as dividends to the shareholders). However, Clint Williams, President and CEO, has discovered an opportunity to retain (and invest) 25% of the earnings beginning three years from today (starting at time 3). This opportunity to invest will continue (for each period) indefinitely. He expects to earn 40% (per year) on this new equity investment (ROE of 40), the return beginning one year after each investment is made. The firm’s equity discount rate is 14% throughout.a. What is the price per share (now at time 0) of Lewin Skis Inc. stock without making the new investment?b. If the new investment is expected to be made, per the preceding information, what would the value of the stock (per share) be now (at time 0)?c. What is the expected capital gain yield for the second period, assuming the proposed investment is made? What is the expected capital gain yield for the second period if the proposed investment is not made?d. What is the expected dividend yield for the second period if the new investment is made? What is the expected dividend yield for the second period if the new investment is not made?Solutionsa. Price = $4 / 0.14 = $28.57Price = 28.57 + (-1 + 0.40 / 0.14) / 0.04(1.14) 3= 28.57 + 31.33The expected return of 14% less the dividend yield of 5% providesa capital gain yield of 9%. If there is no investment the yield is 14%.$3 / $59.90 = .05 and $4 / $28.57 = .14 without the investment.Appendix to Chapter 5 Questions And ProblemsA.1 The appropriate discount rate for cash flows received one year from today is 10 percent. The appropriate annual discount rate for cash flows received two years from today is 11 percent.a. What is the price of a two-year bond that pays an annual coupon of 6 percent?b. What is the yield to maturity of this bond?Solutionsa. P = $60 / 1.10 + $1,060 / (1.11)2= $54.55 + $ 860.32= $914.87$914.87 = $60 / ( 1 + y ) + $1,060 / ( 1 + y )2y = YTM = 10.97%A.2 The one-year spot rate equals 10 percent and the two-year spot rate equals 8 percent. What should a 5-percent coupon two-year bond cost?SolutionsP = $50 / 1.10 + $1,050 / (1.08)2= $45.45 + $900.21= $945.66A.3 If the one-year spot rate is 9 percent and the two-year spot rate is 10 percent, what is the forward rate? Solutions ( 1 + r1 )( 1 + ƒ2 ) = ( 1 + r2 )2( 1.09 ) ( 1 + ƒ2 ) = ( 1.10 )2ƒ2 = .1101A.4 Assume the following spot rates:Maturity Spot Rates (%)1 52 73 10What are the forward rates over each of the three years?Solutions( 1 + r2 )2 = ( 1+ r1 ) ( 1 + ƒ2 )( 1.07 )2 = ( 1.05 )( 1 + ƒ2 )ƒ2 = .0904, one-year forward rate over the 2nd year is 9.04%.( 1 + r3 )3 = ( 1 + r2 )2 ( 1 + ƒ3 )( 1.10 )3 = ( 1.07 )2 ( 1 + ƒ3 )ƒ3 = .1625, one-year forward rate over the 3rd year is 16.25%.。

Chapter 061.The changes in a firm's future cash flows that are a direct consequence of accepting a project arecalled _____ cash flows.A. i ncrementalB. s tand-aloneC. o pportunityD. n et present valueE. e rosion2.The annual annuity stream of payments with the same present value as a project's costs is calledthe project's _____ cost.A. i ncrementalB. s unkC. o pportunityD. e rosionE. e quivalent annual3. A cost that has already been paid, or the liability to pay has already been incurred, is a(n):A. s alvage value expense.B. n et working capital expense.C. s unk cost.D. o pportunity cost.E. e rosion cost.4.The most valuable investment given up if an alternative investment is chosen is a(n):A. s alvage value expense.B. n et working capital expense.C. s unk cost.D. o pportunity cost.E. e rosion cost.5. A decrease in a firm’s current cash flows resulting from the implementation of a new project isreferred to as:A. s alvage value expenses.B. n et working capital expenses.C. s unk costs.D. o pportunity costs.E. e rosion costs.6.The depreciation method currently allowed under U.S. tax law governing the accelerated write-offof property under various lifetime classifications is called _____ depreciation.A. F IFOB. M ACRSC. s traight-lineD. s um-of-years digitsE. c urvilinear7.The cash flow tax savings generated as a result of a firm's tax-deductible depreciation expense iscalled the:A. a ftertax depreciation savings.B. d epreciable basis.C. d epreciation tax shield.D. o perating cash flow.E. a ftertax salvage value.8.The cash flow from a project is computed as the:A. n et operating cash flow generated by the project, less any sunk costs and erosion costs.B. s um of the incremental operating cash flow and aftertax salvage value of the project.C. n et income generated by the project, plus the annual depreciation expense.D. s um of the incremental operating cash flow, capital spending, and net working capital cashflows incurred by the project.E. s um of the sunk costs, opportunity costs, and erosion costs of the project.9.Interest rates or rates of return on investments that have been adjusted for the effects of inflationare called _____ rates.A. r ealB. n ominalC. e ffectiveD. s trippedE. c oupon10.The increase you realize in buying power as a result of owning an investment is referred to as the_____ rate of return.A. i nflatedB. r ealizedC. n ominalD. r ealE. r isk-free11.The pro forma income statement for a cost reduction project:A. w ill reflect a reduction in the sales of the firm.B. w ill generally reflect no incremental sales.C. h as to be prepared reflecting the total sales and expenses of the entire firm.D. c annot be prepared due to the lack of any project related sales.E. w ill always reflect a negative project operating cash flow.12.One purpose of identifying all of the incremental cash flows related to a proposed project is to:A. i solate the total sunk costs so they can be evaluated to determine if the project will add valueto the firm.B. e liminate any cost which has previously been incurred so that it can be omitted from theanalysis of the project.C. m ake each project appear as profitable as possible for the firm.D. i nclude both the proposed and the current operations of a firm in the analysis of the project.E. i dentify any and all changes in the cash flows of the firm for the past year so they can beincluded in the analysis.13.Sunk costs include any cost that:A. w ill change if a project is undertaken.B. w ill be incurred if a project is accepted.C. h as previously been incurred and cannot be changed.D. w ill be paid to a third party and cannot be refunded for any reason whatsoever.E. w ill occur if a project is accepted and once incurred, cannot be recouped.14.You spent $500 last week fixing the transmission in your car. Now, the brakes are acting up andyou are trying to decide whether to fix them or trade the car in for a newer model. In analyzing the brake situation, the $500 you spent fixing the transmission is a(n) _____ cost.A. o pportunityB. f ixedC. i ncrementalD. s unkE. r elevant15.Erosion can be explained as the:A. a dditional income generated from the sales of a newly added product.B. l oss of current sales due to a new project being implemented.C. l oss of revenue due to employee theft.D. l oss of revenue due to customer theft.E. l oss of cash due to the expenses required to fix a parking lot after a heavy rain storm.16.Which one of these is an example of erosion that should be included in project analysis?A. T he anticipated loss of current sales when a new product is launched.B. T he expected decline in sales as a new product ages.C. T he reduction in your sales that occurs when a competitor introduces a new product.D. T he sudden loss of sales due to a major employer in your community implementing massivelayoffs.E. T he reduction in sales price that will most likely be required to sell inventory that has aged.17.Which one of the following should be excluded from the analysis of a project?A. e rosion costsB. i ncremental fixed costsC. i ncremental variable costsD. s unk costsE. o pportunity costs18.All of the following are anticipated effects of a proposed project. Which of these should be considered when computing the cash flow for the final year of a project?A. o perating cash flow and salvage valuesB. s alvage values and net working capital recoveryC.operating cash flow, net working capital recovery, salvage valuesD. n et working capital recovery and operating cash flowE.operating cash flow only19.Changes in the net working capital:A. c an affect the cash flows of a project every year of the project's life.B. o nly affect the initial cash flows of a project.C. a re included in project analysis only if they represent cash outflows.D. a re generally excluded from project analysis due to their irrelevance to the total project.E. a ffect the initial and the final cash flows of a project but not the cash flows of the middle years.20.The net working capital of a firm will decrease if there is:A. a decrease in accounts payable.B. a n increase in inventory.C. a decrease in accounts receivable.D. a n increase in the firm's checking account balance.E. a decrease in fixed assets. working capital:A. c an be ignored in project analysis because any expenditure is normally recouped by the end ofthe project.B. r equirements generally, but not always, create a cash inflow at the beginning of a project.C. e xpenditures commonly occur at the end of a project.D. i s frequently affected by the additional sales generated by a new project.E. i s the only expenditure where at least a partial recovery can be made at the end of a project.22.A company which uses the MACRS system of depreciation:A. w ill have equal depreciation costs each year of an asset's life.B. w ill expense the largest percentage of the cost during an asset’s first year of life.C. c an depreciate the cost of land, if it so desires.D. w ill write off the entire cost of an asset over the asset's class life.E. c annot expense any of the cost of a new asset during the first year of the asset's life.23.Champion Toys just purchased some MACRS 5-year property at a cost of $230,000. TheMACRS rates are 20 percent, 32 percent, 19.2 percent, 11.52 percent, 11.52 percent, and 5.76 percent for Years 1 to 6, respectively. The book value of the asset as of the end of Year 2 can be calculated as:A. $230,000 × (1 −.20 −.32).B. $230,000 × ([1 - (.20 × .32)].B. $230,000 × (1 - .20) × (1 - .32).C. $230,000 / (1 - .20 - .32).D. $230,000 - ($230,000 × .20 × .32).24.Pete’s Garage just purchased some equipment at a cost of $650,000. What is the propermethodology for computing the depreciation expense for Year 3 if the equipment is classified as 5-year property for MACRS? The MACRS rates are 20 percent, 32 percent, 19.2 percent, 11.52 percent, 11.52 percent, and 5.76 percent for Years 1 to 6, respectively.A. $650,000 ×(1 − .20) ×(1 −.32) ×(1 −.192)B. $650,000 ×(1 − .20) ×(1 −.32)C. $650,000 ×(1 − .20) ×(1 − .32) × .192)D. $650,000 ×(1 −.192)E. $650,000 ×.19225.The book value of an asset is primarily used to compute the:A. a nnual depreciation tax shield.B. a mount of cash received from the sale of an asset.C. a mount of tax saved annually due to the depreciation expense.D. a mount of tax due on the sale of an asset.E. c hange in depreciation needed to reflect the market value of the asset.26.The salvage value of an asset creates an aftertax cash flow in an amount equal to the:A. s ales price of the asset.B. s ales price minus the book value.C. s ales price minus the tax due based on the sales price minus the book value.D. s ales price plus the tax due based on the sales price minus the book value.E. s ales price plus the tax due based on the book value minus the sales price.27.The pretax salvage value of an asset is equal to the:A. b ook value if straight-line depreciation is used.B. b ook value if MACRS depreciation is used.C. m arket value minus the book value.D. b ook value minus the market value.E. m arket value.28.A project's operating cash flow will increase when the:A. d epreciation expense increases.B. s ales projections are lowered.C. i nterest expense is lowered.D. n et working capital requirement increases.E. e arnings before interest and taxes decreases.29.The cash flows of a project should:A. b e computed on a pretax basis.B. i nclude all sunk costs and opportunity costs.C. i nclude all incremental and opportunity costs.D. b e applied to the year when the related expense or income is recognized by GAAP.E. i nclude all financing costs related to new debt acquired to finance the project.30.Assume a firm has no interest expense or extraordinary items. Given this, the operating cash flow can be computed as:A. E BIT - Taxes.B. E BIT × (1 - Tax rate) + Depreciation × Tax rate.C. (Sales - Costs) × (1 - Tax rate).D. E BIT - Depreciation + Taxes.E.Net income + Depreciation.31.The bottom-up approach to computing the operating cash flow applies only when:A. b oth the depreciation expense and the interest expense are equal to zero.B. t he interest expense is equal to zero.C. t he project is a cost-cutting project.D. n o fixed assets are required for the project.E. t axes are ignored and the interest expense is equal to zero.32.The top-down approach to computing the operating cash flow:A. i gnores all noncash items.B. a pplies only if a project produces sales.C. c an only be used if the entire cash flows of a firm are included.D. i s equal to Sales −Costs −Taxes + Depreciation.E. i ncludes the interest expense related to a project.33.For a profitable firm, an increase in which one of the following will increase the operating cashflow?A. e mployee salariesB. o ffice rentC. b uilding maintenanceD. d epreciationE. e quipment rental34.Tax shield refers to a reduction in taxes created by:A. a reduction in sales.B. a n increase in interest expense.C. n oncash expenses.D. a project's incremental expenses.E. o pportunity costs.35.A project which is designed to improve the manufacturing efficiency of a firm but will generate noadditional sales revenue is referred to as a(n) _____ project.A. s unk costB. o pportunityC. c ost-cuttingD. r evenue-cuttingE. r evenue-generating36.Toni's Tools is comparing machines to determine which one to purchase. The machines sell fordiffering prices, have differing operating costs, differing machine lives, and will be replaced when worn out. These machines should be compared using:A. n et present value only.B. b oth net present value and the internal rate of return.C. t heir equivalent annual costs.D. t he depreciation tax shield approach.E. t he replacement parts approach.37.The equivalent annual cost method is useful in determining:A. t he annual operating cost of a machine if the annual maintenance is performed versus whenthe maintenance is not performed as recommended.B. t he tax shield benefits of depreciation given the purchase of new assets for a project.C. o perating cash flows for cost-cutting projects of equal duration.D. w hich one of two machines to acquire given equal machine lives but unequal machine costs.E. w hich one of two machines to purchase when the machines are mutually exclusive, havedifferent machine lives, and will be replaced once they are worn out.38.Marshall's purchased a corner lot five years ago at a cost of $498,000 and then spent $63,500 ongrading and drainage so the lot could be used for storing outdoor inventory. The lot was recently appraised at $610,000. The company now wants to build a new retail store on the site. Thebuilding cost is estimated at $1.1 million. What amount should be used as the initial cash flow for this building project?A. $1,661,500B. $1,100,000C. $1,208,635D. $1,710,000E. $1,498,00039.Samson's purchased a lot four years ago at a cost of $398,000. At that time, the firm spent$289,000 to build a small retail outlet on the site. The most recent appraisal on the propertyplaced a value of $629,000 on the property and building. Samson’s now wants to tear down the original structure and build a new strip mall on the site at an estimated cost of $2.3 million. What amount should be used as the initial cash flow for new project?A. $2,987,000B. $2,242,000C. $2,058,000D. $2,300,000E. $2,929,00040.Jamestown Ltd. currently produces boat sails and is considering expanding its operations toinclude awnings. The expansion would require the use of land the firm purchased three years ago at a cost of $142,000 that is currently valued at $137,500. The expansion could use someequipment that is currently sitting idle if $6,700 of modifications were made to it. The equipment originally cost $139,500 six years ago, has a current book value of $24,700, and a current market value of $39,000. Other capital purchases costing $780,000 will also be required. What is the amount of the initial cash flow for this expansion project?A. $953,400B. $962,300C. $948,900D. $927,800E. $963,20041.The Boat Works currently produces boat sails and is considering expanding its operations toinclude awnings. The expansion would require the use of land the firm purchased three years ago at a cost of $197,000 that is currently valued at $209,500. The expansion could use someequipment that is currently sitting idle if $7,500 of modifications were made to it. The equipment originally cost $387,500 five years ago, has a current book value of $132,700, and a current market value of $139,000. Other capital purchases costing $520,000 will also be required. What is the value of the opportunity costs that should be included in the initial cash flow for theexpansion project?A. $425,000B. $485,000C. $329,700D. $348,500E. $537,20042.Walks Softly sells customized shoes. Currently, it sells 14,800 pairs of shoes annually at anaverage price of $59 a pair. It is considering adding a lower-priced line of shoes that will be priced at $39 a pair. Walks Softly estimates it can sell 6,000 pairs of the lower-priced shoes but will sell 3,500 less pairs of the higher-priced shoes by doing so. What annual sales revenue should be used when evaluating the addition of the lower-priced shoes?A. $27,500B. $24,000C. $31,300D. $789,100E. $900,70043.Foamsoft sells customized boat shoes. Currently, it sells 16,850 pairs of shoes annually at anaverage price of $79 a pair. It is considering adding a lower-priced line of shoes which sell for $49a pair. Foamsoft estimates it can sell 5,000 pairs of the lower-priced shoes but will sell 1,250 lesspairs of the higher-priced shoes by doing so. What is the estimated value of the erosion cost that should be charged to the lower-priced shoe project?A. $138,750B. $146,250C. $98,750D. $52,000E. $123,24044.Sue purchased a house for $89,000, spent $56,000 upgrading it, and currently had it appraised at$212,900. The house is being rented to a family for $1,200 a month, the maintenance expenses average $200 a month, and the property taxes are $4,800 a year. If she sells the house she will incur $20,000 in expenses. She is considering converting the house into professional officespace. What opportunity cost, if any, should she assign to this property if she has been renting it for the past two years? A. $178,500A. $120,000B. $185,000C. A NSD. $192,900D. $232,90045.Jamie's Motor Home Sales currently sells 1,100 Class A motor homes, 2,200 Class C motorhomes, and 2,800 pop-up trailers each year. Jamie is considering adding a mid-range camper and expects that if she does so she can sell 1,500 of them. However, if the new camper is added, Jamie expects that her Class A sales will decline to 850 units while the Class C camper sales decline to 2,000. The sales of pop-ups will not be affected. Class A motor homes sell for anaverage of $140,000 each. Class C homes are priced at $59,500 and the pop-ups sell for $5,000 each. The new mid-range camper will sell for $42,900. What is the erosion cost of adding the mid-range camper?A. $54,250,000B. $46,900,000C. $53,750,000D. $63,150,000E. $78,750,00046.Ernie's Electrical is evaluating a project which will increase sales by $50,000 and costs by$30,000. The project will cost $150,000 and will be depreciated straight-line to a zero book value over the 10-year life of the project. The applicable tax rate is 34 percent. What is the operating cash flow for this project?A. $19,200B. $15,000C. $21,300D. $17,900E. $18,30047.Kurt's Cabinets is looking at a project that will require $80,000 in fixed assets and another$20,000 in net working capital. The project is expected to produce sales of $110,000 withassociated costs of $70,000. The project has a 4-year life. The company uses straight-line depreciation to a zero book value over the life of the project. The tax rate is 35 percent. What is the operating cash flow for this project?A. $7,000B. $13,000C. $27,000D. $33,000E. $40,00048.Peter's Boats has sales of $760,000 and a profit margin of 5 percent. The annual depreciationexpense is $80,000. What is the amount of the operating cash flow if the company has no long-term debt?A. $34,000B. $86,400C. $118,000D. $120,400E. $123,90049.Samoa's Tools has sales of $760,000 and a profit margin of 8 percent. The annual depreciationexpense is $50,000. What is the amount of the operating cash flow if the company has no long-term debt?A. $50,000B. $60,800C. $110,800D. $810,000E. $930,00050.Le Place has sales of $439,000, depreciation of $32,000, and net working capital of $56,000. Thefirm has a tax rate of 34 percent and a profit margin of 6 percent. The firm has no interestexpense. What is the amount of the operating cash flow?A. $49,384B. $52,616C. $54,980D. $58,340E. $114,34051.The By-Way has sales of $435,000, costs of $254,000, depreciation of $35,000, interest expenseof $22,000, and taxes of $43,400. What is the amount of the operating cash flow?A. $115,600B. $157,900C. $137,600D. $322,100E. $114,34052.Ben's Border Café is considering a project that will produce sales of $16,000 and increase cashexpenses by $10,000. If the project is implemented, taxes will increase from $23,000 to $24,500 and depreciation will increase from $4,000 to $5,500. What is the amount of the operating cash flow using the top-down approach?A. $4,000B. $4,500C. $6,000D. $7,500E. $8,50053.Camille's Café is considering a project that will not produce any sales but will decrease cashexpenses by $12,000. If the project is implemented, taxes will increase from $23,000 to $24,500 and depreciation will increase from $4,000 to $5,500. What is the amount of the operating cash flow using the top-down approach?A. $15,000B. $10,500C. $5,500D. $17,500E. $13,50054.Ronnie's Coffee House is considering a project which will produce sales of $6,000 and increasecash expenses by $2,500. If the project is implemented, taxes will increase by $1,300. The additional depreciation expense will be $1,000. An initial cash outlay of $2,000 is required for net working capital. What is the amount of the operating cash flow using the top-down approach?A. $200B. $1,500C. $2,200D. $3,500E. $4,20055.A project will increase sales by $60,000 and cash expenses by $51,000. The project will cost$40,000 and will be depreciated using straight-line depreciation to a zero book value over the 4-year life of the project. The company has a marginal tax rate of 35 percent. What is the operating cash flow of the project using the tax shield approach?A. $5,850B. $8,650C. $9,350D. $9,700E. $10,35056.A project will increase sales by $140,000 and cash expenses by $95,000. The project will cost$100,000 and will be depreciated using the straight-line method to a zero book value over the 4-year life of the project. The company has a marginal tax rate of 34 percent. What is the value of the depreciation tax shield?A. $8,500B. $17,000C. $22,500D. $25,000E. $37,75057.Lee's Furniture just purchased $24,000 of fixed assets that are classified as 5-year MACRSproperty. The MACRS rates are 20 percent, 32 percent, 19.2 percent, 11.52 percent, 11.52 percent, and 5.76 percent for Years 1 to 6, respectively. What is the amount of the depreciation expense for the third year?A. $2,304B. $2,507C. $2,765D. $4,608E. $4,80058.Lew just purchased $67,600 of equipment that is classified as 5-year MACRS property. TheMACRS rates are 20 percent, 32 percent, 19.2 percent, 11.52 percent, 11.52 percent, and 5.76 percent for Years 1 to 6, respectively. What will the book value of this equipment be at the end of four years should he decide to resell the equipment at that point in time?A. $11,681.28B. $18,280.20C. $17,040.00D. $19,468.80E. $22,672.0059.Northern Enterprises just purchased $1,900 of fixed assets that are classified as 3-year MACRSproperty. The MACRS rates are 33.33 percent, 44.44 percent, 14.82 percent, and 7.41 percent for Years 1 to 4, respectively. What is the amount of the depreciation expense for Year 2?A. $562.93B. $633.27C. $719.67D. $844.36E. $1,477.6360.The Galley purchased some 3-year MACRS property two years ago at a cost of $19,800. TheMACRS rates are 33.33 percent, 44.44 percent, 14.82 percent, and 7.41 percent. The firm no longer uses this property so is selling it today at a price of $13,500. What is the amount of the pretax profit on the sale?A. $11,140.48B. $9,098.46C. $10,500.00D. $8,016.67E. $10,702.4061.Three years ago, you purchased some 5-year MACRS equipment at a cost of $135,000. TheMACRS rates are 20 percent, 32 percent, 19.2 percent, 11.52 percent, 11.52 percent, and 5.76 percent for Years 1 to 6, respectively. You sold the equipment today for $82,500. Which of these statements is correct if your tax rate is 34 percent?A. T he tax due on the sale is $14,830.80.B. T he book value today is $40,478.C. T he book value today is $37,320.D. T he taxable amount on the sale is $47,380.E. T he tax refund from the sale is $13,219.20.62.Custom Cars purchased some $39,000 of fixed assets two years ago that are classified as 5-yearMACRS property. The MACRS rates are 20 percent, 32 percent, 19.2 percent, 11.52 percent,11.52 percent, and 5.76 percent for Years 1 to 6, respectively. The tax rate is 34 percent. If theassets are sold today for $19,000, what will be the aftertax cash flow from the sale?A. $16,358.88B. $17,909.09C. $18,720.00D. $18,904.80E. $19,000.0063.Winslow Motors purchased $225,000 of MACRS 5-year property. The MACRS rates are 20percent, 32 percent, 19.2 percent, 11.52 percent, 11.52 percent, and 5.76 percent for Years 1 to 6, respectively. The tax rate is 34 percent. If the firm sells the asset after five years for $10,000, what will be the aftertax cash flow from the sale?A. $8,993.60B. $8,880.20C. $11,006.40D. $7,770.40E. $12,892.0064.A project is expected to create operating cash flows of $26,500 a year for four years. The initialcost of the fixed assets is $62,000. These assets will be worthless at the end of the project. An additional $3,000 of net working capital will be required throughout the life of the project. What is the project's net present value if the required rate of return is 12 percent?A. $19,208.11B. $14,028.18C. $15,306.09D. $17,396.31E. $21,954.1765.A project will produce operating cash flows of $45,000 a year for four years. During the life of theproject, inventory will be lowered by $30,000 and accounts receivable will increase by $15,000.Accounts payable will decrease by $10,000. The project requires the purchase of equipment at an initial cost of $120,000. The equipment will be depreciated straight-line to a zero book value over the life of the project. The equipment will be salvaged at the end of the project creating a $25,000 aftertax cash inflow. At the end of the project, net working capital will return to its normal level. What is the net present value of this project given a required return of 15 percent?A. $23,483.48B. $16,117.05C. $24,909.09D. $22,037.86E. $19,876.0266.A project will produce an operating cash flow of $7,300 a year for three years. The initialinvestment for fixed assets will be $11,600, which will be depreciated straight-line to zero over the asset’s 4-year life. The project will require an initial $500 in net working capital plus an additional $500 every year with all net working capital levels restored to their original levels when the project ends. The fixed assets can be sold for an estimated $2,500 at the end of the project, the tax rate is 34 percent, and the required rate of return is 12 percent. What is the net present value of the project?A. $7,532.27B. $9,896.87C. $7,072.72D. $6,353.41E. $8,398.2967.Matty's Place is considering the installation of a new computer system that will cut annualoperating costs by $12,000. The system will cost $42,000 to purchase and install. This system is expected to have a 5-year life and will be depreciated to zero using straight-line depreciation.What is the amount of the earnings before interest and taxes for each year of this project?A. −$20,400B. $5,400C. $3,600D. $12,000E. $8,400。

30.1 The new corporation issues $300,000 in new debt. The merger creates $100,000 ofgoodwill because the merger is a purchase.Balance SheetLager Brewing(in $ thousands)Current assets $480 Current liabilities $200Other assets 140 Long-term debt 400Net fixed assets 580 Equity 700Goodwill 100Total assets $1,300 Total liabilities $1,300 30.2 If the balance sheet for Philadelphia Pretzel shows assets at book value instead of marketvalue, the goodwill will be only $60,000 (=$300,000 - $240,000). Thus, the net fixed assetsare $620,000 (=$1,300,000 - $480,000 - $140,000 - $60,000).Balance SheetLager Brewing(in $ thousands)Current assets $480 Current liabilities $200Other assets 140 Long-term debt 400Net fixed assets 620 Equity 700Goodwill 60Total assets $1,300 Total liabilities $1,300 30.3Balance SheetLager Brewing(in $ thousands)Current assets $480 Current liabilities $280Other assets 140 Long-term debt 100Net fixed assets 580 Equity 820Total assets $1,200 Total liabilities $1,200 30.4 a. False. Although the reasoning seems correct, the Stillman-Eckbo data do not supportthe monopoly power theory.b. True. When managers act in their own interest, acquisitions are an important controldevice for shareholders. It appears that some acquisitions and takeovers are theconsequence of underlying conflicts between managers and shareholders.c. False. Even if markets are efficient, the presence of synergy will make the value ofthe combined firm different from the sum of the values of the separate firms.Incremental cash flows provide the positive NPV of the transaction.d. False. In an efficient market, traders will value takeovers based on “Fundamentalfactors” regardless of the time horizon. Recall that the evidence as a whole suggestsefficiency in the markets. Mergers should be no different.e. False. The tax effect of an acquisition depends on whether the merger is taxable ornon-taxable. In a taxable merger, there are two opposing factors to consider, thecapital gains effect and the write-up effect. The net effect is the sum of these twoeffects.f. True. Because of the coinsurance effect, wealth might be transferred from thestockholders to the bondholders. Acquisition analysis usually disregards this effectand considers only the total value.30.530.6 a. The weather conditions are independent. Thus, the joint probabilities are theproducts of the individual probabilities.Possible states Joint probabilityRain Rain 0.1 x 0.1=0.01Rain Warm 0.1 x 0.4=0.04Rain Hot 0.1 x 0.5=0.05Warm Rain 0.4 x 0.1=0.04Warm Warm 0.4 x 0.4=0.16Warm Hot 0.4 x 0.5=0.20Hot Rain 0.5 x 0.1=0.05Hot Warm 0.5 x 0.4=0.20Hot Hot 0.5 x 0.5=0.25Since the state Rain Warm has the same outcome (revenue) as Warm Rain, theirprobabilities can be added. The same is true of Rain Hot, Hot Rain and Warm Hot,Hot Warm. Thus the joint probabilities arePossibleJoint probabilitystatesRain Rain 0.01Rain Warm 0.08Rain Hot 0.10Warm Warm 0.16Warm Hot 0.40Hot Hot 0.25The joint values are the sums of the values of the two companies for the particularstate.Possible states Joint valueRain Rain $200,000Rain Warm 300,000Warm Warm 400,000Rain Hot 500,000Warm Hot 600,000Hot Hot 800,000b. Recall, if a firm cannot service its debt, the bondholders receive the value of the assets.Thus, the value of the debt is the value of the company if the face value of the debt isgreater than the value of the company. If the value of the company is greater than the value of the debt, the value of the debt is its face value. Here the value of the common stock is always the residual value of the firm over the value of the debt.Joint Prob. Joint Value Debt Value Stock Value0.01 $200,000 $200,000 $00.08 300,000 300,000 00.16 400,000 400,000 00.10 500,000 400,000 100,0000.40 600,000 400,000 200,0000.25 800,000 400,000 400,000c. To show that the value of the combined firm is the sum of the individual values, youmust show that the expected joint value is equal to the sum of the separate expected values.Expected joint value= 0.01($200,000) + 0.08($300,000) + 0.16($400,000) + 0.10($500,000) +0.40($600,000) + 0.25($800,000)= $580,000Since the firms are identical, the sum of the expected values is twice the expectedvalue of either.Expected individual value = 0.1($100,000) + 0.4($200,000) + 0.5($400,000) = $290,000 Expected combined value = 2($290,000) = $580,000d. The bondholders are better off if the value of the debt after the merger is greater thanthe value of the debt before the merger.Value of the debt before the merger:The value of debt for either company= 0.1($100,000) + 0.4($200,000) + 0.5($200,000) = $190,000Total value of debt before the merger = 2($190,000) = $380,000Value of debt after the merger= 0.01($200,000) + 0.08($300,000) + 0.16($400,000) + 0.10($400,000) +0.40($400,000) +0.25($400,000)= $390,000The bondholders are $10,000 better off after the merger.30.7 The decision hinges upon the risk of surviving. The final decision should hinge on thewealth transfer from bondholders to stockholders when risky projects are undertaken.High-risk projects will reduce the expected value of the bondholders’ claims on the firm.The telecommunications business is riskier than the utilities business. If the total value of the firm does not change, the increase in risk should favor the stockholder. Hence,management should approve this transaction. Note, if the total value of the firm dropsbecause of the transaction and the wealth effect is lower than the reduction in total value, management should reject the project.30.8 If the market is “smart,” the P/E ratio will not be constant.a. Value = $2,500 + $1,000 = $3,500b. EPS = Post-merger earnings / Total number of shares=($100 + $100)/200 =$1c. Price per share = Value/Total number of shares=$3,500/200 =$17.50d. If the market is “fooled,” the P/E ratio will be constant at $25.Value = P/E * Total number of shares= 25 * 200 = $5,000EPS = Post-merger earnings / Total number of shares=$5,000/200 = $25.0030.9 a. After the merger, Arcadia Financial will have 130,000 [=10,000 + (50,000)(6/10)]shares outstanding. The earnings of the combined firm will be $325,000. The earningsper share of the combined firm will be $2.50 (=$325,000/130,000). The acquisition will increase the EPS for the stockholders from $2.25 to $2.50.b. There will be no effect on the original Arcadia stockholders. No synergies exist in thismerger since Arcadia is buying Coldran at its market price. Examining the relativevalues of the two firms sees the latter point.Share price of Arcadia = (16 * $225,000) / 100,000=$36Share price of Coldran = (10.8 * $100,000) / 50,000=$21.60The relative value of these prices is $21.6/$36 = 0.6. Since Coldran’s shareholdersreceive 0.6 shares of Arcadia for every share of Coldran, no synergies exist.30.10 a. The synergy will be the discounted incremental cash flows. Since the cash flows areperpetual, this amount isb. The value of Flash-in-the-Pan to Fly-by-Night is the synergy plus the current marketvalue of Flash-in-the-Pan.V = $7,500,000 + $20,000,000= $27,500,000c. Cash alternative = $15,000,000Stock alternative = 0.25($27,500,000 + $35,000,000)= $15,625,000d. NPV of cash alternative = V - Cost=$27,500,000 - $15,000,000=$12,500,000NPV of stock alternative = V - Cost=$27,500,000 - $15,625,000=$11,875,000e. Use the cash alternative, its NPV is greater.30.11 a. The value of Portland Industries before the merger is $9,000,000 (=750,000x12). Thisvalue is also the discounted value of the expected future dividends.$9,000,000 =r = 0.1025 = 10.25%r is the risk-adjusted discount rate for Portland’s expected future dividends.the value of Portland Industries after the merger isThis is the value of Portland Industries to Freeport.b. NPV = Gain - Cost= $14,815,385 - ($40x250, 000)= $4,815,385c. If Freeport offers stock, the value of Portland Industries to Freeport is the same, but thecost differs.Cost = (Fraction of combined firm owned by Portland’s stockholders)x(Value of the combined firm)Value of the combined firm = (Value of Freeport before merger)+ (Value of Portland to Freeport)= $15x1,000,000 + $14,815,385= $29,815,385Cost = 0.375x$29,815,385= $11,180,769NPV= $14,815,385 - $11,180,769=$3,634,616d. The acquisition should be attempted with a cash offer since it provides a higher NPV.e. The value of Portland Industries after the merger isThis is the value of Portland Industries to Freeport.NPV = Gain-Cost=$11,223,529 - ($40x250,000)=$1,223,529If Freeport offers stock, the value of Portland Industries to Freeport is the same, but the cost differs.Cost = (Fraction of combined firm owned by Portland’s stockholders)x(Value of the combined firm)Value of the combined firm = (Value of Freeport before merger)+ (Value of Portland to Freeport)= $15x1,000,000 + $11,223,529= $26,223,529Cost = 0.375 * $26,223,529=$9,833,823NPV = $11,223,529 - $9,833,823=$1,389,706The acquisition should be attempted with a stock offer since it provides a higher NPV.30.12 a. Number of shares after acquisition=30 + 15 = 45 milStock price of Harrods after acquisition = 1,000/45=22.22 poundsb. Value of Selfridge stockholders after merger:α * 1,000 = 300α = 30%New shares issued = 12.86 mil12.86:20 = 0.643:1The proper exchange ratio should be 0.643 to make the stock offer’s value to Selfridgeequivalent to the cash offer.30.13 To evaluate this proposal, look at the present value of the incremental cash flows.Cash Flows to Company A(in $ million)Year 0 1 2 3 4 5Acquisition of B -550Dividends from B 150 32 5 20 30 45Tax-loss carryforwards 25 25Terminal value 600Total -400 32 30 45 30 645 The additional cash flows from the tax-loss carry forwards and the proposed level of debt should be discounted at the cost of debt because they are determined with very littleuncertainty.The after-tax cash flows are subject to normal business risk and must be discounted at anormal rate.Beta coefficient for the bond = 0.25 = [(8%-6%)/8%].Beta coefficient for the company = 1 = [(0.25)2 + (1.25)(0.75)]Discount rate for normal operations:r = 6% + 8% (1) = 14%Discount rate for dividends:The new beta coefficient for the company, 1, must be the weighted average of the debtbeta and the stock beta.1 = 0.5(0.25) + 0.5(βs)βs = 1.75r = 6% + 8%(1.75) = 20%Because the NPV of the acquisition is negative, Company A should not acquireCompany B.30.14 The commonly used defensive tactics by target-firm managers include:i. corporate charter amendments like super-majority amendment or staggering theelection of board members.ii. repurchase standstill agreements.iii. exclusionary self-tenders.iv. going private and leveraged buyouts.v. other devices like golden parachutes, scorched earth strategy, poison pill, ..., etc.Mini Case: U.S.Steel’s case.You have 3 choices: tender, or do not tender or sell in the market. If you do sell your shares in the market, at some point, somebody else would need to make a decision in “tender” or “not tender” as well.It is important to recognize that the firm has about 60 million shares outstanding (since 30 million shares will give US Steel 50.1% of Marathon shares). Let’s consider the possible sellingthe market price.If you choose not to tender, and 30 million shares were tendered US Steel succeeds to gain50.1% control, you will only receive $85 a share. If you do tender, the price you will receive will be no worse than $85 a share and can be as high as $125 a share. Depending on the number of shares tendered, you will receive one of the following prices.If only 50.1% tendered, you will get $125 per share.If the shares tendered exceed 50.1% but less than 100%, you will get more than $105 ashare.If all 60 million shares were tendered, you will get $105 per share. (which is )It is clear that, in the above 3 cases, when you are not sure about whether US Steel will succeed or not, you will be better off to tender your shares than not tender. This is because at best, you will only receive $85 per share if you choose not to tender.版权申明本文部分内容，包括文字、图片、以及设计等在网上搜集整理。

Concept Questions◆Define pure discount bonds, level-coupon bonds, and consols.A pure discount bond is one that makes no intervening interest payments. One receives a single lump sum payment at maturity. A level-coupon bond is a combination of an annuity and a lump sum at maturity. A consol is a bond that makes interest payments forever.◆Contrast the state interest rate and the effective annual interest rate for bonds paying semi-annual interest. Effective annual interest rate on a bond takes into account two periods of compounding per year received on the coupon payments. The state rate does not take this into account.◆What is the relationship between interest rates and bond prices?There is an inverse relationship. When one goes up, the other goes down.◆How does one calculate the yield to maturity on a bond?One finds the discount rate that equates the promised future cash flows with the price of the bond.◆What are the three factors determining a firm's P/E ratio?Today's expectations of future growth opportunities.The discount rate.The accounting method.◆What is the closing price of General Data?The closing price of General Data is 6 3/16.◆What is the PE of General House?The PE of General House is 29.◆What is the annual dividend of General Host?The annual dividend of General Host is zero.Concept Questions- Appendix To Chapter 5◆What is the difference between a spot interest rate and the yield to maturity?The yield to maturity is the geometric average of the spot rates during the life of the bond.◆Define the forward rate.Given a one-year bond and a two-year bond, one knows the spot rates for both. The forward rate is the rate of return implicit on a one-year bond purchased in the second year that would equate the terminal wealth of purchasing the one-year bond today and another in one year with that of the two-year bond.◆What is the relationship between the one-year spot rate, the two-year spot rate and the forward rate over the second year?The forward rate f2 = [(1+r2)2 /(1+r1 )] - 1◆What is the expectation hypothesis?Investors set interest rates such that the forward rate over a given period equals the spot rate for that period.◆What is the liquidity-preference hypothesis?This hypothesis maintains that investors require a risk premium for holding longer-term bonds (i.e. they prefer to be liquid or short-term investors). This implies that the market sets the forward rate for a given period above the expected spot rate for that period.Questions And ProblemsHow to Value Bonds5.1 What is the present value of a 10-year, pure discount bond that pays $1,000 at maturity andis priced to yield the following rates?a. 5 percentb. 10 percentc. 15 percentSolutions a. $1,000 / 1.0510 = $613.91b. $1,000 / 1.1010 = $385.54c. $1,000 / 1.1510 = $247.185.2 Microhard has issued a bond with the following characteristics:Principal: $1,000Term to maturity: 20 yearsCoupon rate: 8 percentSemiannual paymentsCalculate the price of the Microhard bond if the stated annual interest rate is:a. 8 percentb. 10 percentc. 6 percentSolutions The amount of the semi-annual interest payment is $40 (=$1,000 ⨯ 0.08 / 2). There are a total of 40 periods; i.e., two half years in each of the twenty years in the term to maturity.The annuity factor tables can be used to price these bonds. The appropriate discount rate touse is the semi-annual rate. That rate is simply the annual rate divided by two. Thus, for part b the rate to be used is 5% and for part c is it 3%.a. $40 (19.7928) + $1,000 / 1.0440 = $1,000Notice that whenever the coupon rate and the market rate are the same, the bond ispriced at par.b. $40 (17.1591) + $1,000 / 1.0540 = $828.41Notice that whenever the coupon rate is below the market rate, the bond is pricedbelow par.c. $40 (23.1148) + $1,000 / 1.0340 = $1,231.15Notice that whenever the coupon rate is above the market rate, the bond is pricedabove par.5.3 Consider a bond with a face value of $1,000. The coupon is paid semiannually and themarket interest rate (effective annual interest rate) is 12 percent. How much would you payfor the bond ifa. the coupon rate is 8 percent and the remaining time to maturity is 20 years?b. the coupon rate is 10 percent and the remaining time to maturity is 15 years?Solutions Semi-annual discount factor = (1.12)1/2 - 1 = 0.05830 = 5.83%a. Price = $40400583.0A+ $1,000 / 1.058340= $614.98 + $103.67= $718.65b. Price = $50300583.0A+ $1,000 / 1.058330= $700.94 + $182.70 = $883.645.4 Pettit Trucking has issued an 8-percent, 20-year bond that pays interest semiannually. If themarket prices the bond to yield an effective annual rate of 10 percent, what is the price ofthe bond? Solutions Effective annual rate of 10%:Semi-annual discount factor = (1.1)0.5 - 1 = 0.04881 = 4.881%Price = $404004881.0A+ $1,000 / 1.0488140= $846.335.5 A bond is sold at $923.14 (below its par value of $1,000). The bond has 15 years tomaturity and investors require a 10-percent yield on the bond. What is the coupon rate forthe bond if the coupon is paid semiannually?Solutions $923.14 = C3005.0A+ $1,000 / 1.0530= (15.37245) C + $231.38C = $45The annual coupon rate = $45 ⨯ 2 / $1,000 = 0.09 = 9%5.6 You have just purchased a newly issued $1,000 five-year Vanguard Company bond at par.This five-year bond pays $60 in interest semiannually. You are also considering the purchaseof another Vanguard Company bond that returns $30 in semiannual interest payments andhas six years remaining before it matures. This bond has a face value of $1,000.a. What is effective annual return on the five-year bond?b. Assume that the rate you calculated in part (a) is the correct rate for the bond with sixyears remaining before it matures. What should you be willing to pay for that bond?c. How will your answer to part (b) change if the five-year bond pays $40 in semiannualinterest? Solutionsa. The semi-annual interest rate is $60 / $1,000 = 0.06. Thus, the effective annual rate is 1.062 - 1 =0.1236 = 12.36%.b. Price = $301206.0A+ $1,000 / 1.0612= $748.48c. Price = $301204.0A+ $1,000 / 1.0412= $906.15Note: In parts b and c we are implicitly assuming that the yield curve is flat. That is, the yield in year 5 applies for year 6 as well.Bond Concepts5.7 Consider two bonds, bond A and bond B, with equal rates of 10 percent and the same facevalues of $1,000. The coupons are paid annually for both bonds. Bond A has 20 years tomaturity while bond B has10 years to maturity.a. What are the prices of the two bonds if the relevant market interest rate is 10 percent?b. If the market interest rate increases to 12 percent, what will be the prices of the two bonds?c. If the market interest rate decreases to 8 percent, what will be the prices of the two bonds? Solutionsa. PA = $1002010.0A+ $1,000 / 1.1020 = $1,000PB = $1001010.0A+ $1,000 / 1.1010 = $1,000b. PA = $1002012.0A+ $1,000 / 1.1220 = $850.61PB = $1001012.0A+ $1,000 / 1.1210 = $887.00c. PA = $1002008.0A+ $1,000 / 1.0820 = $1,196.36PB = $1001008.0A+ $1,000 / 1.0810 = $1,134.205.8 a. If the market interest rate (the required rate of return that investors demand)unexpectedly increases, what effect would you expect this increase to have on theprices of long-term bonds? Why?b. What would be the effect of the rise in the interest rate on the general level of stockprices? Why? Solutionsa. The price of long-term bonds should fall. The price is the PV of the cash flowsassociated with the bond. As the interest rate rises, the PV of those flows falls.This can be easily seen by looking at a one-year, pure discount bond.Price = $1,000 / (1 + i)As i. increases, the denominator rises. This increase causes the price to fall.b. The effect upon stocks is not as certain as that upon the bonds. The nominalinterest rate is a function of both the real interest rate and the inflation rate; i.e.,(1 + i) = (1 + r) (1 + inflation)From this relationship it is easy to conclude that as inflation rises, the nominal interest rate rises. Stock prices are a function of dividends and future prices as well as the interest rate. Those dividends and future prices are determined by the earning power of the firm. When inflation occurs, it may increase or decrease firm earnings. Thus, the effect of a rise in the level of general prices upon the level of stock prices is uncertain.5.9 Consider a bond that pays an $80 coupon annually and has a face value of $1,000.Calculate the yield to maturity if the bond hasa. 20 years remaining to maturity and it is sold at $1,200.b. 10 years remaining to maturity and it is sold at $950.Solutions a. $1,200 = $8020rA+ $1,000 / (1 + r)20r = 0.0622 = 6.22%b. $950 = $8010rA+ $1,000 / (1 + r)10r = 0.0877 = 8.77%5.10 The Sue Fleming Corporation has two different bonds currently outstanding. Bond A has aface value of $40,000 and matures in 20 years. The bond makes no payments for the firstsix years and then pays $2,000 semiannually for the subsequent eight years, and finallypays $2,500 semiannually for the last six years. Bond B also has a face value of $40,000and a maturity of 20 years; it makes no coupon payments over the life of the bond. If therequired rate of return is 12 percent compounded semiannually, what is the current price ofBond A? of Bond B?Solutions PA = ($2,0001606.0A) / (1.06)12 + ($2,5001206.0A) / (1.06)28 + $40,000 / (1.06)40= $18,033.86PB = $ 40,000 / (1.06)40 = $3,888.89The Present Value of Common Stocks5.11 Use the following February 11, 2000, WSJ quotation for AT&T Corp. Which of thefollowing statements is false?a. The closing price of the bond with the shortest time to maturity was $1,000.b. The annual coupon for the bond maturing in year 2016 is $90.00.c. The price on the day before this quotation (i.e., February 9) for the ATT bond maturingin year 2022 was $1.075 per bond contract.d. The current yield on the ATT bond maturing in year 2002 was 7.125%e. The ATT bond maturing in year 2002 has a yield to maturity less than 7.125%.Bonds Cur Yld Vol Close Net ChgATT 9s 16 ? 10 117 _ 1/4ATT 5 1/8 01 ? 5 100 _ 3/4ATT 7 1/8 02 ? 193 104 1/8 _ 1/4ATT 8 1/8 22 ? 39 107 3/8 _ 1/8Solutions a. TrueTrueFalseFalseTrue5.12 Following are selected quotations for New York Exchange Bonds from the Wall StreetJournal. Which of the following statements about Wilson’s bond is false?a. The bond maturing in year 2000 has a yield to maturity greater than 63⁄8%.b. The closing price of the bond with the shortest time to maturity on the day before thisquotation was $1,003.25.c. This annual coupon for the bond maturing in year 2013 is $75.00.d. The current yield on the Wilson’s bond with the longest time to maturity was 7.29%.e. None of the above.Quotations as of 4 P.M. Eastern TimeFriday, April 23, 1999Bonds Current Yield Vol Close NetWILSON 6 3/8 99 ? 76 100 3/8 _ 1/8WILSON 6 3/8 00 ? 9 98 1/2WILSON 7 1/4 02 ? 39 103 5/8 1/8WILSON 7 1/2 13 ? 225 102 7/8 _ 1/8Solutions a. TrueFalseTrueTrueFalse5.13 A common stock pays a current dividend of $2. The dividend is expected to grow at an8-percent annual rate for the next three years; then it will grow at 4 percent in perpetuity.The appropriate discount rate is 12 percent. What is the price of this stock?Solutions Price = $2 (1.08) / 1.12 + $2 (1.082) / 1.122 + $2 (1.083) / 1.123+ {$2 (1.083) (1.04) / (0.12 - 0.04)} / 1.123= $28.895.14 Use the following February 12, 1998, WSJ quotation for Merck & Co. to answer the nextquestion. 52 Weeks Yld Vol NetHi Lo Stock Sym Div % PE 100s Hi Lo Close Chg120. 80.19 Merck MRK 1.80 ? 30 195111 115.9 114.5 115 _1.25Which of the following statements is false?a. The dividend yield was about 1.6%.b. The 52 weeks’ trading range was $39.81.c. The closing price per share on February 10, 1998, was $113.75.d. The closing price per share on February 11, 1998, was $115.e. The earnings per share were about $3.83.Solutions a. FalseTrueFalseFalseTrue5.15 Use the following stock quote.52 Weeks Yld Vol NetHi Lo Stock Sym Div % PE 100s Hi Lo Close Chg126.25 72.50 Citigroup CCI 1.30 1.32 16 20925 98.4 97.8 98.13 _.13The expected growth rate in Citigroup’s dividends is 7% a year. Suppose you use thediscounted dividend model to price Citigroup’s shares. The constant growth dividendmodel would suggest that the required return on the Citigroup’s stock is what?98.125 = 1.30 ( 1.07) / r - 0.07r = 8.4175 %5.16 You own $100,000 worth of Smart Money stock. At the end of the first year you receive adividend of $2 per share; at the end of year 2 you receive a $4 dividend. At the end of year3 you sell the stock for $50 per share. Only ordinary (dividend) income is taxed at the rateof 28 percent. Taxes are paid at the time dividends are received. The required rate of returnis 15 percent. How many shares of stock do you own? Solutions Price = $2 (0.72) / 1.15 + $4 (0.72) / 1.152 + $50 / 1.153= $36.31The number of shares you own = $100,000 / $36.31 = 2,754 shares5.17 Consider the stock of Davidson Company that will pay an annual dividend of $2 in thecoming year. The dividend is expected to grow at a constant rate of 5 percent permanently.The market requires a 12-percent return on the company.a. What is the current price of a share of the stock?b. What will the stock price be 10 years from today?Solutionsa. P = $2 / (0.12 - 0.05) = $28.57b. P10 = D11 / (r - g)= $2 (1.0510) / (0.12 - 0.05) = $46.545.18 Easy Type, Inc., is one of a myriad of companies selling word processor programs.Their newest program will cost $5 million to develop. First-year net cash flows will be$2 million. As a result of competition, profits will fall by 2 percent each year thereafter.All cash inflows will occur at year-end. If the market discount rate is 14 percent, what isthe value of this new program?SolutionsValue = -$5,000,000 + $2,000,000 / {0.14 - (-0.02)}= $7,500,0005.19 Whizzkids, Inc., is experiencing a period of rapid growth. Earnings and dividends pershare are expected to grow at a rate of 18 percent during the next two years, 15 percent inthe third year, and at a constant rate of 6 percent thereafter. Whizzkids’ last dividend,which has just been paid, was $1.15. If the required rate of return on the stock is 12percent, what is the price of a share of the stock today?SolutionsPrice = $1.15 (1.18) / 1.12 + $1.15 (1.182) / 1.122 + $1.152 (1.182) / 1.123+ {$1.152 (1.182) (1.06) / (0.12 - 0.06)} / 1.123= $26.955.20 Allen, Inc., is expected to pay an equal amount of dividends at the end of the first twoyears. Thereafter, the dividend will grow at a constant rate of 4 percent indefinitely. Thestock is currently traded at $30. What is the expected dividend per share for the next yearif the required rate of return is 12 percent?Solutions$30 = D / 1.12 + D / 1.122 + {D (1 + 0.04) / (0.12 - 0.04)} / 1.122= 12.053571 DD = $2.495.21 Calamity Mining Company’s reserves of ore are being depleted, and its costs ofrecovering a declining quantity of ore are rising each year. As a result, the company’searnings are declining at the rate of 10 percent per year. If the dividend per share that isabout to be paid is $5 and the required rate of return is 14 percent, what is the value of thefirm’s stock?SolutionsDividend one year from now = $5 (1 - 0.10) = $4.50Price = $5 + $4.50 / {0.14 - (-0.10)} = $23.75Since the current $5 dividend has not yet been paid, it is still included in the stock price.5.22 The Highest Potential, Inc., will pay a quarterly dividend per share of $1 at the end of eachof the next 12 quarters. Subsequently, the dividend will grow at a quarterly rate of 0.5percent indefinitely. The appropriate rate of return on the stock is 10 percent. What is thecurrent stock price?Estimates of Parameters in the Dividend-Discount ModelSolutionsPrice = $112025.0A+ {$1 (1 + 0.005) / (0.025 - 0.005)} / 1.02512= $10.26 + $37.36= $47.625.23 The newspaper reported last week that Bradley Enterprises earned $20 million. The reportalso stated that the firm’s return on equity remains on its historical trend of 14 percent.Bradley retains 60 percent of its earnings. What is the firm’s growth rate of earnings?What will next year’s earnings be?SolutionsGrowth rate g = 0.6 ⨯ 0.14 = 0.084 = 8.4%Next year earnings = $20 million ⨯ 1.084 = $21.68 million5.24 Von Neumann Enterprises has just reported earnings of $10 million, and it plans to retain 75percent of its earnings. The company has 1.25 million shares of common stock outstanding.The stock is selling at $30. The historical return on equity (ROE) of 12 percent is expectedto continue in the future. What is the required rate of return on the stock?Growth Opportunitiesg = retention ratio ⨯ ROE = 0.75 ⨯ 0.12= 0.09 = 9%Dividend per share = $10 million ⨯ (1 - 0.75) / 1.25 million= $2The required rate of return = $2 (1.09) / $30 + 0.09= 0.1627 = 16.27%5.25 Rite Bite Enterprises sells toothpicks. Gross revenues last year were $3 million, and totalcosts were $1.5 million. Rite Bite has 1 million shares of common stock outstanding.Gross revenues and costs are expected to grow at 5 percent per year. Rite Bite pays noincome taxes, and all earnings are paid out as dividends.a. If the appropriate discount rate is 15 percent and all cash flows are received at year’send, what is the price per share of Rite Bite stock?b. The president of Rite Bite decided to begin a program to produce toothbrushes. Theproject requires an immediate outlay of $15 million. In one year, another outlay of$5 million will be needed. The year after that, net cash inflows will be $6 million. Thisprofit level will be maintained in perpetuity. What effect will undertaking this projecthave on the price per share of the stock?Solutionsa. Price = ($3 - $1.5) ⨯ 1.05 / (0.15 - 0.05)= $15.75b. NPVGO = -$15,000,000 - $5,000,000 / 1.15 + ($6,000,000 / 0.15) / 1.15= $15,434,783The price increases by $15.43 per share.5.26 California Electronics, Inc., expects to earn $100 million per year in perpetuity if it doesnot undertake any new projects. The firm has an opportunity that requires an investment of$15 million today and $5 million in one year. The new investment will begin to generateadditional annual earnings of $10 million two years from today in perpetuity. The firm has20 million shares of common stock outstanding, and the required rate of return on thestock is 15 percent.a. What is the price of a share of the stock if the firm does not undertake the new project?b. What is the value of the growth opportunities resulting from the new project?c. What is the price of a share of the stock if the firm undertakes the new project?Solutionsa. Price = EPS / r = {$100 million / 20 million} / 0.15= $33.33b. NPV = -$15 million - $5 million / 1.15 + ($10 million / 0.15) / 1.15= $38,623,188c. Price = $33.33 + $38,623,188 / 20,000,000= $35.265.27 Suppose Smithfield Foods, Inc., has just paid a dividend of $1.40 per share. Sales andprofits for Smithfield Foods are expected to grow at a rate of 5% per year. Its dividend isexpected to grow by the same rate. If the required return is 10%, what is the value of ashare of Smithfield Foods?SolutionsPrice = 1.40 (1.05) / 0.10 - 0.05Price = $29.405.28 In order to buy back its own shares, Pennzoil Co. has decided to suspend its dividends forthe next two years. It will resume its annual cash dividend of $2.00 a share 3 years fromnow. This level of dividendswill be maintained for one more year. Thereafter, Pennzoil isexpected to increase its cash dividend payments by an annual growth rate of 6% per yearforever. The required rate of return on Pennzoil’s stock is 16%. According to thediscounted dividend model, what should Pennzoil’s current share price be? SolutionsPrice = 2 / (1.16) 3 + 2 / (1.16)4 + 2.12 / 0.16 - 0.06= 1.28 + 1.10 + 21.20= $23.585.29 Four years ago, Ultramar Diamond Inc. paid a dividend of $0.80 per share. This yearUltramar paid a dividend of $1.66 per share. It is expected that the company will paydividends growing at the same rate for the next 5 years. Thereafter, the growth rate willlevel at 8% per year. The required return on this stock is 18%. According to the discounteddividend model, what would Ultramar’s cash dividend be in 7 years?a. $2.86c. $3.68d. $4.30e. $4.82Solutionsa. g = 0.4 ⨯ 0.15 = 0.06 = 6%b. Dividend per share = $1.5 million ⨯ 0.6 / 300,000= $3Price = $3 (1.06) / (0.13 - 0.06)= $45.43c. Assuming the additional earnings generated are all paid out as cash dividends.NPV = -$1.2 million + $0.3 million {1 / (0.13 - 0.10)} {1 - (1.10 / 1.13)10}= $1,159,136.93d. Price = $45.43 + $1,159,136.93 / 300,000= $49.295.30 The Webster Co. has just paid a dividend of $5.25 per share. The company will increase itsdividend by 15 percent next year and will then reduce its dividend growth by 3 percenteach year until it reaches the industry average of 5 percent growth, after which thecompany will keep a constant growth, forever. The required rate of return for the WebsterCo. is 14 percent. What will a share of stock sell for?SolutionsPrice = 3 / 1.15 + 4.5 / ( 1.15)2 + 4.725 / 0.15- 0.05= 2.61 + 3.40 + 47.52= $53.535.31 Consider Pacific Energy Company and U.S. Bluechips, Inc., both of which reported recentearnings of $800,000 and have 500,000 shares of common stock outstanding. Assume bothfirms have the same required rate of return of 15 percent a year.a. Pacific Energy Company has a new project that will generate cash flows of $100,000each year in perpetuity. Calculate the P/E ratio of the company.Chapter 5 How to Value Bonds and Stocks 129b. U.S. Bluechips has a new project that will increase earnings by $200,000 in the comingyear. The increased earnings will grow at 10 percent a year in perpetuity. Calculate theP/E ratio of the firm. Solutionsa. P/E of Pacific Energy Company:EPS = ($800,000 / 500,000) = $1.6NPVGO = {$100,000 / 500,000} / 0.15 = $1.33P/E = 1 / 0.15 + 1.33 / 1.6 = 7.50b. P/E of U. S. Bluechips, Inc.:NPVGO = {$200,000 / 500,000} / (0.15 - 0.10) = $8P/E = 1 / 0.15 + 8 / 1.6 = 11.675.32 (Challenge Question) Lewin Skis Inc. (today) expects to earn $4.00 per share for each ofthe future operating periods (beginning at time 1) if the firm makes no new investments(and returns the earnings as dividends to the shareholders). However, Clint Williams,President and CEO, has discovered an opportunity to retain (and invest) 25% of theearnings beginning three years from today (starting at time 3). This opportunity to investwill continue (for each period) indefinitely. He expects to earn 40% (per year) on this newequity investment (ROE of 40), the return beginning one year after each investment ismade. The firm’s equity discount rate is 14% throughout.a. What is the price per share (now at time 0) of Lewin Skis Inc. stock without making thenew investment?b. If the new investment is expected to be made, per the preceding information, whatwould the value of the stock (per share) be now (at time 0)?c. What is the expected capital gain yield for the second period, assuming the proposedinvestment is made? What is the expected capital gain yield for the second period if theproposed investment is not made?d. What is the expected dividend yield for the second period if the new investment ismade? What is the expected dividend yield for the second period if the new investmentis not made?Solutionsa. Price = $4 / 0.14 = $28.57Price = 28.57 + (-1 + 0.40 / 0.14) / 0.04(1.14) 3= 28.57 + 31.33The expected return of 14% less the dividend yield of 5% providesa capital gain yield of 9%. If there is no investment the yield is 14%.$3 / $59.90 = .05 and $4 / $28.57 = .14 without the investment.Appendix to Chapter 5Questions And ProblemsA.1 The appropriate discount rate for cash flows received one year from today is 10 percent. Theappropriate annual discount rate for cash flows received two years from today is 11 percent.a. What is the price of a two-year bond that pays an annual coupon of 6 percent?b. What is the yield to maturity of this bond?Solutionsa. P = $60 / 1.10 + $1,060 / (1.11)2= $54.55 + $ 860.32= $914.87$914.87 = $60 / ( 1 + y ) + $1,060 / ( 1 + y )2y = YTM = 10.97%A.2 The one-year spot rate equals 10 percent and the two-year spot rate equals 8 percent. Whatshould a 5-percent coupon two-year bond cost?SolutionsP = $50 / 1.10 + $1,050 / (1.08)2= $45.45 + $900.21= $945.66A.3 If the one-year spot rate is 9 percent and the two-year spot rate is 10 percent, what is theforward rate? Solutions ( 1 + r1 )( 1 + ƒ2 ) = ( 1 + r2 )2( 1.09 ) ( 1 + ƒ2 ) = ( 1.10 )2ƒ2 = .1101A.4 Assume the following spot rates:Maturity Spot Rates (%)1 52 73 10What are the forward rates over each of the three years?Solutions( 1 + r2 )2 = ( 1+ r1 ) ( 1 + ƒ2 )( 1.07 )2 = ( 1.05 )( 1 + ƒ2 )ƒ2 = .0904, one-year forward rate over the 2nd year is 9.04%.( 1 + r3 )3 = ( 1 + r2 )2 ( 1 + ƒ3 )( 1.10 )3 = ( 1.07 )2 ( 1 + ƒ3 )ƒ3 = .1625, one-year forward rate over the 3rd year is 16.25%.。

公司理财习题答案第十九章Chapter 19: Issuing Equity Securities to the Public19.1 a. A general cash offer is a public issue of a security that is sold to all interestedinvestors. A general cash offer is not restricted to current stockholders.b. A rights offer is an issuance that gives the current stockholders the opportunity tomaintain a proportionate ownership of the company. The shares are offered to thecurrent shareholders before they are offered to the general public.c. A registration statement is the filing with the SEC, which discloses all pertinentinformation concerning the corporation that wants to make a public offering.d. A prospectus is the legal document that must be given to every investor whocontemplates purchasing registered securities in a public offering. The prospectusdescribes the details of the company and the particular issue.e. An initial public offering (IPO) is the original sale of a company’s securities to thepublic. An IPO is also called an unseasoned issue.f. A seasoned new issue is a new issue of stock after the company’s securities havepreviously been publicly traded.g. Shelf registration is an SEC procedure, which allows a firm to file a masterregistration statement summarizing the planned financing for a two year period.The firm files short forms whenever it wishes to sell any of the approved masterregistration securities during the two year period.19.2 a. The Securities Exchange Act of 1933 regulates the trading of new, unseasonedsecurities.b. The Securities Exchange Act of 1934 regulates the trading of seasoned securities.This act regulates trading in what is called the secondary market.19.3 Competitive offer and negotiated offer are two methods to select investment bankers forunderwriting. Under the competitive offers, the issuing firm can award its securities to the underwriter with the highest bid, which in turn implies the lowest cost. On the other hand, in negotiated deals, underwriter gains much information about the issuing firm throughnegotiation, which helps increase the possibility of a successful offering.19.4 a. Firm commitment underwriting is an underwriting in which an investment bankingfirm commits to buy the entire issue. It will then sell the shares to the public. Theinvestment banking firm assumes all financial responsibility for any unsold shares.b. A syndicate is a group of investment banking companies that agree to cooperate in ajoint venture to underwrite an offering of securities.c. The spread is the difference between the underwriter’s buying price and the offeringprice. The spread is a fee for the services of the underwriting syndicate.d. Best efforts underwriting is an offering in which the underwriter agrees to distributeas much of the offering as possible. Any unsold portions of the offering are returnedto the issuing firm.19.5 a. The risk in a firm commitment underwriting is borne by the underwriter(s). Thesyndicate agrees to purchase all of an offering. Then they sell as much of it aspossible. Any unsold shares remain the responsibility of the underwriter(s). Therisk that the security’s price may become unfavorable also lies with theunderwriter(s).b. The issuing firm bears the risk in a best efforts underwriting. The underwriter(s)agrees to make its best effort to sell the securities for the firm. Any unsoldsecurities are the responsibility of the firm.19.6 In general, the new price per share after the offering is:P = (market value + proceeds from offering) / total number of sharesi. At $40 P = ($400,000 + ($40 x 5,000)) / 15,000 =$40ii. At $20 P = ($400,000 + ($20 x 5,000)) / 15,000 = $33.33iii. At $10 P = ($400,000 + ($10 x 5,000)) / 15,000 = $3019.7 The poor performance result should not surprise the professor. Since he subscribed to everyinitial public offering, he was bound to get fewer superior performers and more poorperformers. Financial analysts studied the companies and separated the bad prospects from the good ones. The analysts invested in only the good prospects. These issues becameoversubscribed. Since these good prospects were oversubscribed, the professor received a limited amount of stock from them. The poor prospects were probably under-subscribed, so he received as much of their stock as he desired. The result was that his performance was below average because the weight on the poor performers in his portfolio was greater than the weight on the superio r performers. This result is called the winner’s curse. The professor “won” the shares, but his bane was that the shares he “won” were poorperformers.19.8 There are two possible reasons for stock price drops on the announcement of a new equityissue:i. M anagement may attempt to issue new shares of stock when the stock is over-valued, that is, the intrinsic value is lower than the market price. The price drop isthe result of the downward adjustment of the overvaluation.ii. W ith the increase of financial distress possibility, the firm is more likely to raise capital through equity than debt. The market price drops because it interprets theequity issue announcement as bad news.19.9 The costs of new issues include underwriter’s spread, direct and indirect expenses, negativeabnormal returns associated with the equity offer announcement, under-pricing, and green-shoe option.19.10 a. $12,000,000/$15 = 800,000b. 2,400,000/800,000 = 3c. The shareholders must remit $15 and three rights for each share of new stock theywish to purchase.19.11 a. In general, the ex-rights price isP = (Market value + Proceeds from offering) / Total number of sharesP = ($25 x 100,000 + $20 x 10,000) / (100,000 + 10,000) = $24.55b. The value of a right is the difference between the rights-on price of the stock andthe ex-rights price of the stock. The value of a right is $0.45 (=$25 - $24.55).Alternative solution:The value of a right can also be computed as:(Ex-rights price - Subscription price) / Number of rights required to buy a share ofstockValue of a right = ($24.55 - $20) / 10 = $0.45c. The market value of the firm after the issue is the number of shares times the ex-rights price.Value = 110,000 x $24.55 $2,700,000 (Note that the exact ex-rights price is$24.5454.)公司理财习题答案第十九章d. The most important reason to offer rights is to reduce issuance costs. Also, rightsofferings do not dilute ownership and they provide shareholders with moreflexibility. Shareholders can either exercise or sell their rights.19.12 The value of a right = $50 - $45 = $5The number of new shares = $5,000,000 / $25 = 200,000The number of rights / share = ($45 - $25) / $5 = 4The number of old shares = 200,000 x 4 = 800,00019.13 a. Assume you hold three shares of the company’s stock. The value of your holdingsbefore you exercise your rights is 3 x $45 = $135. When you exercise, you mustremit the three rights you receive for owning three shares, and ten dollars. You haveincreased your equity investment by $10. The value of your holdings is $135 + $10= $145. After exercise, you own four shares of stock. Thus, the price per share ofyour stock is $145 / 4 = $36.25.b. The value of a right is the difference between the rights-on price of the stock andthe ex-rights price of the stock. The value of a right is $8.75 (=$45 - $36.25).c. The price drop will occur on the ex-rights date. Although the ex-rights date isneither the expiration date nor the date on which the rights are first exercisable, it isthe day that the price will drop. If you purchase the stock before the ex-rights date,you will receive the rights. If you purchase the stock on or after the ex-rights date,you will not receive the rights. Since rights have value, the stockholder receivingthe rights must pay for them. The stock price drop on the ex-rights day is similar tothe stock price drop on an ex-dividend day.19.14 a. Stock price (ex-right) = (13+2) / (1+0.5) = $10Subscription price = 2 / 0.5 = $4Right’s price = 13-10 = $3= (10-4) / 2 = $3b. Stock price (ex-right) = (13+2) / (1+0.25) = $12Subscription price = 2 / 0.25 = $8Right’s price = 13-12 = $1= (12-8) / 4 = $1c. The stockholders’ wealth is the same between the two arrangements.19.15 If the interest of management is to increase the wealth of the current shareholders, a rightsoffering may be preferable because issuing costs as a percentage of capital raised is lower for rights offerings. Management does not have to worry about underpricing becauseshareholders get the rights, which are worth something. Rights offerings also preventexisting shareholders from losing proportionate ownership control. Finally, whether the shareholders exercise or sell their rights, they are the only beneficiaries.19.16 Reasons for shelf registration include:i. Flexibility in raising money only when necessary without incurring additional issuancecosts.ii. As Bhagat, Marr and Thompson showed, shelf registration is less costly than conventional underwritten issues.iii. Issuance of securities is greatly simplified.19.17 Suppliers of venture capital can include:i. Wealthy families / individuals.ii. Investment funds provided by a number of private partnerships and corporations.iii. Venture capital subsidiaries established by large industrial or financial corporations.iv. “Angels” in an informal venture capital market.19.18 The proceeds from IPO are used to:i. exchange inside equity ownership for outside equity ownershipii. finance the present and future operations of the IPO firms.19.19 Basic empirical regularities in IPOs include:i. underpricing of the offer price,ii. best-efforts offerings are generally used for small IPOs and firm-commitment offerings are generally used for large IPOs,iii. the underwriter price stabilization of the after market and,iv. that issuing costs are higher in negotiated deals than in competitive ones.。

CHAPTER 7NET PRESENT VALUE AND OTHER INVESTMENT CRITERIAAnswers to Concepts Review and Critical Thinking Questions1. A payback period less than the project’s life means that the NPV is positive for a zero discount rate,but nothing more definitive can be said. For discount rates greater than zero, the payback period will still be less than the project’s life, but the NPV may be positive, zero, or negative, depending on whether the discount rate is less than, equal to, or greater than the IRR. The discounted payback includes the effect of the relevant discount rate. If a project’s discounted payback period is less than the project’s life, it must be the case that NPV is positive.2.If a project has a positive NPV for a certain discount rate, then it will also have a positive NPV for azero discount rate; thus, the payback period must be less than the project life. Since discounted payback is calculated at the same discount rate as is NPV, if NPV is positive, the discounted payback period must be less than the project’s life. If NPV is positive, then the present value of future cash inflows is greater than the initial investment cost; thus PI must be greater than 1. If NPV is positive for a certain discount rate R, then it will be zero for some larger discount rate R*; thus, the IRR must be greater than the required return.3. a.Payback period is simply the accounting break-even point of a series of cash flows. To actuallycompute the payback period, it is assumed that any cash flow occurring during a given period isrealized continuously throughout the period, and not at a single point in time. The payback isthen the point in time for the series of cash flows when the initial cash outlays are fullyrecovered. Given some predetermined cutoff for the payback period, the decision rule is toaccept projects that payback before this cutoff, and reject projects that take longer to payback.The worst problem associated with payback period is that it ignores the time value of money. Inaddition, the selection of a hurdle point for payback period is an arbitrary exercise that lacksany steadfast rule or method. The payback period is biased towards short-term projects; it fullyignores any cash flows that occur after the cutoff point.b.The average accounting return is interpreted as an average measure of the accountingperformance of a project over time, computed as some average profit measure attributable tothe project divided by some average balance sheet value for the project. This text computesAAR as average net income with respect to average (total) book value. Given somepredetermined cutoff for AAR, the decision rule is to accept projects with an AAR in excess ofthe target measure, and reject all other projects. AAR is not a measure of cash flows and marketvalue, but a measure of financial statement accounts that often bear little resemblance to therelevant value of a project. In addition, the selection of a cutoff is arbitrary, and the time valueof money is ignored. For a financial manager, both the reliance on accounting numbers ratherthan relevant market data and the exclusion of time value of money considerations are troubling.Despite these problems, AAR continues to be used in practice because (1) the accountinginformation is usually available, (2) analysts often use accounting ratios to analyze firmperformance, and (3) managerial compensation is often tied to the attainment of targetaccounting ratio goals.c.The IRR is the discount rate that causes the NPV of a series of cash flows to be identically zero.IRR can thus be interpreted as a financial break-even rate of return; at the IRR discount rate,the net value of the project is zero. The acceptance and rejection criteria are:If C0 < 0 and all future cash flows are positive, accept the project if the internal rate ofreturn is greater than or equal to the discount rate.If C0 < 0 and all future cash flows are positive, reject the project if the internal rate ofreturn is less than the discount rate.If C0 > 0 and all future cash flows are negative, accept the project if the internal rate ofreturn is less than or equal to the discount rate.If C0 > 0 and all future cash flows are negative, reject the project if the internal rate ofreturn is greater than the discount rate.IRR is the interest rate that causes NPV for a series of cash flows to be zero. NPV is preferred in all situations to IRR; IRR can lead to ambiguous results if there are non-conventional cash flows, and it also ambiguously ranks some mutually exclusive projects. However, for stand-alone projects with conventional cash flows, IRR and NPV are interchangeable techniques. The IRR decision rule for projectsd.The profitability index is the present value of cash inflows relative to the project cost. As such,it is a benefit/cost ratio, providing a measure of the relative profitability of a project. The profitability index decision rule is to accept projects with a PI greater than one, and to reject projects with a PI less than one. The profitability index can be expressed as: PI = (NPV + cost)/cost = 1 + (NPV/cost). If a firm has a basket of positive NPV projects and is subject to capital rationing, PI may provide a good ranking measure of the projects, indicating the “bang for the buck” of each particu lar project.e.NPV is simply the present value of a project’s cash flows. NPV specifically measures, afterconsidering the time value of money, the net increase or decrease in firm wealth due to the project. The decision rule is to accept projects that have a positive NPV, and reject projects with a negative NPV. NPV is superior to the other methods of analysis presented in the text because it has no serious flaws. The method unambiguously ranks mutually exclusive projects, and can differentiate between projects of different scale and time horizon. The only drawback to NPV is that it relies on cash flow and discount rate values that are often estimates and not certain, but this is a problem shared by the other performance criteria as well. A project with NPV = $2,500 implies that the total shareholder wealth of the firm will increase by $2,500 if the project is accepted.4.For a project with future cash flows that are an annuity:Payback = I / CAnd the IRR is:0 = – I + C / IRRSolving the IRR equation for IRR, we get:IRR = C / INotice this is just the reciprocal of the payback. So:IRR = 1 / PBFor long-lived projects with relatively constant cash flows, the sooner the project pays back, the greater is the IRR.5.There are a number of reasons. Two of the most important have to do with transportation costs andexchange rates. Manufacturing in the U.S. places the finished product much closer to the point of sale, resulting in significant savings in transportation costs. It also reduces inventories because goods spend less time in transit. Higher labor costs tend to offset these savings to some degree, at least compared to other possible manufacturing locations. Of great importance is the fact that manufacturing in the U.S. means that a much higher proportion of the costs are paid in dollars. Since sales are in dollars, the net effect is to immunize profits to a large extent against fluctuations in exchange rates. This issue is discussed in greater detail in the chapter on international finance.6.The single biggest difficulty, by far, is coming up with reliable cash flow estimates. Determining anappropriate discount rate is also not a simple task. These issues are discussed in greater depth in the next several chapters. The payback approach is probably the simplest, followed by the AAR, but even these require revenue and cost projections. The discounted cash flow measures (discounted payback, NPV, IRR, and profitability index) are really only slightly more difficult in practice.7.Yes, they are. Such entities generally need to allocate available capital efficiently, just as for-profitsdo. However, it is frequently the case that the “revenues” from not-for-profit ventures are not tangible. For example, charitable giving has real opportunity costs, but the benefits are generally hard to measure. To the extent that benefits are measurable, the question of an appropriate required return remains. Payback rules are commonly used in such cases. Finally, realistic cost/benefit analysis along the lines indicated should definitely be used by the U.S. government and would go a long way toward balancing the budget!8.The statement is false. If the cash flows of Project B occur early and the cash flows of Project Aoccur late, then for a low discount rate the NPV of A can exceed the NPV of B. Observe the following example.C0C1C2IRR NPV @ 0% Project A –$1,000,000 $0 $1,440,000 20% $440,000 Project B –$2,000,000 $2,400,000 $0 20% 400,000However, in one particular case, the statement is true for equally risky Projects. If the lives of the two Projects are equal and the cash flows of Project B are twice the cash flows of Project A in every time period, the NPV of Project B will be twice the NPV of Project A.9. Although the profitability index (PI) is higher for Project B than for Project A, Project A should bechosen because it has the greater NPV. Confusion arises because Project B requires a smaller investment than Project A requires. Since the denominator of the PI ratio is lower for Project B than for Project A, B can have a higher PI yet have a lower NPV. Only in the case of capital rationing could the company’s decision have been incorrect.10. a.Project A would have a higher IRR since initial investment for Project A is less than that ofProject B, if the cash flows for the two projects are identical.b.Yes, since both the cash flows as well as the initial investment are twice that of Project B.11.Project B would have a more sensitive NPV to changes in the discount rate. The reason is the timevalue of money. Cash flows that occur further out in the future are always more sensitive to changes in the interest rate. This is similar to the interest rate risk of a bond.12.The MIRR is calculated by finding the present value of all cash outflows, the future value of all cashinflows to the end of the project, and then calculating the IRR of the two cash flows. As a result, the cash flows have been discounted or compounded by one interest rate (the required return), and then the interest rate between the two remaining cash flows is calculated. As such, the MIRR is not a true interest rate. In contrast, consider the IRR. If you take the initial investment, and calculate the future value at the IRR, you can replicate the future cash flows of the project exactly.13.The criticism is incorrect. It is true that if you calculate the future value of all intermediate cashflows to the end of the project at the required return, then calculate the NPV of this future value and the initial investment, you will get the same NPV. However, NPV says nothing about reinvestment of intermediate cash flows. The NPV is the present value of the project cash flows. The fact that the reinvestment works is an artifact of the time value of money.14.The criticism is incorrect for several reasons. It is true that if you calculate the future value of allintermediate cash flows to the end of the project at the IRR, then calculate the IRR of this future value and the initial investment, you will get the same IRR. This only occurs if the intermediate cash flows are reinvested at the IRR. However, similar to the previous question, IRR deals with the present value of the cash flows, not the future value. There is also another important point. This criticism deals with the reinvestment of the intermediate cash flows. As we will see in the next chapter, any reinvestment assumption concerning the intermediate cash flows is incorrect. The reason is that when we are calculating the cash flows for a project, we are concerned with the incremental cash flows from the project, that is, the cash flows the project creates. Reinvestment violates this principal. Consider the following example:C0C1C2IRR Project A –$100 $10 $110 10% Suppose this is a deposit into a bank account. The IRR of the cash flows is 10 percent. Does it the IRR change if the Year 1 cash flow is reinvested in the account, or if it is withdrawn and spent on pizza? No. Finally, think back to the yield to maturity calculation on a bond. The YTM is the IRR of the bond investment, but no mention of a reinvestment assumption of the bond coupons is inferred.The reason is that the reinvestment assumption is irrelevant to calculating the YTM on a bond; in the same way, the reinvestment assumption is irrelevant in the IRR calculation.Solutions to Questions and ProblemsNOTE: All end-of-chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to space and readability constraints, when these intermediate steps are included in this solutions manual, rounding may appear to have occurred. However, the final answer for each problem is found without rounding during any step in the problem.Basic1. a.The payback period is the time that it takes for the cumulative undiscounted cash inflows toequal the initial investment.Project A:Cumulative cash flows Year 1 = €4,000 = €4,000Cumulative cash flows Year 2 = €4,000 +3,500 = €7,500 Payback period = 2 yearsProject B:Cumulative cash flows Year 1 = €2,500 = €2,500Cumulative cash flows Year 2 = €2,500 + 1,200 = €3,700Cumulative cash flows Year 3 = €2,500 + 1,200 + 3,000 = €6,700 Companies can calculate a more precise value using fractional years. To calculate the fractionalpayba ck period, find the fraction of year 3’s cash flows that is needed for the company to have cumulative undiscounted cash flows of €5,000. Divide the difference between the initial investment and the cumulative undiscounted cash flows as of year 2 by the undiscounted cashflow of year 3.Payback period = 2 + (€5,000 –€3,700) / €3,000Payback period = 2.43Since project A has a shorter payback period than project B has, the company should chooseproject A.b.Discount each project’s cash flows at 15 percent. Choose the project with the highest NPV.Project A:NPV = –€7,500 + €4,000 / 1.15 + €3,500 / 1.152 + €1,500 / 1.153NPV = –€388.96Project B:NPV = –€5,000 + €2,500 / 1.15 + €1,200 / 1.152 + €3,000 / 1.153NPV = €53.83The firm should choose Project B since it has a higher NPV than Project A has.2.To calculate the payback period, we need to find the time that the project has recovered its initialinvestment. The cash flows in this problem are an annuity, so the calculation is simpler. If the initial cost is £3,000, the payback period is:Payback = 3 + (£300 / £900) = 3.33 yearsThere is a shortcut to calculate the payback period if the future cash flows are an annuity. Just divide the initial cost by the annual cash flow. For the £3,000 cost, the payback period is:Payback = £3,000 / £900 = 3.33 yearsFor an initial cost of £5,000, the payback period is:Payback = 5 + (£500 / £900) = 5.55 yearsThe payback period for an initial cost of £10,000 is a little trickier. Notice that the total cash inflows after nine years will be:Total cash inflows = 8(£900) = £7,200If the initial cost is £10,000, the project never pays back. Notice that if you use the shortcut forannuity cash flows, you get:Payback = £10,000 / £900 = 11.11 years.This answer does not make sense since the cash flows stop after nine years, so the payback period is never.3.When we use discounted payback, we need to find the value of all cash flows today. The value todayof the project cash flows for the first four years is:Value today of Year 1 cash flow = $7,000/1.14 = $6,140.35Value today of Year 2 cash flow = $7,500/1.142 = $5,771.01Value today of Year 3 cash flow = $8,000/1.143 = $5,399.77Value today of Year 4 cash flow = $8,500/1.144 = $5,032.68To find the discounted payback, we use these values to find the payback period. The discounted first year cash flow is $6,140.35, so the discounted payback for an $8,000 initial cost is:Discounted payback = 1 + ($8,000 – 6,140.35)/$5,771.01 = 1.32 yearsFor an initial cost of $13,000, the discounted payback is:Discounted payback = 2 + ($13,000 – 6,140.35 – 5,771.01)/$5,399.77 = 2.20 yearsNotice the calculation of discounted payback. We know the payback period is between two and three years, so we subtract the discounted values of the Year 1 and Year 2 cash flows from the initial cost.This is the numerator, which is the discounted amount we still need to make to recover our initial investment. We divide this amount by the discounted amount we will earn in Year 3 to get the fractional portion of the discounted payback.If the initial cost is $18,000, the discounted payback is:Discounted payback = 3 + ($18,000 – 6,140.35 – 5,771.01 – 5,399.77) / $5,032.68 = 3.14 years4.To calculate the discounted payback, discount all future cash flows back to the present, and use thesediscounted cash flows to calculate the payback period. Doing so, we find:R = 0%: 4 + (£1,100 / £2,100) = 4.52 yearsDiscounted payback = Regular payback = 4.52 yearsR = 5%: £2,100/1.05 + £2,100/1.052 + £2,100/1.053 + £2,100/1.054 + £2,100/1.055 = £9,091.90 £2,100/1.056 = £1,567.05Discounted payback = 5 + (£9,500 – 9,091.90) / £1,567.05 = 5.26 years R = 15%: £2,100/1.15 + £2,100/1.152 + £2,100/1.153 + £2,100/1.154 + £2,100/1.155 + £2,100/1.156 = £7,947.41; The project never pays back.5. a.The average accounting return is the average project earnings after taxes, divided by theaverage book value, or average net investment, of the machine during its life. The book value of the machine is the gross investment minus the accumulated depreciation.Average book value = (Book Value0 + Book Value1 + Book Value2 + Book Value3 +Book Value4 + Book Value5) / (Economic Life)Average book value = ($16,000 + 12,000 + 8,000 + 4,000 + 0) / (5 years)Average book value = $8,000Average Project Earnings = $4,500To find the average accounting return, we divide the average project earnings by the average book value of the machine to calculate the average accounting return. Doing so, we find:Average Accounting Return = Average Project Earnings / Average Book ValueAverage Accounting Return = $4,500 / $8,000Average Accounting Return = 0.5625 or 56.25%6.First, we need to determine the average book value of the project. The book value is the grossinvestment minus accumulated depreciation.Purchase Date Year 1 Year 2 Year 3 Gross Investment €8,000 €8,000 €8,000 €8,000Less: Accumulated Depreciation 0 4,000 6,500 8,000Net Investment €8,000 €4,000 €1,500 €0 Now, we can calculate the average book value as:Average book value = (€8,000 + 4,000 + 1,500 + 0) / (4 years)Average book value = €3,375To calculate the average accounting return, we must remember to use the aftertax average netincome when calculating the average accounting return. So, the average aftertax net income is:Average aftertax net income = (1 – t c) Annual pretax net incomeAverage aftertax net income = (1 – 0.25) €2,000Average aftertax net income = €1,500The average accounting return is the average after-tax net income divided by the average book value, which is:Average accounting return = €1,500 / €3,375Average accounting return = 0.4444 or 44.44%7.The IRR is the interest rate that makes the NPV of the project equal to zero. So, the equation that definesthe IRR for this project is:0 = C0 + C1 / (1 + IRR) + C2 / (1 + IRR)2 + C3 / (1 + IRR)30 = –¥8,000,000 + ¥4,000,000/(1 + IRR) + ¥3,000,000/(1 + IRR)2 + ¥2,000,000/(1 + IRR)3Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: IRR = 6.93%Since the IRR is less than the required return we would reject the project.8.The IRR is the interest rate that makes the NPV of the project equal to zero. So, the equation that definesthe IRR for this Project A is:0 = C0 + C1 / (1 + IRR) + C2 / (1 + IRR)2 + C3 / (1 + IRR)30 = – £2,000 + £1,000/(1 + IRR) + £1,500/(1 + IRR)2 + £2,000/(1 + IRR)3Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: IRR = 47.15%And the IRR for Project B is:0 = C0 + C1 / (1 + IRR) + C2 / (1 + IRR)2 + C3 / (1 + IRR)30 = – £1,500 + £500/(1 + IRR) + £1,000/(1 + IRR)2 + £1,500/(1 + IRR)3Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: IRR = 36.19%9.The profitability index is defined as the PV of the cash inflows divided by the PV of the cashoutflows. The cash flows from this project are an annuity, so the equation for the profitability index is:PI = C(PVIFA R,t) / C0PI = €41,000(PVIFA15%,7) / €160,000PI = 1.066110. a.The profitability index is the present value of the future cash flows divided by the initial cost.So, for Project Alpha, the profitability index is:PI Alpha = [$300 / 1.10 + $700 / 1.102 + $600 / 1.103] / $500 = 2.604And for Project Beta the profitability index is:PI Beta = [$300 / 1.10 + $1,800 / 1.102 + $1,700 / 1.103] / $2,000 = 1.519b.According to the profitability index, you would accept Project Alpha. However, remember theprofitability index rule can lead to incorrect decision when ranking mutually exclusive projects.Intermediate11. a.To have a payback equal to the project’s life, given C is a constant cash flow for N years:C = I/Nb.To have a positive NPV, I < C (PVIFA R%, N). Thus, C > I / (PVIFA R%, N).c.Benefits = C (PVIFA R%, N) = 2 × costs = 2IC = 2I / (PVIFA R%, N)12. a.The IRR is the interest rate that makes the NPV of the project equal to zero. So, the equationthat defines the IRR for this project is:0 = C0 + C1 / (1 + IRR) + C2 / (1 + IRR)2 + C3 / (1 + IRR)3 + C4 / (1 + IRR)40 = ₩5,000 –₩2,500 / (1 + IRR) –₩2,000 / (1 + IRR)2–₩1,000 / (1 + IRR)3–₩1,000 / (1 +IRR)4Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:IRR = 13.99%b.This problem differs from previous ones because the initial cash flow is positive and all futurecash flows are negative. In other words, this is a financing-type project, while previous projects were investing-type projects. For financing situations, accept the project when the IRR is less than the discount rate. Reject the project when the IRR is greater than the discount rate.IRR = 13.99%Discount Rate = 12%IRR > Discount RateReject the offer when the discount rate is less than the IRR.ing the same reason as part b., we would accept the project if the discount rate is 20 percent.IRR = 13.99%Discount Rate = 19%IRR < Discount RateAccept the offer when the discount rate is greater than the IRR.d.The NPV is the sum of the present value of all cash flows, so the NPV of the project if thediscount rate is 10 percent will be:NPV = ₩5,000 –₩2,500 / 1.12 –₩2,000 / 1.122–₩1,000 / 1.123–₩1,000 / 1.124NPV = –₩173.83When the discount rate is 12 percent, the NPV of the offer is –₩359.95. Reject the offer.And the NPV of the project is the discount rate is 19 percent will be:NPV = ₩5,000 –₩2,500 / 1.19 –₩2,000 / 1.192–₩1,000 / 1.193–₩1,000 / 1.194NPV = ₩394.75When the discount rate is 19 percent, the NPV of the offer is ₩466.82. Accept the offer.e.Yes, the decisions under the NPV rule are consistent with the choices made under the IRR rulesince the signs of the cash flows change only once.13. a.The IRR is the interest rate that makes the NPV of the project equal to zero. So, the IRR foreach project is:Deepwater Fishing IRR:0 = C0 + C1 / (1 + IRR) + C2 / (1 + IRR)2 + C3 / (1 + IRR)30 = –$600,000 + $270,000 / (1 + IRR) + $350,000 / (1 + IRR)2 + $300,000 / (1 + IRR)3Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:IRR = 24.30%Submarine Ride IRR:0 = C0 + C1 / (1 + IRR) + C2 / (1 + IRR)2 + C3 / (1 + IRR)30 = –$1,800,000 + $1,000,000 / (1 + IRR) + $700,000 / (1 + IRR)2 + $900,000 / (1 + IRR)3Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:IRR = 21.46%Based on the IRR rule, the deepwater fishing project should be chosen because it has the higher IRR.b.To calculate the incremental IRR, we s ubtract the smaller project’s cash flows from the largerproject’s cash flows. In this case, we subtract the deepwater fishing cash flows from the submarine ride cash flows. The incremental IRR is the IRR of these incremental cash flows. So, the incremental cash flows of the submarine ride are:Year 0Year 1Year 2 Year 3 Submarine Ride –$1,800,000 $1,000,000 $700,000 $900,000Deepwater Fishing –600,000 270,000 350,000 300,000Submarine – Fishing –$1,200,000 $730,000 $350,000 $600,000 Setting the present value of these incremental cash flows equal to zero, we find the incremental IRR is:0 = C0 + C1 / (1 + IRR) + C2 / (1 + IRR)2 + C3 / (1 + IRR)30 = –$1,200,000 + $730,000 / (1 + IRR) + $350,000 / (1 + IRR)2 + $600,000 / (1 + IRR)3Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:Incremental IRR = 19.92%For investing-type projects, accept the larger project when the incremental IRR is greater than the discount rate. Since the incremental IRR, 19.92%, is greater than the required rate of return of 15 percent, choose the submarine ride project. Note that this is the choice when evaluating only the IRR of each project. The IRR decision rule is flawed because there is a scale problem.That is, the submarine ride has a greater initial investment than does the deepwater fishing project. This problem is corrected by calculating the IRR of the incremental cash flows, or by evaluating the NPV of each project.c.The NPV is the sum of the present value of the cash flows from the project, so the NPV of eachproject will be:Deepwater fishing:NPV = –$600,000 + $270,000 / 1.15 + $350,000 / 1.152 + $300,000 / 1.153NPV = $96,687.76Submarine ride:NPV = –$1,800,000 + $1,000,000 / 1.15 + $700,000 / 1.152 + $900,000 / 1.153NPV = $190,630.39Since the NPV of the submarine ride project is greater than the NPV of the deepwater fishingproject, choose the submarine ride project. The incremental IRR rule is always consistent withthe NPV rule.14. a.The profitability index is the PV of the future cash flows divided by the initial investment. Thecash flows for both projects are an annuity, so:PI I = 元15,000(PVIFA10%,3 ) / 元30,000 = 1.243PI II = 元2,800(PVIFA10%,3) / 元5,000 = 1.393The profitability index decision rule implies that we accept project II, since PI II is greater thanthe PI I.b.The NPV of each project is:NPV I = –元30,000 + 元15,000(PVIFA10%,3) = 元7,302.78NPV II = –元5,000 + 元2,800(PVIFA10%,3) = 元1,963.19The NPV decision rule implies accepting Project I, since the NPV I is greater than the NPV II.ing the profitability index to compare mutually exclusive projects can be ambiguous whenthe magnitudes of the cash flows for the two projects are of different scale. In this problem,project I is roughly 3 times as large as project II and produces a larger NPV, yet the profit-ability index criterion implies that project II is more acceptable.15. a.The equation for the NPV of the project is:NPV = –₦28,000,000 + ₦53,000,000/1.11 –₦8,000,000/1.112 = ₦13,254,768.28The NPV is greater than 0, so we would accept the project.b.The equation for the IRR of the project is:0 = –₦28,000,000 + ₦53,000,000/(1+IRR) –₦8,000,000/(1+IRR)2From Descartes rule of signs, we know there are two IRRs since the cash flows change signstwice. From trial and error, the two IRRs are:IRR = 72.75%, –83.46%。

CHAPTER 6STOCK VALUATIONAnswers to Concepts Review and Critical Thinking Questions1.The value of any investment depends on its cash flows; i.e., what investors will actually receive. Thecash flows from a share of stock are the dividends.2.Investors believe the company will eventually start paying dividends (or be sold to anothercompany).3.In general, companies that need the cash will often forgo dividends since dividends are a cashexpense. Young, growing companies with profitable investment opportunities are one example;another example is a company in financial distress. This question is examined in depth in a later chapter.4.The general method for valuing a share of stock is to find the present value of all expected futuredividends. The dividend growth model presented in the text is only valid (i) if dividends are expected to occur forever; that is, the stock provides dividends in perpetuity, and (ii) if a constant growth rate of dividends occurs forever. A violation of the first assumption might be a company that is expected to cease operations and dissolve itself some finite number of years from now. The stock of such a company would be valued by applying the general method of valuation explained in this chapter. A violation of the second assumption might be a start-up firm that isn’t currently paying any dividends, but is expected to eventually start making dividend payments some number of years from now. This stock would also be valued by the general dividend valuation method explained in this chapter.5.The common stock probably has a higher price because the dividend can grow, whereas it is fixed onthe preferred. However, the preferred is less risky because of the dividend and liquidation preference, so it is possible the preferred could be worth more, depending on the circumstances.6.The two components are the dividend yield and the capital gains yield. For most companies, thecapital gains yield is larger. This is easy to see for companies that pay no dividends. For companies that do pay dividends, the dividend yields are rarely over five percent and are often much less.7.Yes. If the dividend grows at a steady rate, so does the stock price. In other words, the dividendgrowth rate and the capital gains yield are the same.8.The three factors are: 1) The company’s future growth opportunities. 2) The company’s level of risk,which determines the interest rate used to discount cash flows. 3) The accounting method used.9.In a corporate election, you can buy votes (by buying shares), so money can be used to influence oreven determine the outcome. Many would argue the same is true in political elections, but, in principle at least, no one has more than one vote.10. It wouldn’t seem to be. Investors who don’t like the voting features of a particular class of stock areunder no obligation to buy it.11.Investors buy such stock because they want it, recognizing that the shares have no voting power.Presumably, investors pay a little less for such shares than they would otherwise.12.Presumably, the current stock value reflects the risk, timing and magnitude of all future cash flows,both short-term and long-term. If this is correct, then the statement is false.Solutions to Questions and ProblemsNOTE: All end-of-chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to space and readability constraints, when these intermediate steps are included in this solutions manual, rounding may appear to have occurred. However, the final answer for each problem is found without rounding during any step in the problem.Basic1.The constant dividend growth model is:P t = D t × (1 + g) / (R–g)So, the price of the stock today is:P0 = D0(1 + g) / (R–g) = €1.40 (1.06) / (.12 – .06) = €24.73The dividend at year 4 is the dividend today times the FVIF for the growth rate in dividends and four years, so:P3 = D3(1 + g) / (R–g) = D0(1 + g)4/ (R– g) = €1.40 (1.06)4/ (.12 – .06) = €29.46We can do the same thing to find the dividend in Year 16, which gives us the price in Year 15, so: P15 = D15(1 + g) / (R–g) = D0(1 + g)16/ (R–g) = €1.40 (1.06)16/ (.12 – .06) = €59.27There is another feature of the constant dividend growth model: The stock price grows at the dividend growth rate. So, if we know the stock price today, we can find the future value for any time in the future we want to calculate the stock price. In this problem, we want to know the stock price in three years, and we have already calculated the stock price today. The stock price in three years will be:P3 = P0(1 + g)3 = €24.73(1 + .06)3 = €29.46And the stock price in 20 years will be:P15 = P0(1 + g)20 = €24.73(1 + .06)20 = €79.312.We need to find the required return of the stock. Using the constant growth model, we can solve theequation for R. Doing so, we find:R = (D1 / P0) + g = ($3.10 / $50.00) + .05 = 11.20%3.The dividend yield is the dividend next year divided by the current price, so the dividend yield is:Dividend yield = D1 / P0 = $3.10 / $50.00 = 6.20%The capital gains yield, or percentage increase in the stock price, is the same as the dividend growth rate, so:Capital gains yield = 5%ing the constant growth model, we find the price of the stock today is:P0 = D1 / (R– g) = £3.60 / (.13 – .062) = £52.945.The required return of a stock is made up of two parts: The dividend yield and the capital gains yield.So, the required return of this stock is:R = Dividend yield + Capital gains yield = .039 + .09 = 9.90%6.We know the stock has a required return of 14 percent, and the dividend and capital gains yield areequal, so:Dividend yield = 1/2(.14) = .07 = Capital gains yieldNow we know both the dividend yield and capital gains yield. The dividend is simply the stock price times the dividend yield, so:D1 = .07(元70) = 元4.90This is the dividend next year. The question asks for the dividend this year. Using the relationship between the dividend this year and the dividend next year:D1 = D0(1 + g)We can solve for the dividend that was just paid:元4.90 = D0 (1 + .07)D0 = 元4.90 / 1.07 = 元4.587.The price of any financial instrument is the PV of the future cash flows. The future dividends of thisstock are an annuity for eight years, so the price of the stock is the PVA, which will be:P0 = R12.00(PVIFA10%,8) = R64.028.The price a share of preferred stock is the dividend divided by the required return. This is the sameequation as the constant growth model, with a dividend growth rate of zero percent. Remember that most preferred stock pays a fixed dividend, so the growth rate is zero. Using this equation, we find the price per share of the preferred stock is:R = D/P0 = ¥820/¥11,350 = 7.22%9.The growth rate of earnings is the return on equity times the retention ratio, so:g = ROE ×bg = .14(.60)g = .084 or 8.40%To find next year’s earnings, we simply multiply the current earnings times one plus the growth rate, so:Next year’s earnings = Current earnings(1 + g)Next year’s earnings = Rs.20,000,000(1 + .084)Next year’s earnings = Rs.21,680,000Intermediate10.This stock has a constant growth rate of dividends, but the required return changes twice. To find thevalue of the stock today, we will begin by finding the price of the stock at Year 6, when both the dividend growth rate and the required return are stable forever. The price of the stock in Year 6 will be the dividend in Year 7, divided by the required return minus the growth rate in dividends. So:P6 = D6(1 + g) / (R–g) = D0(1 + g)7/ (R–g) = $3.00 (1.05)7/ (.11 – .05) = $70.36Now we can find the price of the stock in Year 3. We need to find the price here since the required return changes at that time. The price of the stock in Year 3 is the PV of the dividends in Years 4, 5, and 6, plus the PV of the stock price in Year 6. The price of the stock in Year 3 is:P3= $3.00(1.050)4/ 1.14 + $3.00(1.050)5/ 1.142 + $3.00(1.05)6/ 1.143 + $70.36 / 1.143P3= $56.35Finally, we can find the price of the stock today. The price today will be the PV of the dividends in Years 1, 2, and 3, plus the PV of the stock in Year 3. The price of the stock today is:P0 = $3.00(1.050) / 1.16 + $3.00(1.050)2 / (1.16)2 + $3.00(1.050)3 / (1.16)3 + $56.35 / (1.16)3 = $43.5011.Here we have a stock that pays no dividends for 10 years. Once the stock begins paying dividends, itwill have a constant growth rate of dividends. We can use the constant growth model at that point. It is important to remember that general constant dividend growth formula is:P t = [D t × (1 + g)] / (R–g)This means that since we will use the dividend in Year 10, we will be finding the stock price in Year9. The dividend growth model is similar to the PVA and the PV of a perpetuity: The equation givesyou the PV one period before the first payment. So, the price of the stock in Year 9 will be:P9 = D10/ (R–g) = €8.00 / (.13 – .06) = €114.29The price of the stock today is simply the PV of the stock price in the future. We simply discount the future stock price at the required return. The price of the stock today will be:P0 = €114.29 / 1.139 = €38.0412.The price of a stock is the PV of the future dividends. This stock is paying four dividends, so theprice of the stock is the PV of these dividends using the required return. The price of the stock is: P0 = $12 / 1.11 + $15 / 1.112 + $18 / 1.113 + $21 / 1.114 = $49.9813.With supernormal dividends, we find the price of the stock when the dividends level off at a constantgrowth rate, and then find the PV of the future stock price, plus the PV of all dividends during the supernormal growth period. The stock begins constant growth in Year 4, so we can find the price of the stock in Year 3, one year before the constant dividend growth begins, as:P4 = D4(1 + g) / (R–g) = £2.00(1.05) / (.13 – .05) = £26.25The price of the stock today is the PV of the first three dividends, plus the PV of the Year 3 stock price. So, the price of the stock today will be:P0 = £8.00 / 1.13 + £6.00 / 1.132 + £3.00 / 1.133 + £2.00 / 1.134 + £26.25 / 1.134 = £31.1814.With supernormal dividends, we find the price of the stock when the dividends level off at a constantgrowth rate, and then find the PV of the future stock price, plus the PV of all dividends during the supernormal growth period. The stock begins constant growth in Year 4, so we can find the price of the stock in Year 3, one year before the constant dividend growth begins as:P3 = D3(1 + g) / (R–g) = D0(1 + g1)3(1 + g2) / (R–g) = €2.80(1.25)3(1.07) / (.13 – .07) = €97.53 The price of the stock today is the PV of the first three dividends, plus the PV of the Year 3 stock price. The price of the stock today will be:P0 = 2.80(1.25) / 1.13 + €2.80(1.25)2/ 1.132 + €2.80(1.25)3/ 1.133 + €97.53 / 1.133P0= €77.9015.Here we need to find the dividend next year for a stock experiencing supernormal growth. We knowthe stock price, the dividend growth rates, and the required return, but not the dividend. First, we need to realize that the dividend in Year 3 is the current dividend times the FVIF. The dividend in Year 3 will be:D3 = D0(1.30)3And the dividend in Year 4 will be the dividend in Year 3 times one plus the growth rate, or:D4 = D0(1.30)3(1.18)The stock begins constant growth in Year 4, so we can find the price of the stock in Year 4 as the dividend in Year 5, divided by the required return minus the growth rate. The equation for the price of the stock in Year 4 is:P4 = D4(1 + g) / (R– g)Now we can substitute the previous dividend in Year 4 into this equation as follows:P4 = D0(1 + g1)3(1 + g2) (1 + g3) / (R–g)P4= D0(1.30)3(1.18) (1.08) / (.14 – .08) = 46.66D0When we solve this equation, we find that the stock price in Year 4 is 46.66 times as large as the dividend today. Now we need to find the equation for the stock price today. The stock price today is the PV of the dividends in Years 1, 2, 3, and 4, plus the PV of the Year 4 price. So:P0 = D0(1.30)/1.14 + D0(1.30)2/1.142 + D0(1.30)3/1.143+ D0(1.30)3(1.18)/1.144 + 46.66D0/1.144We can factor out D0 in the equation, and combine the last two terms. Doing so, we get:P0 = $70.00 = D0{1.30/1.14 + 1.302/1.142 + 1.303/1.143 + [(1.30)3(1.18) + 46.66] / 1.144}Reducing the equation even further by solving all of the terms in the braces, we get:$70 = $33.04D0D0 = $70.00 / $33.04 = $2.12This is the dividend today, so the projected dividend for the next year will be:D1 = $2.12(1.30) = $2.7516.The constant growth model can be applied even if the dividends are declining by a constantpercentage, just make sure to recognize the negative growth. So, the price of the stock today will be: P0 = D0(1 + g) / (R– g) = ZW$215(1 – .08) / [(.11 – (–.08)] = ZW$1,041.0517.We are given the stock price, the dividend growth rate, and the required return, and are asked to findthe dividend. Using the constant dividend growth model, we get:P0 = €50 = D0(1 + g) / (R–g)Solving this equation for the dividend gives us:D0 = €50(.14 – .08) / (1.08) = €2.7818.The price of a share of preferred stock is the dividend payment divided by the required return. Weknow the dividend payment in Year 6, so we can find the price of the stock in Year 5, one year before the first dividend payment. Doing so, we get:P5 = ¥295 / .07 = ¥4,214.28The price of the stock today is the PV of the stock price in the future, so the price today will be: P0 = ¥4,214.28 / (1.07)5 = ¥3,004.7219.The annual dividend paid to stockholders is $0.15, and the dividend yield is 0.2 percent. Using theequation for the dividend yield:Dividend yield = Dividend / Stock priceWe can plug the numbers in and solve for the stock price:.002 = $0.15 / P0P0 = $0.15/.002 = $75.00The “Net Chg” of the stock shows the stock increased by $2.20 on this day, so the closing stock price yesterday was:Y esterday’s closing price = $75.00 – 2.20 = $72.80To find the net income, we need to find the EPS. The stock quote tells us the P/E ratio for the stock is 14. Since we know the stock price as well, we can use the P/E ratio to solve for EPS as follows: P/E = 14 = Stock price / EPS = $75.00 / EPSEPS = $75.00 / 14 = $5.357We know that EPS is just the total net income divided by the number of shares outstanding, so:EPS = NI / Shares = $5.357 = NI / 25,000,000NI = $5.357(25,000,000) = $133,928,57120.To find the number of shares owned, we can divide the amount invested by the stock price. Theshare price of any financial asset is the present value of the cash flows, so, to find the price of the stock we need to find the cash flows. The cash flows are the two dividend payments plus the sale price. We also need to find the aftertax dividends since the assumption is all dividends are taxed at the same rate for all investors. The aftertax dividends are the dividends times one minus the tax rate, so:Year 1 aftertax dividend = $2.00(1 – .28)Year 1 aftertax dividend = $1.44Year 2 aftertax dividend = $4.00(1 – .28)Year 2 aftertax dividend = $2.88We can now discount all cash flows from the stock at the required return. Doing so, we find the price of the stock is:P = $1.44/1.15 + $2.88/(1.15)2 + $50/(1+.15)3P = $36.31The number of shares owned is the total investment divided by the stock price, which is:Shares owned = $100,000 / $36.31Shares owned = 2,75421.If the company’s earnings are declining at a constant rate, the dividends will decline at the same ratesince the dividends are assumed to be a constant percentage of income. The dividend next year will less tha n this year’s dividend, soP0 = D0(1 + g) / (R– g) = ₦5.00(1 – .08) / [(.14 – (–.08)] = ₦20.9122.Here we have a stock paying a constant dividend for a fixed period, and an increasing dividend after.We need to find the present value of the two different cash flows using the appropriate quarterly interest rate. The constant dividend is an annuity, so the present value of these dividends is:PVA = C(PVIFA R,t)PVA = ₪1(PVIFA2.5%,12)PVA = ₪10.26Now we can find the present value of the dividends beyond the constant dividend phase. Using the present value of a growing annuity equation, we find:P12 = D13/ (R–g)P12 = ₪1(1 + .005) / (.025 – .005)P12 = ₪50.25This is the price of the stock immediately after it has paid the last constant dividend. So, the present value of the future price is:PV = ₪50.25 / (1 + .025)12PV = ₪37.36The price today is the sum of the present value of the two cash flows, so:P0 = ₪10.26 + 37.36P0 = ₪47.6223. We can find the price of the stock in Year 4 when it begins a constant increase in dividends using thegrowing perpetuity equation. So, the price of the stock in Year 4, immediately after the dividend payment, is:P4 = D4(1 + g) / (R–g)P4 = 元2(1 + .07) / (.16 – .07)P4 = 元23.78The stock price today is the sum of the present value of the two fixed dividends plus the present value of the future price, so:P0 = 元2 / (1 + .16)3 + 元2 / (1 + .16)4 + 元23.78 / (1 + .16)4P0 = 元15.5124.Here we need to find the dividend next year for a stock with nonconstant growth. We know the stockprice, the dividend growth rates, and the required return, but not the dividend. First, we need to realize that the dividend in Year 3 is the constant dividend times the FVIF. The dividend in Year 3 will be:D3 = D(1.04)The equation for the stock price will be the present value of the constant dividends, plus the present value of the future stock price, or:P0 = D / 1.12 + D/1.122 + D(1.04)/(.12 – .04)]/1.122£30 = D / 1.12 + D/1.122 + D(1.04)/(.12 – .04)]/1.122We can factor out D0 in the equation, and combine the last two terms. Doing so, we get:£30 = D{1/1.12 + 1/1.122 + [(1.04)/(.12 – .04)] / 1.122}Reducing the equation even further by solving all of the terms in the braces, we get:£30 = D(12.0536)D = £30 / 12.0536 = £2.49This is the dividend today, so the projected dividend for the next year will be:D1 = £2.49(1.30) = £2.4925.The required return of a stock consists of two components, the capital gains yield and the dividendyield. In the constant dividend growth model (growing perpetuity equation), the capital gains yield is the same as the dividend growth rate, or algebraically:R = D1/P0 + gWe can find the dividend growth rate by the growth rate equation, or:g = ROE ×bg = .11 × .75g = .0825 or 8.25%This is also the growth rate in dividends. To find the current dividend, we can use the information provided about the net income, shares outstanding, and payout ratio. The total dividends paid is the net income times the payout ratio. To find the dividend per share, we can divide the total dividends paid by the number of shares outstanding. So:Dividend per share = (Net income × Payout ratio) / Shares outstandingDividend per share = ($10,000,000 × .25) / 1,250,000Dividend per share = $2.00Now we can use the initial equation for the required return. We must remember that the equation uses the dividend in one year, so:R = D1/P0 + gR = $2(1 + .0825)/$40 + .0825R = .1366 or 13.66%26.First, we need to find the annual dividend growth rate over the past four years. To do this, we canuse the future value of a lump sum equation, and solve for the interest rate. Doing so, we find the dividend growth rate over the past four years was:FV = PV(1 + R)t$1.66 = $0.90(1 + R)4R = .1654 or 16.54%We know the dividend will grow at this rate for five years before slowing to a constant rate indefinitely. So, the dividend amount in seven years will be:D7 = D0(1 + g1)5(1 + g2)2D7 = $1.66(1 + .1654)5(1 + .08)2D7 = $4.1627. a.We can find the price of the all the outstanding company stock by using the dividends the sameway we would value an individual share. Since earnings are equal to dividends, and there is no growth, the value of the company’s st ock today is the present value of a perpetuity, so:P = D / RP = £800,000 / .15P = £5,333,333.33The price-earnings ratio is the stock price divided by the current earnings, so the price-earnings ratio of each company with no growth is:P/E = Price / EarningsP/E = £5,333,333.33 / £800,000P/E = 6.67 timesb.Since the earnings have increased, the price of the stock will increase. The new price of the allthe outstanding company stock is:P = D / RP = (£800,000 + 100,000) / .15P = £6,000,000.00The price-earnings ratio is the stock price divided by the current earnings, so the price-earnings with the increased earnings is:P/E = Price / EarningsP/E = £6,000,000 / £800,000P/E = 7.50 timesc.Since the earnings have increased, the price of the stock will increase. The new price of the allthe outstanding company stock is:P = D / RP = (£800,000 + 200,000) / .15P = £6,666,666.67The price-earnings ratio is the stock price divided by the current earnings, so the price-earnings with the increased earnings is:P/E = Price / EarningsP/E = £6,666,666.67 / £800,000P/E = 8.33 times28. a.If the company does not make any new investments, the stock price will be the present value ofthe constant perpetual dividends. In this case, all earnings are paid dividends, so, applying the perpetuity equation, we get:P = Dividend / RP = €7 / .12P = €58.33b.The investment is a one-time investment that creates an increase in EPS for two years. Tocalculate the new stock price, we need the cash cow price plus the NPVGO. In this case, the NPVGO is simply the present value of the investment plus the present value of the increases in EPS. SO, the NPVGO will be:NPVGO = C1 / (1 + R) + C2 / (1 + R)2 + C3 / (1 + R)3NPVGO = –€1.75 / 1.12 + €1.90 / 1.122 + €2.10 / 1.123NPVGO = €1.45So, the price of the stock if the company undertakes the investment opportunity will be:P = €58.33 + 1.45P = €59.78c.After the project is over, and the earnings increase no longer exists, the price of the stock willrevert back to €58.33, the value of the company as a cash cow.29. a.The price of the stock is the present value of the dividends. Since earnings are equal todividends, we can find the present value of the earnings to calculate the stock price. Also, since we are excluding taxes, the earnings will be the revenues minus the costs. We simply need to find the present value of all future earnings to find the price of the stock. The present value of the revenues is:PV Revenue = C1 / (R–g)PV Revenue = $3,000,000(1 + .05) / (.15 – .05)PV Revenue = $31,500,000And the present value of the costs will be:PV Costs = C1 / (R–g)PV Costs = $1,500,000(1 + .05) / (.15 – .05)PV Costs = $15,750,000So, the prese nt value of the company’s earnings and dividends will be:PV Dividends = $31,500,000 – 15,750,000PV Dividends = $15,750,000Note that since revenues and costs increase at the same rate, we could have found the present value of future dividends as the present value of current dividends. Doing so, we find:D0 = Revenue0– Costs0D0 = $3,000,000 – 1,500,000D0 = $1,500,000Now, applying the growing perpetuity equation, we find:PV Dividends = C1 / (R–g)PV Dividends = $1,500,000(1 + .05) / (.15 – .05)PV Dividends = $15,750,000This is the same answer we found previously. The price per share of stock is the total value of the company’s stock divided by the shares outstanding, or:P = Value of all stock / Shares outstandingP = $15,750,000 / 1,000,000P = $15.75b.The value of a share of stock in a company is the present value of its current operations, plusthe present value of growth opportunities. To find the present value of the growth opportunities, we need to discount the cash outlay in Year 1 back to the present, and find the value today of the increase in earnings. The increase in earnings is a perpetuity, which we must discount back to today. So, the value of the growth opportunity is:NPVGO = C0 + C1 / (1 + R) + (C2 / R) / (1 + R)NPVGO = –$15,000,000 – $5,000,000 / (1 + .15) + ($6,000,000 / .15) / (1 + .15)NPVGO = $15,434,782.61To find the value of the growth opportunity on a per share basis, we must divide this amount by the number of shares outstanding, which gives us:NPVGO Per share = $15,434,782.61 / $1,000,000NPVGO Per share = $15.43The stock price will increase by $15.43 per share. The new stock price will be:New stock price = $15.75 + 15.43New stock price = $31.1830. a.If the company continues its current operations, it will not grow, so we can value the companyas a cash cow. The total value of the company as a cash cow is the present value of the future earnings, which are a perpetuity, so:Cash cow value of company = C / RCash cow value of company = ฿110,000,000 / .15Cash cow value of company = ฿733,333,333.33The value per share is the total value of the company divided by the shares outstanding, so:Share price = ฿733,333,333.33 / 20,000,000Share price = ฿36.67b.To find the value of the investment, we need to find the NPV of the growth opportunities. Theinitial cash flow occurs today, so it does not need to be discounted. The earnings growth is a perpetuity. Using the present value of a perpetuity equation will give us the value of the earnings growth one period from today, so we need to discount this back to today. The NPVGO of the investment opportunity is:NPVGO = C0 + C1 + (C2 / R) / (1 + R)NPVGO = –฿12,000,000 – 7,000,000 + (฿10,000,000 / .15) / (1 + .15)NPVGO = ฿39,884,057.97c.The price of a share of stock is the cash cow value plus the NPVGO. We have alreadycalculated the NPVGO for the entire project, so we need to find the NPVGO on a per share basis. The NPVGO on a per share basis is the NPVGO of the project divided by the shares outstanding, which is:NPVGO per share = ฿39,884,057.97 / 20,000,000NPVGO per share = ฿1.99This means the per share stock price if the company undertakes the project is:Share price = Cash cow price + NPVGO per shareShare price = ฿36.67 + 1.99Share price = ฿38.6631. a.If the company does not make any new investments, the stock price will be the present value ofthe constant perpetual dividends. In this case, all earnings are paid dividends, so, applying the perpetuity equation, we get:P = Dividend / RP = £5 / .14P = £35.71b.The investment occurs every year in the growth opportunity, so the opportunity is a growingperpetuity. So, we first need to find the growth rate. The growth rate is:g = Retention Ratio Return on Retained Earningsg = 0.25 × 0.40g = 0.10 or 10%Next, we need to calculate the NPV of the investment. During year 3, twenty-five percent ofthe earnings will be reinvested. Therefore, £1.25 is invested (£5 .25). One year later, theshareholders receive a 40 percent return on the investment, or £0.50 (£1.25 × .40), in perpetuity.The perpetuity formula values that stream as of year 3. Since the investment opportunity will continue indefinitely and grows at 10 percent, apply the growing perpetuity formula to calculate the NPV of the investment as of year 2. Discount that value back two years to today.NPVGO = [(Investment + Return / R) / (R– g)] / (1 + R)2NPVGO = [(–£1.25 + £0.50 / .14) / (0.14 – 0.1)] / (1.14)2NPVGO = £44.66The value of the stock is the PV of the firm without making the investment plus the NPV of theinvestment, or:P = PV(EPS) + NPVGOP = £35.71 + £44.66P = £80.37Challenge32.We are asked to find the dividend yield and capital gains yield for each of the stocks. All of thestocks have a 15 percent required return, which is the sum of the dividend yield and the capital gains yield. To find the components of the total return, we need to find the stock price for each stock.Using this stock price and the dividend, we can calculate the dividend yield. The capital gains yield for the stock will be the total return (required return) minus the dividend yield.W: P0 = D0(1 + g) / (R–g) = Au$4.50(1.10)/(.15 – .10) = Au$99.00Dividend yield = D1/P0 = 4.50(1.10)/99.00 = 5%Capital gains yield = .15 – .05 = 10%X: P0 = D0(1 + g) / (R–g) = Au$4.50/(.15 – 0) = Au$30.00Dividend yield = D1/P0 = 4.50/30.00 = 15%Capital gains yield = .15 – .15 = 0%Y: P0 = D0(1 + g) / (R–g) = Au$4.50(1 – .05)/(.15 + .05) = Au$21.38 Dividend yield = D1/P0 = 4.50(0.95)/21.38 = 20%Capital gains yield = .15 – .20 = – 5%。

CHAPTER 16DIVIDENDS AND DIVIDEND POLICYAnswers to Concepts Review and Critical Thinking Questions1.Dividend policy deals with the timing of dividend payments, not the amounts ultimately paid.Dividend policy is irrelevant when the timing of dividend payments doesn’t affect the present value of all future dividends.2. A stock repurchase reduces equity while leaving debt unchanged. The debt ratio rises. A firm could,if desired, use excess cash to reduce debt instead. This is a capital structure decision.3.The chief drawback to a strict dividend policy is the variability in dividend payments. This is aproblem because investors tend to want a somewhat predictable cash flow. Also, if there is information content to dividend announcements, then the firm may be inadvertently telling the market that it is expecting a downturn in earnings prospects when it cuts a dividend, when in reality its prospects are very good. In a compromise policy, the firm maintains a relatively constant dividend. It increases dividends only when it expects earnings to remain at a sufficiently high level to pay the larger dividends, and it lowers the dividend only if it absolutely has to.4.Friday, December 29 is the ex-dividend day. Remember not to count January 1 because it is aholiday, and the exchanges are closed. Anyone who buys the stock before December 29 is entitled to the dividend, assuming they do not sell it again before December 29.5.No, because the money could be better invested in stocks that pay dividends in cash which benefitthe fundholders directly.6.The change in price is due to the change in dividends, not due to the change in dividend policy.Dividend policy can still be irrelevant without a contradiction.7.The stock price dropped because of an expected drop in future dividends. Since the stock price is thepresent value of all future dividend payments, if the expected future dividend payments decrease, then the stock price will decline.8. The plan will probably have little effect on shareholder wealth. The shareholders can reinvest ontheir own, and the shareholders must pay the taxes on the dividends either way. However, the shareholders who take the option may benefit at the expense of the ones who don’t (because of the discount). Also as a result of the plan, the firm will be able to raise equity by paying a 10% flotation cost (the discount), which may be a smaller discount than the market flotation costs of a new issue for some companies.9.If these firms just went public, they probably did so because they were growing and needed theadditional capital. Growth firms typically pay very small cash dividends, if they pay a dividend at all.This is because they have numerous projects available, and they reinvest the earnings in the firm instead of paying cash dividends.B-2 SOLUTIONS10.It would not be irrational to find low-dividend, high-growth stocks. The trust should be indifferentbetween receiving dividends or capital gains since it does not pay taxes on either one (ignoring possible restrictions on invasion of principal, etc.). It would be irrational, however, to hold municipal bonds. Since the trust does not pay taxes on the interest income it receives, it does not need the tax break associated with the municipal bonds. Therefore, it should prefer to hold higher yield, taxable bonds.11.The stock price drop on the ex-dividend date should be lower. With taxes, stock prices should dropby the amount of the dividend, less the taxes investors must pay on the dividends. A lower tax rate lowers the investors’ tax liability.12.With a high tax on dividends and a low tax on capital gains, investors, in general, will prefer capitalgains. If the dividend tax rate declines, the attractiveness of dividends increases.13.Knowing that share price can be expressed as the present value of expected future dividends doesnot make dividend policy relevant. Under the growing perpetuity model, if overall corporate cash flows are unchanged, then a change in dividend policy only changes the timing of the dividends.The PV of those dividends is the same. This is true because, given that future earnings are held constant, dividend policy simply represents a transfer between current and future stockholders.In a more realistic context and assuming a finite holding period, the value of the shares should represent the future stock price as well as the dividends. Any cash flow not paid as a dividend will be reflected in the future stock price. As such the PV of the flows will not change with shifts in dividend policy; dividend policy is still irrelevant.14.T he bird-in-the-hand argument is based upon the erroneous assumption that increased dividendsmake a firm less risky. If capital spending and investment spending are unchanged, the firm’s overall cash flows are not affected by the dividend policy.15.This argument is theoretically correct. In the real world, with transaction costs of security trading,home-made dividends can be more expensive than dividends directly paid out by the firms. However, the existence of financial intermediaries, such as mutual funds, reduces the transaction costs for individuals greatly. Thus, as a whole, the desire for current income shouldn’t be a major factor favoring high-current-dividend policy.16. a.Cap’s past behavior suggests a preference for capital gains, while Widow Jones exhibits apreference for current income.b. Cap could show the Widow how to construct homemade dividends through the sale of stock.Of course, Cap will also have to convince her that she lives in an MM world. Remember thathomemade dividends can only be constructed under the MM assumptions.c.Widow Jones may still not invest in Neotech because of the transaction costs involved inconstructing homemade dividends. Also, the Widow may desire the uncertainty resolutionwhich comes with high dividend stocks.17.To minimize her tax burden, your aunt should divest herself of high dividend yield stocks and investin low dividend yield stock. Or, if possible, she should keep her high dividend stocks, borrow an equivalent amount of money and invest that money in a tax-deferred account.CHAPTER 16 B-3 18. The capital investment needs of small, growing companies are very high. Therefore, payment ofdividends could curtail their investment opportunities. Their other option is to issue stock to pay the dividend, thereby incurring issuance costs. In either case, the companies and thus their investors are better off with a zero dividend policy during the firms’ rapid growth phases. This fact makes these firms attractive only to low dividend clienteles.This example demonstrates that dividend policy is relevant when there are issuance costs. Indeed, it may be relevant whenever the assumptions behind the MM model are not met.19. Unless there is an unsatisfied high dividend clientele, a firm cannot improve its share price byswitching policies. If the market is in equilibrium, the number of people who desire high dividend payout stocks should exactly equal the number of such stocks available. The supplies and demands of each clientele will be exactly met in equilibrium. If the market is not in equilibrium, the supply of high dividend payout stocks may be less than the demand. Only in such a situation could a firm benefit from a policy shift.20. This finding implies that firms use initial dividends to “signal” their potential growth and positiveNPV prospects to the stock market. The initiation of regular cash dividends also serves to convince the market that their high current earnings are not temporary.Solutions to Questions and ProblemsNOTE: All end-of-chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to space and readability constraints, when these intermediate steps are included in this solutions manual, rounding may appear to have occurred. However, the final answer for each problem is found without rounding during any step in the problem.Basic1.The aftertax dividend is the pretax dividend times one minus the tax rate, so:Aftertax dividend = $6.00(1 – .20) = $4.80The stock price should drop by the aftertax dividend amount, or:Ex-dividend price = $80 – 4.80 = $75.202. a.The shares outstanding increases by 10 percent, so:New shares outstanding = 10,000(1.10) = 11,000New shares issued = 1,000Since the par value of the new shares is £1, the capital surplus per share is £24. The total capital surplus is therefore:B-4 SOLUTIONSCapital surplus on new shares = 1,000(£24) = £24,000Common stock (£1 par value) £ 11,000Capital surplus 204,000Retained earnings 561,500£776,500b.The shares outstanding increases by 25 percent, so:New shares outstanding = 10,000(1.25) = 12,500New shares issued = 2,500Since the par value of the new shares is £1, the capital surplus per share is £24. The total capital surplus is therefore:Capital surplus on new shares = 2,500(£24) = £60,000Common stock (£1 par value) £ 12,500Capital surplus 240,000Retained earnings 524,000£776,5003. a.To find the new shares outstanding, we multiply the current shares outstanding times the ratioof new shares to old shares, so:New shares outstanding = 10,000(3/1) = 30,000The equity accounts are unchanged except that the par value of the stock is changed by the ratio of new shares to old shares, so the new par value is:New par value = £1(1/3) = £.3333 per share.b.To find the new shares outstanding, we multiply the current shares outstanding times the ratioof new shares to old shares, so:New shares outstanding = 10,000(1/5) = 2,000.The equity accounts are unchanged except that the par value of the stock is changed by the ratio of new shares to old shares, so the new par value is:New par value = £1(5/1) = £5.00 per share.CHAPTER 16 B-5 4.To find the new stock price, we multiply the current stock price by the ratio of old shares to newshares, so:a.€65(2/5) = €26.00b.€65(1/1.18) = €55.08c.€65(1/1.40) = €46.43d.€65(7/4) = €113.75e.To find the new shares outstanding, we multiply the current shares outstanding times the ratioof new shares to old shares, so:a: 150,000(5/2) = 375,000b: 150,000(1.18) = 177,000c: 150,000(1.40) = 210,000d: 150,000(4/7) = 85,7145.The stock price is the total market value of equity divided by the shares outstanding, so:P0 = Au$175,000 equity/5,000 shares = Au$35.00 per shareIgnoring tax effects, the stock price will drop by the amount of the dividend, so:P X = Au$35.00 – 1.50 = Au$33.50The total dividends paid will be:Au$1.50 per share(5,000 shares) = Au$7,500The equity and cash accounts will both decline by Au$7,500.6.Repurchasing the shares will reduce shareholders’ equity by Au$4,025. The shares repurchased willbe the total purchase amount divided by the stock price, so:Shares bought = Au$4,025/Au$35.00 = 115And the new shares outstanding will be:New shares outstanding = 5,000 – 115 = 4,885B-6 SOLUTIONSAfter repurchase, the new stock price is:Share price = Au$170,975/4,885 shares = Au$35.00The repurchase is effectively the same as the cash dividend because you either hold a share worth Au$35.00, or a share worth Au$33.50 and Au$1.50 in cash. Therefore, you participate in the repurchase according to the dividend payout percentage; you are unaffected.7. The stock price is the total market value of equity divided by the shares outstanding, so:P0 = ₦360,000 equity/15,000 shares = ₦24 per shareThe shares outstanding will increase by 25 percent, so:New shares outstanding = 15,000(1.25) = 18,750The new stock price is the market value of equity divided by the new shares outstanding, so:P X = ₦360,000/18,750 shares = ₦19.208.With a stock dividend, the shares outstanding will increase by one plus the dividend amount, so:New shares outstanding = 350,000(1.12) = 392,000The capital surplus is the capital paid in excess of par value, which is €1, so:Capital surplus for new shares = 42,000(€19) = €798,000The new capital surplus will be the old capital surplus plus the additional capital surplus for the new shares, so:Capital surplus = €1,650,000 + 798,000 = €2,448,000The new equity portion of the balance sheet will look like this:Common stock (€1 par value) € 392,000Capital surplus 2,448,000Retained earnings 2,160,000€5,000,0009.The only equity account that will be affected is the par value of the stock. The par value will changeby the ratio of old shares to new shares, so:New par value = €1(1/5) = €0.20 per share.CHAPTER 16 B-7The total dividends paid this year will be the dividend amount times the number of shares outstanding. The company had 350,000 shares outstanding before the split. We must remember to adjust the shares outstanding for the stock split, so:Total dividends paid this year = €0.70(350,000 shares)(5/1 split) = €1,225,000The dividends increased by 10 percent, so the total dividends paid last year were:Last year’s dividends = €1,225,000/1.10 = €1,113,636.36And to find the dividends per share, we simply divide this amount by the shares outstanding last year. Doing so, we get:Dividends per share last year = €1,113,636.36/350,000 shares = €3.1810.The equity portion of capital outlays is the retained earnings. Subtracting dividends from net income,we get:Equity portion of capital outlays = $1,200 – 600 = $600Since the debt-equity ratio is .80, we can find the new borrowings for the company by multiplying the equity investment by the debt-equity ratio, so:New borrowings = .80($600) = $480And the total capital outlay will be the sum of the new equity and the new debt, which is:Total capital outlays = $600 + 480 =$1,080.11. a.The payout ratio is the dividend per share divided by the earnings per share, so:Payout ratio = ₩0.80/₩7Payout ratio = .1143 or 11.43%b.Under a residual dividend policy, the additions to retained earnings, which is the equity portionof the planned capital outlays, is the retained earnings per share times the number of shares outstanding, so:Equity portion of capital outlays = 7M shares (₩7 – .80) = ₩43.4MThis means the total investment outlay will be:Total investment outlay = ₩43.4M + 18MTotal investment outlay = ₩61.4MThe debt-equity ratio is the new borrowing divided by the new equity, so:D/E ratio = ₩18M/₩43.4M = .4147B-8 SOLUTIONSCHAPTER 16 B-9 12. a.Since the company has a debt-equity ratio of 3, they can raise ₡3 in debt for every ₡1 of equity.The maximum capital outlay with no outside equity financing is:Maximum capital outlay = ₡180,000 + 3(₡180,000) = ₡720,000.b.If planned capital spending is ₡800,000, then no dividend will be paid and new equity will beissued since this exceeds the amount calculated in a.c.No, they do not maintain a constant dividend payout because, with the strict residual policy,the dividend will depend on the investment opportunities and earnings. As these two things vary, the dividend payout will also vary.13. a.We can find the new borrowings for the company by multiplying the equity investment by thedebt-equity ratio, so we get:New debt = 2(₪56M) = ₪112MAdding the new retained earnings, we get:Maximum investment with no outside equity financing = ₪56M + 2(₪56M) = ₪168Mb. A debt-equity ratio of 2 implies capital structure is 2/3 debt and 1/3 equity. The equity portionof the planned new investment will be:Equity portion of investment funds = 1/3(₪72M) = ₪24MThis is the addition to retained earnings, so the total available for dividend payments is:Residual = ₪56M – 24M = ₪32MThis makes the dividend per share:Dividend per share = ₪32M/12M shares = ₪2.67c.The borrowing will be:Borrowing = ₪72M – 24M = ₪48MAlternatively, we could calculate the new borrowing as the weight of debt in the capital structure times the planned capital outlays, so:Borrowing = 2/3(₪72M) = ₪48MThe addition to retained earnings is ₪24M, which we calculated in part b.B-10 SOLUTIONSd.If the company plans no capital outlays, no new borrowing will take place. The dividend pershare will be:Dividend per share = ₪56M/12M shares = ₪4.6714. a.If the dividend is declared, the price of the stock will drop on the ex-dividend date by the valueof the dividend, ¥5. It will then trade for ¥95.b.If it is not declared, the price will remain at ¥100.c.Nakumura’s outflows for inves tments are ¥5,000,000. These outflows occur immediately. Oneyear from now, the firm will realize ¥1,000,000 in net income and it will pay ¥500,000 in dividends, but the need for financing is immediate. Nakumura must finance ¥2,000,000 through the sale of shares worth ¥100. It must sell ¥5,000,000 / ¥100 = 50,000 shares.d.The MM model is not realistic since it does not account for taxes, brokerage fees, uncertaintyover future cash flows, investors’ preferences, signaling effects, and agency costs.Intermediate15.The price of the stock today is the PV of the dividends, so:P0 = Rs.0.70/1.15 + Rs.40/1.152 = Rs.30.85To find the equal two year dividends with the same present value as the price of the stock, we set up the following equation and solve for the dividend (Note: The dividend is a two year annuity, so we could solve with the annuity factor as well):Rs.30.85 = D/1.15 + D/1.152D = Rs.18.98We now know the cash flow per share we want each of the next two years. We can find the price of stock in one year, which will be:P1 = Rs.40/1.15 = Rs.34.78Since you own 1,000 shares, in one year you want:Cash flow in Year one = 1,000(Rs.18.98) = Rs.18,979.07B ut you’ll only get:Dividends received in one year = 1,000(Rs.0.70) = Rs.700.00CHAPTER 16 B-11 Thus, in one year you will need to sell additional shares in order to increase your cash flow. The number of shares to sell in year one is:Shares to sell at time one = (Rs.18,979.07 – 700)/Rs.34.78 = 525.52 sharesAt Year 2, you cash flow will be the dividend payment times the number of shares you still own, so the Year 2 cash flow is:Year 2 cash flow = Rs.40(1,000 – 525.52) = Rs.18,979.0716.If you only want Rs.200 in Year 1, you will buy:(Rs.700 – 200)/Rs.34.78 = 14.38 sharesat Year 1. Your dividend payment in Year 2 will be:Year 2 dividend = (1,000 + 14.38)(Rs.40) = Rs.40,575Note that the present value of each cash flow stream is the same. Below we show this by finding the present values as:PV = Rs.200/1.15 + Rs.40,575/1.152 = Rs.30,854.44PV = 1,000(Rs.0.70)/1.15 + 1,000(Rs.40)/1.152 = Rs.30,854.4417. a.If the company makes a dividend payment, we can calculate the wealth of a shareholder as:Dividend per share = 元5,000/200 shares = 元25.00The stock price after the dividend payment will be:P X = 元40 – 25 = 元15 per shareThe shareholder will have a stock worth 元15 and a 元25 dividend for a total wealth of 元40.If the company makes a repurchase, the company will repurchase:Shares repurchased = 元5,000/元40 = 125 sharesIf the shareholder lets their shares be repurchased, they will have 元40 in cash. If the shareholder keeps their shares, they’re still worth 元40.b.If the company pays dividends, the current EPS is 元0.95, and the P/E ratio is:P/E = 元15/元0.95 = 15.79B-12 SOLUTIONSCHAPTER 16 B-13 If the company repurchases stock, the number of shares will decrease. The total net income is the EPS times the current number of shares outstanding. Dividing net income by the new number of shares outstanding, we find the EPS under the repurchase is:EPS = 元0.95(200)/(200 125) = 元2.53The stock price will remain at 元40 per share, so the P/E ratio is:P/E = 元40/元2.53 = 15.79c. A share repurchase would seem to be the preferred course of action. Only those shareholderswho wish to sell will do so, giving the shareholder a tax timing option that he or she doesn’t get with a dividend payment.18. a.Since the firm has a 100 percent payout policy, the entire net income, ฿32,000 will be paid as adividend. The current value of the firm is the discounted value one year from now, plus the current income, which is:Value = ฿32,000 + ฿1,545,600/1.12Value = ฿1,412,000b.The current stock price is the value of the firm, divided by the shares outstanding, which is:Stock price = ฿1,412,000/10,000Stock price = ฿141.20Since the company has a 100 percent payout policy, the current dividend per share will be the company’s net income, divided by the shares outstanding, or:Current dividend = ฿32,000/10,000Current dividend = ฿3.20The stock price will fall by the value of the dividend to:Ex-dividend stock price = ฿141.20 – 3.20Ex-dividend stock price = ฿138.00c. i.According to MM, it cannot be true that the low dividend is depressing the price. Sincedividend policy is irrelevant, the level of the dividend should not matter. Any funds notdistributed as dividends add to the value of the firm, hence the stock price. Thesedirectors merely want to change the timing of the dividends (more now, less in the future).As the calculations below indicate, the value of the firm is unchanged by their proposal.Therefore, share price will be unchanged.B-14 SOLUTIONSTo show this, consider what would happen if the dividend was increased to ฿4.25. Sinceonly the existing shareholders will get the dividend, the required baht amount to pay thedividends is:Total dividends = ฿4.25(10,000)Total dividends = ฿42,500To fund this dividend payment, the company must raise:Bahts raised = Required funds – Net incomeBahts raised = ฿42,500 – 32,000Bahts raised = ฿10,500This money can only be raised with the sale of new equity to maintain the all-equityfinancing. Since those new shareholders must also earn 12 percent, their share of the firmone year from now is:New shareholder value in one year = ฿10,500(1.12)New shareholder value in one year = ฿11,760This means that the old shareholders' interest falls to:Old shareholder value in one year = ฿1,545,600 – 11,760Old shareholder value in one year = ฿1,533,840Under this scenario, the current value of the firm is:Value = ฿42,500 + ฿1,533,840/1.12Value = ฿1,412,000Since the firm value is the same as in part a, the change in dividend policy had no effect.ii.The new shareholders are not entitled to receive the current dividend. They will receive only the value of the equity one year hence. The present value of those flows is:Present value = ฿1,533,840/1.12Present value = ฿1,369,500And the current share price will be:Current share price = ฿1,369,500/10,000Current share price = ฿136.95So, the number of new shares the company must sell will be:Shares sold = ฿10,500/฿136.95Shares sold = 76.67 sharesCHAPTER 16 B-15 19. a.The current price is the current cash flow of the company plus the present value of theexpected cash flows, divided by the number of shares outstanding. So, the current stock price is: Stock price = ($1,200,000 + 15,000,000) / 1,000,000Stock price = $16.20b.To achieve a zero dividend payout policy, he can invest the dividends back into the company’sstock. The dividends per share will be:Dividends per share = [($1,200,000)(.50)]/1,000,000Dividends per share = $0.60And the stockholder in question will receive:Dividends paid to shareholder = $0.60(1,000)Dividends paid to shareholder = $600The new stock price after the dividends are paid will be:Ex-dividend stock price = $16.20 – 0.60Ex-dividend stock price = $15.60So, the number of shares the investor will buy is:Number of shares to buy = $600 / $15.60Number of shares to buy = 38.4620. ing the formula from the text proposed by Lintner:Div1 = Div0 + s(t EPS1– Div0)Div1 = €1.25 + .3[(.4)(€4.50) –€1.25]Div1 = €1.415b.Now we use an adjustment rate of 0.60, so the dividend next year will be:Div1 = Div0 + s(t EPS1– Div0)Div1 = €1.25 + .7[(.4)(€4.50) –€1.25]Div1= €1.635c.The lower adjustment factor in part a is more conservative. The lower adjustment factor willalways result in a lower future dividend.B-16 SOLUTIONSChallenge21.Assuming no capital gains tax, the aftertax return for the Gordon Company is the capital gainsgrowth rate, plus the dividend yield times one minus the tax rate. Using the constant growth dividend model, we get:Aftertax return = g + D(1 – t) = .15Solving for g, we get:.15 = g + .06(1 – .35)g = .1110The equivalent pretax return for Gecko Company, which pays no dividend, is:Pretax return = g + D = .1110 + .06 = 17.10%22. Using the equation for the decline in the stock price ex-dividend for each of the tax ratepolicies, we get:(P0– P X)/D = (1 – T P)/(1 – T G)a.P0– P X = D(1 – 0)/(1 – 0)P0– P X = Db.P0– P X = D(1 – .15)/(1 – 0)P0– P X = .85Dc.P0– P X = D(1 – .15)/(1 – .25)P0– P X = 1.1333Dd.With this tax policy, we simply need to multiply the personal tax rate times one minus thedividend exemption percentage, so:P0– P X = D[1 – (.35)(.30)]/(1 – .35)P0– P X = 1.3769De.Since different investors have widely varying tax rates on ordinary income and capital gains,dividend payments have different after-tax implications for different investors. This differential taxation among investors is one aspect of what we have called the clientele effect.CHAPTER 16 B-17 23.Since the ¥2,000,000 cash is after corporate tax, the full amount will be invested. So, the value ofeach alternative is:Alternative 1:The firm invests in T-bills or in preferred stock, and then pays out as special dividend in 3 years If the firm invests in T-Bills:If the firm invests in T-bills, the aftertax yield of the T-bills will be:Aftertax corporate yield = .07(1 – .35)Aftertax corporate yield = .0455 or 4.55%So, the future value of the corporate investment in T-bills will be:FV of investment in T-bills = ¥2,000,000(1 + .0455)3FV of investment in T-bills = ¥2,285,609.89Since the future value will be paid to shareholders as a dividend, the aftertax cash flow will be:Aftertax cash flow to shareholders = ¥2,285,609.89(1 – .15)Aftertax cash flow to shareholders = ¥1,942,768.41If the firm invests in preferred stock:If the firm invests in preferred stock, the assumption would be that the dividends received will be reinvested in the same preferred stock. The preferred stock will pay a dividend of:Preferred dividend = .11(¥2,000,000)Preferred dividend = ¥220,000Since 70 percent of the dividends are excluded from tax:Taxable preferred dividends = (1 – .70)(¥220,000)Taxable preferred dividends = ¥66,000And the taxes the company must pay on the preferred dividends will be:Taxes on preferred dividends = .35(¥66,000)Taxes on preferred dividends = ¥23,100So, the aftertax dividend for the corporation will be:Aftertax corporate dividend = ¥220,000 – 23,100Aftertax corporate dividend = ¥196,900B-18 SOLUTIONSThis means the aftertax corporate dividend yield is:Aftertax corporate dividend yield = ¥196,900 / ¥2,000,000Aftertax corporate dividend yield = .09845 or 9.845%The future value of the company’s investment in preferred stock will be:FV of investment in preferred stock = ¥2,000,000(1 + .09845)3FV of investment in preferred stock = ¥2,650,762.85Since the future value will be paid to shareholders as a dividend, the aftertax cash flow will be: Aftertax cash flow to shareholders = ¥2,650,762.85(1 – .15)Aftertax cash flow to shareholders = ¥2,253,148.42Alternative 2:The firm pays out dividend now, and individuals invest on their own. The aftertax cash received by shareholders now will be:Aftertax cash received today = ¥2,000,000(1 – .15)Aftertax cash received today = ¥1,700,000The individuals invest in Treasury bills:If the shareholders invest the current aftertax dividends in Treasury bills, the aftertax individual yield will be:Aftertax individual yield on T-bills = .07(1 – .31)Aftertax individual yield on T-bills = .0483 or 4.83%So, the future value of the individual investment in Treasury bills will be:FV of investment in T-bills = ¥1,700,000(1 + .0483)3FV of investment in T-bills = ¥1,958,419.29The individuals invest in preferred stock:If the individual invests in preferred stock, the assumption would be that the dividends received will be reinvested in the same preferred stock. The preferred stock will pay a dividend of:Preferred dividend = .11(¥1,700,000)Preferred dividend = ¥187,000。

Chapter 2: Accounting Statements and Cash Flow2.10AssetsCurrent assetsCash $ 4,000Accounts receivable 8,000Total current assets $ 12,000Fixed assetsMachinery $ 34,000Patents 82,000Total fixed assets $116,000Total assets $128,000Liabilities and equityCurrent liabilitiesAccounts payable $ 6,000Taxes payable 2,000Total current liabilities $ 8,000Long-term liabilitiesBonds payable $7,000Stockholders equityCommon stock ($100 par) $ 88,000Capital surplus 19,000Retained earnings 6,000Total stockholders equity $113,000Total liabilities and equity $128,0002.11One year ago TodayLong-term debt $50,000,000 $50,000,000Preferred stock 30,000,000 30,000,000Common stock 100,000,000 110,000,000Retained earnings 20,000,000 22,000,000Total $200,000,000 $212,000,0002.12Total Cash Flow ofthe Stancil CompanyCash flows from the firmCapital spending $(1,000)Additions to working capital (4,000)Total $(5,000)Cash flows to investors of the firmShort-term debt $(6,000)Long-term debt (20,000)Equity (Dividend - Financing) 21,000Total $(5,000)[Note: This table isn’t the Statement of Cash Flows, which is only covered in Appendix 2B, since the latter has th e change in cash (on the balance sheet) as a final entry.]2.13 a. The changes in net working capital can be computed from:Sources of net working capitalNet income $100Depreciation 50Increases in long-term debt 75Total sources $225Uses of net working capitalDividends $50Increases in fixed assets* 150Total uses $200Additions to net working capital $25*Includes $50 of depreciation.b.Cash flow from the firmOperating cash flow $150Capital spending (150)Additions to net working capital (25)Total $(25)Cash flow to the investorsDebt $(75)Equity 50Total $(25)Chapter 3: Financial Markets and Net Present Value: First Principles of Finance (Advanced)3.14 $120,000 - ($150,000 - $100,000) (1.1) = $65,0003.15 $40,000 + ($50,000 - $20,000) (1.12) = $73,6003.16 a. ($7 million + $3 million) (1.10) = $11.0 millionb.i. They could spend $10 million by borrowing $5 million today.ii. They will have to spend $5.5 million [= $11 million - ($5 million x 1.1)] at t=1.Chapter 4: Net Present Valuea. $1,000 ⨯ 1.0510 = $1,628.89b. $1,000 ⨯ 1.0710 = $1,967.15c. $1,000 ⨯ 1.0520 = $2,653.30d. Interest compounds on the interest already earned. Therefore, the interest earned inSince this bond has no interim coupon payments, its present value is simply the present value of the $1,000 that will be received in 25 years. Note: As will be discussed in the next chapter, the present value of the payments associated with a bond is the price of that bond.PV = $1,000 /1.125 = $92.30PV = $1,500,000 / 1.0827 = $187,780.23a. At a discount rate of zero, the future value and present value are always the same. Remember, FV =PV (1 + r) t. If r = 0, then the formula reduces to FV = PV. Therefore, the values of the options are $10,000 and $20,000, respectively. You should choose the second option.b. Option one: $10,000 / 1.1 = $9,090.91Option two: $20,000 / 1.15 = $12,418.43Choose the second option.c. Option one: $10,000 / 1.2 = $8,333.33Option two: $20,000 / 1.25 = $8,037.55Choose the first option.d. You are indifferent at the rate that equates the PVs of the two alternatives. You know that rate mustfall between 10% and 20% because the option you would choose differs at these rates. Let r be thediscount rate that makes you indifferent between the options.$10,000 / (1 + r) = $20,000 / (1 + r)5(1 + r)4 = $20,000 / $10,000 = 21 + r = 1.18921r = 0.18921 = 18.921%The $1,000 that you place in the account at the end of the first year will earn interest for six years. The $1,000 that you place in the account at the end of the second year will earn interest for five years, etc. Thus, the account will have a balance of$1,000 (1.12)6 + $1,000 (1.12)5 + $1,000 (1.12)4 + $1,000 (1.12)3= $6,714.61PV = $5,000,000 / 1.1210 = $1,609,866.18a. $1.000 (1.08)3 = $1,259.71b. $1,000 [1 + (0.08 / 2)]2 ⨯ 3 = $1,000 (1.04)6 = $1,265.32c. $1,000 [1 + (0.08 / 12)]12 ⨯ 3 = $1,000 (1.00667)36 = $1,270.24d. $1,000 e0.08 ⨯ 3 = $1,271.25e. The future value increases because of the compounding. The account is earning interest on interest. Essentially, the interest is added to the account balance at the e nd of every compounding period. During the next period, the account earns interest on the new balance. When the compounding period shortens, the balance that earns interest is rising faster.The price of the consol bond is the present value of the coupon payments. Apply the perpetuity formula to find the present value. PV = $120 / 0.15 = $800a. $1,000 / 0.1 = $10,000b. $500 / 0.1 = $5,000 is the value one year from now of the perpetual stream. Thus, the value of theperpetuity is $5,000 / 1.1 = $4,545.45.c. $2,420 / 0.1 = $24,200 is the value two years from now of the perpetual stream. Thus, the value of the perpetuity is $24,200 / 1.12 = $20,000.pply the NPV technique. Since the inflows are an annuity you can use the present value of an annuity factor.ANPV = -$6,200 + $1,200 81.0= -$6,200 + $1,200 (5.3349)= $201.88Yes, you should buy the asset.Use an annuity factor to compute the value two years from today of the twenty payments. Remember, the annuity formula gives you the value of the stream one year before the first payment. Hence, the annuity factor will give you the value at the end of year two of the stream of payments.A= $2,000 (9.8181)Value at the end of year two = $2,000 20.008= $19,636.20The present value is simply that amount discounted back two years.PV = $19,636.20 / 1.082 = $16,834.88The easiest way to do this problem is to use the annuity factor. The annuity factor must be equal to $12,800 / $2,000 = 6.4; remember PV =C A T r. The annuity factors are in the appendix to the text. To use the factor table to solve this problem, scan across the row labeled 10 years until you find 6.4. It is close to the factor for 9%, 6.4177. Thus, the rate you will receive on this note is slightly more than 9%.You can find a more precise answer by interpolating between nine and ten percent.[ 10% ⎤[6.1446 ⎤a ⎡r ⎥bc ⎡6.4 ⎪ d⎣9%⎦⎣6.4177 ⎦By interpolating, you are presuming that the ratio of a to b is equal to the ratio of c to d.(9 - r ) / (9 - 10) = (6.4177 - 6.4 ) / (6.4177 - 6.1446)r = 9.0648%The exact value could be obtained by solving the annuity formula for the interest rate. Sophisticated calculators can compute the rate directly as 9.0626%.[Note: A standard financial calculator’s TVM keys can solve for this rate. With annuity flows, the IRR key on “advanced” financial c alculators is unnecessary.]a. The annuity amount can be computed by first calculating the PV of the $25,000 which youThat amount is $17,824.65 [= $25,000 / 1.075]. Next compute the annuity which has the same present value.A$17,824.65 = C 507.0$17,824.65 = C (4.1002)C = $4,347.26Thus, putting $4,347.26 into the 7% account each year will provide $25,000 five years from today.b. The lump sum payment must be the present value of the $25,000, i.e., $25,000 / 1.075 =$17,824.65The formula for future value of any annuity can be used to solve the problem (see footnote 11 of the text).Option one: This cash flow is an annuity due. To value it, you must use the after-tax amounts. Theafter-tax payment is $160,000 (1 - 0.28) = $115,200. Value all except the first payment using the standard annuity formula, then add back the first payment of $115,200 to obtain the value of this option.AValue = $115,200 + $115,200 30.010= $115,200 + $115,200 (9.4269)= $1,201,178.88Option two: This option is valued similarly. You are able to have $446,000 now; this is already on an after-tax basis. You will receive an annuity of $101,055 for each of the next thirty years. Those payments are taxable when you receive them, so your after-tax payment is $72,759.60 [= $101,055 (1 - 0.28)].AValue = $446,000 + $72,759.60 30.010= $446,000 + $72,759.60 (9.4269)= $1,131,897.47Since option one has a higher PV, you should choose it.et r be the rate of interest you must earn.$10,000(1 + r)12 = $80,000(1 + r)12= 8r = 0.18921 = 18.921%First compute the present value of all the payments you must make for your children’s educati on. The value as of one year before matriculation of one child’s education isA= $21,000 (2.8550) = $59,955.$21,000 415.0This is the value of the elder child’s education fourteen years from now. It is the value of the younger child’s education sixteen years from today. The present value of these isPV = $59,955 / 1.1514 + $59,955 / 1.1516= $14,880.44You want to make fifteen equal payments into an account that yields 15% so that the present value of the equal payments is $14,880.44.A= $14,880.44 / 5.8474 = $2,544.80Payment = $14,880.44 / 15.015This problem applies the growing annuity formula. The first payment is$50,000(1.04)2(0.02) = $1,081.60.PV = $1,081.60 [1 / (0.08 - 0.04) - {1 / (0.08 - 0.04)}{1.04 / 1.08}40]= $21,064.28This is the present value of the payments, so the value forty years from today is$21,064.28 (1.0840) = $457,611.46se the discount factors to discount the individual cash flows. Then compute the NPV of the project. NoticeYou can still use the factor tables to compute their PV. Essentially, they form cash flows that are a six year annuity less a two year annuity. Thus, the appropriate annuity factor to use with them is 2.6198 (= 4.3553 - 1.7355).Year Cash Flow Factor PV0.9091 $636.371$70020.8264 743.769003 1,000 ⎤4 1,000 ⎥ 2.6198 2,619.805 1,000 ⎥6 1,000 ⎦7 1,250 0.5132 641.508 1,375 0.4665 641.44Total $5,282.87NPV = -$5,000 + $5,282.87= $282.87Purchase the machine.Chapter 5: How to Value Bonds and StocksThe amount of the semi-annual interest payment is $40 (=$1,000 ⨯ 0.08 / 2). There are a total of 40 periods;i.e., two half years in each of the twenty years in the term to maturity. The annuity factor tables can be usedto price these bonds. The appropriate discount rate to use is the semi-annual rate. That rate is simply the annual rate divided by two. Thus, for part b the rate to be used is 5% and for part c is it 3%.A+F/(1+r)40PV=C Tra. $40 (19.7928) + $1,000 / 1.0440 = $1,000Notice that whenever the coupon rate and the market rate are the same, the bond is priced at par.b. $40 (17.1591) + $1,000 / 1.0540 = $828.41Notice that whenever the coupon rate is below the market rate, the bond is priced below par.c. $40 (23.1148) + $1,000 / 1.0340 = $1,231.15Notice that whenever the coupon rate is above the market rate, the bond is priced above par.a. The semi-annual interest rate is $60 / $1,000 = 0.06. Thus, the effective annual rate is 1.062 - 1 =0.1236 = 12.36%.A+ $1,000 / 1.0612b. Price = $30 12.006= $748.48A+ $1,000 / 1.0412c. Price = $30 1204.0= $906.15Note: In parts b and c we are implicitly assuming that the yield curve is flat. That is, the yield in year 5applies for year 6 as well.rice = $2 (0.72) / 1.15 + $4 (0.72) / 1.152 + $50 / 1.153= $36.31The number of shares you own = $100,000 / $36.31 = 2,754 sharesPrice = $1.15 (1.18) / 1.12 + $1.15 (1.182) / 1.122 + $1.152 (1.182) / 1.123+ {$1.152 (1.182)(1.06) / (0.12 - 0.06)} / 1.123= $26.95[Insert before last sentence of question: Assume that dividends are a fixed proportion of earnings.] Dividend one year from now = $5 (1 - 0.10) = $4.50Price = $5 + $4.50 / {0.14 - (-0.10)}= $23.75Since the current $5 dividend has not yet been paid, it is still included in the stock price.Chapter 6: Some Alternative Investment Rulesa. Payback period of Project A = 1 + ($7,500 - $4,000) / $3,500 = 2 yearsPayback period of Project B = 2 + ($5,000 - $2,500 -$1,200) / $3,000 = 2.43 yearsProject A should be chosen.b. NPV A = -$7,500 + $4,000 / 1.15 + $3,500 / 1.152 + $1,500 / 1.153 = -$388.96NPV B = -$5,000 + $2,500 / 1.15 + $1,200 / 1.152 + $3,000 / 1.153 = $53.83Project B should be chosen.a. Average Investment:($16,000 + $12,000 + $8,000 + $4,000 + 0) / 5 = $8,000Average accounting return:$4,500 / $8,000 = 0.5625 = 56.25%b. 1. AAR does not consider the timing of the cash flows, hence it does not consider the timevalue of money.2. AAR uses an arbitrary firm standard as the decision rule.3. AAR uses accounting data rather than net cash flows.aAverage Investment = (8000 + 4000 + 1500 + 0)/4 = 3375.00Average Net Income = 2000(1-0.75) = 1500=> AAR = 1500/3375=44.44%a. Solve x by trial and error:-$8,000 + $4,000 / (1 + x) + $3000 / (1 + x)2 + $2,000 / (1 + x)3 = 0x = 6.93%b. No, since the IRR (6.93%) is less than the discount rate of 8%.Alternatively, the NPV @ a discount rate of 0.08 = -$136.62.a. Solve r in the equation:$5,000 - $2,500 / (1 + r) - $2,000 / (1 + r)2 - $1,000 / (1 + r)3- $1,000 / (1 + r)4 = 0By trial and error,IRR = r = 13.99%b. Since this problem is the case of financing, accept the project if the IRR is less than the required rate of return.IRR = 13.99% > 10%Reject the offer.c. IRR = 13.99% < 20%Accept the offer.d. When r = 10%:NPV = $5,000 - $2,500 / 1.1 - $2,000 / 1.12 - $1,000 / 1.13 - $1,000 / 1.14When r = 20%:NPV = $5,000 - $2,500 / 1.2 - $2,000 / 1.22 - $1,000 / 1.23 - $1,000 / 1.24= $466.82Yes, they are consistent with the choices of the IRR rule since the signs of the cash flows change only once.A/ $160,000 = 1.04PI = $40,000 715.0Since the PI exceeds one accept the project.Chapter 7: Net Present Value and Capital BudgetingSince there is uncertainty surrounding the bonus payments, which McRae might receive, you must use the expected value of McRae’s bonuses in the computation of the PV of his contract. McRae’s salary plus the expected value of his bonuses in years one through three is$250,000 + 0.6 ⨯ $75,000 + 0.4 ⨯ $0 = $295,000.Thus the total PV of his three-year contract isPV = $400,000 + $295,000 [(1 - 1 / 1.12363) / 0.1236]+ {$125,000 / 1.12363} [(1 - 1 / 1.123610 / 0.1236]= $1,594,825.68EPS = $800,000 / 200,000 = $4NPVGO = (-$400,000 + $1,000,000) / 200,000 = $3Price = EPS / r + NPVGO= $4 / 0.12 + $3=$36.33Year 0 Year 1 Year 2 Year 3 Year 4 Year 51. Annual Salary$120,000 $120,000 $120,000 $120,000 $120,000 Savings2. Depreciation 100,000 160,000 96,000 57,600 57,6003. Taxable Income 20,000 -40,000 24,000 62,400 62,4004. Taxes 6,800 -13,600 8,160 21,216 21,2165. Operating Cash Flow113,200 133,600 111,840 98,784 98,784 (line 1-4)$100,000 -100,0006. ∆ Net workingcapital7. Investment $500,000 75,792*8. Total Cash Flow -$400,000 $113,200 $133,600 $111,840 $98,784 $74,576*75,792 = $100,000 - 0.34 ($100,000 - $28,800)NPV = -$400,000+ $113,200 / 1.12 + $133,600 / 1.122 + $111,840 / 1.123+ $98,784 / 1.124 + $74,576 / 1.125= -$7,722.52Real interest rate = (1.15 / 1.04) - 1 = 10.58%NPV A = -$40,000+ $20,000 / 1.1058 + $15,000 / 1.10582 + $15,000 / 1.10583= $1,446.76NPV B = -$50,000+ $10,000 / 1.15 + $20,000 / 1.152 + $40,000 / 1.153= $119.17Choose project A.PV = $120,000 / {0.11 - (-0.06)}t = 0 t = 1 t = 2 t = 3 t = 4 t = 5 t = 6 ...$12,000 $6,000 $6,000 $6,000$4,000$12,000 $6,000 $6,000 ...The present value of one cycle is:A+ $4,000 / 1.064PV = $12,000 + $6,000 306.0= $12,000 + $6,000 (2.6730) + $4,000 / 1.064= $31,206.37The cycle is four years long, so use a four year annuity factor to compute the equivalent annual cost (EAC).AEAC = $31,206.37 / 406.0= $31,206.37 / 3.4651= $9,006The present value of such a stream in perpetuity is$9,006 / 0.06 = $150,100o evaluate the word processors, compute their equivalent annual costs (EAC).BangAPV(costs) = (10 ⨯ $8,000) + (10 ⨯ $2,000) 414.0= $80,000 + $20,000 (2.9137)= $138,274EAC = $138,274 / 2.9137= $47,456IOUAPV(costs) = (11 ⨯ $5,000) + (11 ⨯ $2,500) 3.014- (11 ⨯ $500) / 1.143= $55,000 + $27,500 (2.3216) - $5,500 / 1.143= $115,132EAC = $115,132 / 2.3216= $49,592BYO should purchase the Bang word processors.Chapter 8: Strategy and Analysis in Using Net Present ValueThe accounting break-even= (120,000 + 20,000) / (1,500 - 1,100)= 350 units. The accounting break-even= 340,000 / (2.00 - 0.72)= 265,625 abalonesb. [($2.00 ⨯ 300,000) - (340,000 + 0.72 ⨯ 300,000)] (0.65)= $28,600This is the after tax profit.Chapter 9: Capital Market Theory: An Overviewa. Capital gains = $38 - $37 = $1 per shareb. Total dollar returns = Dividends + Capital Gains = $1,000 + ($1*500) = $1,500 On a per share basis, this calculation is $2 + $1 = $3 per sharec. On a per share basis, $3/$37 = 0.0811 = 8.11% On a total dollar basis, $1,500/(500*$37) = 0.0811 = 8.11%d. No, you do not need to sell the shares to include the capital gains in the computation of the returns. The capital gain is included whether or not you realize the gain. Since you could realize the gain if you choose, you should include it.The expected holding period return is:()[]%865.1515865.052$/52$75.54$50.5$==-+There appears to be a lack of clarity about the meaning of holding period returns. The method used in the answer to this question is the one used in Section 9.1. However, the correspondence is not exact, because in this question, unlike Section 9.1, there are cash flows within the holding period. The answer above ignores the dividend paid in the first year. Although the answer above technically conforms to the eqn at the bottom of Fig. 9.2, the presence of intermediate cash flows that aren’t accounted for renders th is measure questionable, at best. There is no similar example in the body of the text, and I have never seen holding period returns calculated in this way before.Although not discussed in this book, there are two generally accepted methods of computing holding period returns in the presence of intermediate cash flows. First, the time weighted return calculates averages (geometric or arithmetic) of returns between cash flows. Unfortunately, that method can’t be used here, because we are not given the va lue of the stock at the end of year one. Second, the dollar weighted measure calculates the internal rate of return over the entire holding period. Theoretically, that method can be applied here, as follows: 0 = -52 + 5.50/(1+r) + 60.25/(1+r)2 => r = 0.1306.This produces a two year holding period return of (1.1306)2 – 1 = 0.2782. Unfortunately, this book does not teach the dollar weighted method.In order to salvage this question in a financially meaningful way, you would need the value of the stock at the end of one year. Then an illustration of the correct use of the time-weighted return would be appropriate. A complicating factor is that, while Section 9.2 illustrates the holding period return using the geometric return for historical data, the arithmetic return is more appropriate for expected future returns.E(R) = T-Bill rate + Average Excess Return = 6.2% + (13.0% -3.8%) = 15.4%. Common Treasury Realized Stocks Bills Risk Premium -7 32.4% 11.2% 21.2%-6 -4.9 14.7 -19.6-5 21.4 10.5 10.9 -4 22.5 8.8 13.7 -3 6.3 9.9 -3.6 -2 32.2 7.7 24.5 Last 18.5 6.2 12.3 b. The average risk premium is 8.49%.49.873.125.246.37.139.106.192.21=++-++- c. Yes, it is possible for the observed risk premium to be negative. This can happen in any single year. The.b.Standard deviation = 03311.0001096.0=.b.Standard deviation = = 0.03137 = 3.137%.b.Chapter 10: Return and Risk: The Capital-Asset-Pricing Model (CAPM)a. = 0.1 (– 4.5%) + 0.2 (4.4%) + 0.5 (12.0%) + 0.2 (20.7%) = 10.57%b.σ2 = 0.1 (–0.045 – 0.1057)2 + 0.2 (0.044 – 0.1057)2 + 0.5 (0.12 – 0.1057)2+ 0.2 (0.207 – 0.1057)2 = 0.0052σ = (0.0052)1/2 = 0.072 = 7.20%Holdings of Atlas stock = 120 ⨯ $50 = $6,000 ⨯ $20 = $3,000Weight of Atlas stock = $6,000 / $9,000 = 2 / 3Weight of Babcock stock = $3,000 / $9,000 = 1 / 3a. = 0.3 (0.12) + 0.7 (0.18) = 0.162 = 16.2%σP 2= 0.32 (0.09)2 + 0.72 (0.25)2 + 2 (0.3) (0.7) (0.09) (0.25) (0.2)= 0.033244σP= (0.033244)1/2 = 0.1823 = 18.23%a.State Return on A Return on B Probability1 15% 35% 0.4 ⨯ 0.5 = 0.22 15% -5% 0.4 ⨯ 0.5 = 0.23 10% 35% 0.6 ⨯ 0.5 = 0.34 10% -5% 0.6 ⨯ 0.5 = 0.3b. = 0.2 [0.5 (0.15) + 0.5 (0.35)] + 0.2[0.5 (0.15) + 0.5 (-0.05)]+ 0.3 [0.5 (0.10) + 0.5 (0.35)] + 0.3 [0.5 (0.10) + 0.5 (-0.05)]= 0.135= 13.5%Note: The solution to this problem requires calculus.Specifically, the solution is found by minimizing a function subject to a constraint. Calculus ability is not necessary to understand the principles behind a minimum variance portfolio.Min { X A2 σA2 + X B2σB2+ 2 X A X B Cov(R A , R B)}subject to X A + X B = 1Let X A = 1 - X B. Then,Min {(1 - X B)2σA2 + X B2σB2+ 2(1 - X B) X B Cov (R A, R B)}Take a derivative with respect to X B.d{∙} / dX B = (2 X B - 2) σA2+ 2 X B σB2 + 2 Cov(R A, R B) - 4 X B Cov(R A, R B)Set the derivative equal to zero, cancel the common 2 and solve for X B.X BσA2- σA2+ X B σB2 + Cov(R A, R B) - 2 X B Cov(R A, R B) = 0X B = {σA2 - Cov(R A, R B)} / {σA2+ σB2 - 2 Cov(R A, R B)}andX A = {σB2 - Cov(R A, R B)} / {σA2+ σB2 - 2 Cov(R A, R B)}Using the data from the problem yields,X A = 0.8125 andX B = 0.1875.a. Using the weights calculated above, the expected return on the minimum variance portfolio isE(R P) = 0.8125 E(R A) + 0.1875 E(R B)= 0.8125 (5%) + 0.1875 (10%)= 5.9375%b. Using the formula derived above, the weights areX A = 2 / 3 andX B = 1 / 3c. The variance of this portfolio is zero.σP 2= X A2 σA2 + X B2σB2+ 2 X A X B Cov(R A , R B)= (4 / 9) (0.01) + (1 / 9) (0.04) + 2 (2 / 3) (1 / 3) (-0.02)= 0This demonstrates that assets can be combined to form a risk-free portfolio.14.2%= 3.7%+β(7.5%) ⇒β = 1.40.25 = R f + 1.4 [R M– R f] (I)0.14 = R f + 0.7 [R M– R f] (II)(I) – (II)=0.11 = 0.7 [R M– R f] (III)[R M– R f ]= 0.1571Put (III) into (I) 0.25 = R f + 1.4[0.1571]R f = 3%[R M– R f ]= 0.1571R M = 0.1571 + 0.03= 18.71%a. = 4.9% + βi (9.4%)βD= Cov(R D, R M) / σM 2 = 0.0635 / 0.04326 = 1.468= 4.9 + 1.468 (9.4) = 18.70%Weights:X A = 5 / 30 = 0.1667X B = 10 / 30 = 0.3333X C = 8 / 30 = 0.2667X D = 1 - X A - X B - X C = 0.2333Beta of portfolio= 0.1667 (0.75) + 0.3333 (1.10) + 0.2667 (1.36) + 0.2333 (1.88)= 1.293= 4 + 1.293 (15 - 4) = 18.22%a. (i) βA= ρA,MσA / σMρA,M= βA σM / σA= (0.9) (0.10) / 0.12= 0.75(ii) σB= βB σM / ρB,M= (1.10) (0.10) / 0.40= 0.275(iii) βC= ρC,MσC / σM= (0.75) (0.24) / 0.10= 1.80(iv) ρM,M= 1(v) βM= 1(vi) σf= 0(vii) ρf,M= 0(viii) βf= 0b. SML:E(R i) = R f + βi {E(R M) - R f}= 0.05 + (0.10) βiSecurity βi E(R i)A 0.13 0.90 0.14B 0.16 1.10 0.16C 0.25 1.80 0.23Security A performed worse than the market, while security C performed better than the market.Security B is fairly priced.c. According to the SML, security A is overpriced while security C is under-priced. Thus, you could invest in security C while sell security A (if you currently hold it).a. The typical risk-averse investor seeks high returns and low risks. To assess thetwo stocks, find theReturns:State of economy ProbabilityReturn on A*Recession 0.1 -0.20 Normal 0.8 0.10 Expansion0.10.20* Since security A pays no dividend, the return on A is simply (P 1 / P 0) - 1. = 0.1 (-0.20) + 0.8 (0.10) + 0.1 (0.20) = 0.08 = 0.09 This was given in the problem.Risk:R A - (R A -)2 P ⨯ (R A -)2 -0.28 0.0784 0.00784 0.02 0.0004 0.00032 0.12 0.0144 0.00144 Variance 0.00960Standard deviation (R A ) = 0.0980βA = {Corr(R A , R M ) σ(R A )} / σ(R M ) = 0.8 (0.0980) / 0.10= 0.784βB = {Corr(R B , R M ) σ(R B )} / σ(R M ) = 0.2 (0.12) / 0.10= 0.24The return on stock B is higher than the return on stock A. The risk of stock B, as measured by itsbeta, is lower than the risk of A. Thus, a typical risk-averse investor will prefer stock B.b. = (0.7) + (0.3) = (0.7) (0.8) + (0.3) (0.09) = 0.083σP 2= 0.72 σA 2 + 0.32 σB 2 + 2 (0.7) (0.3) Corr (R A , R B ) σA σB = (0.49) (0.0096) + (0.09) (0.0144) + (0.42) (0.6) (0.0980) (0.12) = 0.0089635 σP = = 0.0947 c. The beta of a portfolio is the weighted average of the betas of the components of the portfolio. βP = (0.7) βA + (0.3) βB = (0.7) (0.784) + (0.3) (0.240) = 0.621Chapter 11:An Alternative View of Risk and Return: The Arbitrage Pricing Theorya. Stock A:()()R R R R R A A A m m Am A=+-+=+-+βεε105%12142%...Stock B:()()R R R R R B B m m Bm B=+-+=+-+βεε130%098142%...Stock C:()R R R R R C C C m m Cm C=+-+=+-+βεε157%137142%)..(.b.()[]()[]()[]()()()()()()[]()()CB A m cB A m c m B m A m CB A P 25.045.030.0%2.14R 1435.1%925.1225.045.030.0%2.14R 37.125.098.045.02.130.0%7.1525.0%1345.0%5.1030.0%2.14R 37.1%7.1525.0%2.14R 98.0%0.1345.0%2.14R 2.1%5.1030.0R 25.0R 45.0R 30.0R ε+ε+ε+-+=ε+ε+ε+-+++++=ε+-++ε+-++ε+-+=++= c.i.()R R R A B C =+-==+-==+-=105%1215%142%)1113%09815%142%)137%157%13715%142%168%..(..46%.(......ii.R P =+-=12925%1143515%142%)138398%..(..To determine which investment investor would prefer, you must compute the variance of portfolios created bymany stocks from either market. Note, because you know that diversification is good, it is reasonable to assume that once an investor chose the market in which he or she will invest, he or she will buy many stocks in that market.Known:E EF ====001002 and and for all i.i σσεε..Assume: The weight of each stock is 1/N; that is, X N i =1/for all i.If a portfolio is composed of N stocks each forming 1/N proportion of the portfolio, the return on the portfolio is 1/N times the sum of the returns on the N stocks. Recall that the return on each stock is 0.1+βF+ε.()()()()()()[]()()()()()()()[]()[]()[]()()[]()()()()()j i 2j i 22j i i 2222222222P P P P iP ,0.04Corr 0.01,Cov s =isvariance the ,N as limit In the ,Cov 1/N 1s 1/N s )(1/N 1/N F 2F E 1/N F E 0.10.1/N F 0.1E R E R E R Var 0.101/N 00.1E 1/N F E 0.11/N F 0.1E R E 1/N F 0.1F 0.1(1/N)R 1/N R εε+β=εε+β∞⇒εε-+ε+β=ε∑+εβ+β=ε+β=-ε+β+=-==+β+=ε+β+=ε∑+β+=ε+β+=ε+β+==∑∑∑∑∑∑∑∑()()()()()()Thus,F R f E R E R Var R Corr Var R Corr ii ip P p i j PijR 1i =++=++===+=+010*********002250040002500412212111222.........,,εεεεεεa.()()()()Corr Corr Var R Var R i j i j p pεεεε112212000225000225,,..====Since Var ()()R p 1 Var R 2p 〉, a risk averse investor will prefer to invest in the second market.b. Corr ()()εεεε112090i j j ,.,== and Corr 2i()()Var R Var R pp120058500025==..。

公司理财习题答案第六章Chapter 6: Some Alternative Investment Rules6.1 a. Payback period of Project A = 1 + ($7,500 - $4,000) / $3,500 = 2 yearsPayback period of Project B = 2 + ($5,000 - $2,500 -$1,200) / $3,000 = 2.43 yearsProject A should be chosen.b. NPV A = -$7,500 + $4,000 / 1.15 + $3,500 / 1.152 + $1,500 / 1.153 = -$388.96NPV B = -$5,000 + $2,500 / 1.15 + $1,200 / 1.152 + $3,000 / 1.153 = $53.83Project B should be chosen.6.2 a. Payback period = 6 + {$1,000,000 - ($150,000 ⨯ 6)} / $150,000 = 6.67 yearsYes, the project should be adopted.b. $150,000 11A= $974,259.010The discounted payback period = 11 + ($1,000,000 - $974,259) / ($150,000 / 1.112)= 11.54 yearsc. NPV = -$1,000,000 + $150,000 / 0.10 = $500,0006.3 a. Average Investment:($16,000 + $12,000 + $8,000 + $4,000 + 0) / 5 = $8,000Average accounting return:$4,500 / $8,000 = 0.5625 = 56.25%b. 1. AAR does not consider the timing of the cash flows, hence it does notconsider the time value of money.2. AAR uses an arbitrary firm standard as the decision rule.3. AAR uses accounting data rather than net cash flows.6.4 Average Investment = ($2,000,000 + 0) / 2 = $1,000,000Average net income = [$100,000 {(1 + g)5 - 1} / g] / 5= {$100,000A (1.075 - 1} / 0.07} / 5= $115,014.78AAR = $115,014.78 / $1,000,000 = 11.50%No, since the machine’s AAR is less than the firm’s cutoff AAR.6.5 a6.6PI = $40,000 7A / $160,000 = 1.04.015Since the PI exceeds one accept the project.6.7 The IRR is the discount rate at which the NPV = 0.-$3,000 + $2,500 / (1 + IRR A) + $1,000 / (1 + IRR A)2 = 0By trial and error, IRR A = 12.87%Since project B’s cash flows are two times of those of project A, the IRR B = IRR A =12.87%6.8 a. Solve x by trial and error:-$4,000 + $2,000 / (1 + x) + $1,500 / (1 + x)2 + $1,000 / (1 + x)3 = 0x = 6.93%b. No, since the IRR (6.93%) is less than the discount rate of 8%.6.9 Find the IRRs of project A analytically. Since the IRR is the discount rate that makes the NPVequal to zero, the following equation must hold.-$200 + $200 / (1 + r) + $800 / (1 + r)2 - $800 / (1 + r)3 = 0$200 [-1 + 1 / (1 + r)] - {$800 / (1 + r)2}[-1 + 1 / (1 + r)] = 0[-1 + 1 / (1 + r)] [$200 - $800 / (1 + r)2] = 0For this equation to hold, either [-1 + 1 / (1 + r)] = 0 or [$200 - $800 / (1 + r)2] = 0.Solve each of these factors for the r that would cause the factor to equal zero. Theresulting rates are the two IRRs for project A. They are either r = 0% or r = 100%.Note: By inspection you should have known that one of the IRRs of project A iszero. Notice that the sum of the un-discounted cash flows for project A is zero.Thus, not discounting the cash flows would yield a zero NPV. The discount ratewhich is tantamount to not discounting is zero.Here are some of the interactions used to find the IRR by trial and error.Sophisticated calculators can compute this rate without all of the tedium involved inthe trial-and-error method.NPV = -$150 + $50 / 1.3 + $100 / 1.32 + $150 / 1.33 = $15.91NPV = -$150 + $50 / 1.4 + $100 / 1.42 + $150 / 1.43 = -$8.60NPV = -$150 + $50 / 1.37 + $100 / 1.372 + $150 / 1.373 = -$1.89NPV = -$150 + $50 / 1.36 + $100 / 1.36 2 + $150 / 1.363 = $0.46NPV = -$150 + $50 / 1.36194 + $100 / 1.361942 + $150 / 1.361943= $0.0010NPV = -$150 + $50 / 1.36195 + $100 / 1.361952 + $150 / 1.361953= -$0.0013NPV = -$150 + $50 / 1.361944 + $100 / 1.3619442 + $150 / 1.3619443= $0.0000906Thus, the IRR is approximately 36.1944%.6.10 a. Solve r in the equation:$5,000 - $2,500 / (1 + r) - $2,000 / (1 + r)2 - $1,000 / (1 + r)3- $1,000 / (1 + r)4 = 0By trial and error,IRR = r = 13.99%b. Since this problem is the case of financing, accept the project if the IRR is less thanthe required rate of return.IRR = 13.99% > 10%Reject the offer.c. IRR = 13.99% < 20%Accept the offer.d. When r = 10%:NPV = $5,000 - $2,500 / 1.1 - $2,000 / 1.12 - $1,000 / 1.13 - $1,000 / 1.14= -$359.95When r = 20%:NPV = $5,000 - $2,500 / 1.2 - $2,000 / 1.22 - $1,000 / 1.23 - $1,000 / 1.24= $466.82Yes, they are consistent with the choices of the IRR rule since the signs of the cashflows change only once.公司理财习题答案第六章6.11 a. Project A:NPV = -$5,000 + $3,500 / (1 + r) + $3,500 / (1 + r)2 = 0IRR = r = 25.69%Project B:NPV = -$100,000 + $65,000 / (1 + r) + $65,000 / (1 + r)2 = 0IRR = r = 19.43%b. Choose project A because it has a higher IRR.c. The difference in scale is ignored.d. Apply the incremental IRR method.e.C0C1C2B - A -$95,000 $61,500 $61,500NPV = -$95,000 + $61,500 / (1 + r) + $61,500 / (1 + r)2 = 0Incremental IRR = r = 19.09%f. If the discount rate is less than 19.09%, choose project B.Otherwise, choose project A.g. NPV A = -$5,000 + $3,500 / 1.15 + $3,500 / 1.152 = $689.98NPV B = -$100,000 + $65,000 / 1.15 + $65,000 / 1.152 = $5,671.08Choose project B.6.12 a. PV A = {$5,000 / (0.12 - 0.04)} / 1.122 = $49,824.61PV B = (-$6,000 / 0.12) / 1.12 = -$44,642.86b. The IRR for project C must solve{$5,000 / (x - 0.04)} / (1 + x)2 + (-$6,000 / x) / (1 + x) = 0$5,000 / (x - 0.04) - $6,000 (1 + x) / x = 025 x2 + 3.17 x - 1 =0x = {-3.17 - (110.0489)0.5} / 50 or {-3.17 + (110.0489)0.5} / 50The relevant positive root is IRR = x = 0.1464 = 14.64%c. To arrive at the appropriate decision rule, we must graph the NPV as a function ofthe discount rate. At a discount rate of 14.64% the NPV is zero. To determine if thegraph is upward or downward sloping, check the NPV at another discount rate. At adiscount rate of 10% the NPV is $14,325.07 [= $68,870.52 - $54,545.54]. Thus, thegraph of the NPV is downward sloping. From the discussion in the text, if an NPVgraph is downward sloping, the project is an investing project. The correct decisionrule for an investing project is to accept the project if the discount rate is below14.64%.14.64% 10% rNPV0 $14,325.076.13 Generally, the statement is false. If the cash flows of project B occur early and the cashflows of project A occur late, then for a low discount rate the NPV of A can exceed theNPV of B. Examples are easy to construct.C0C1C2IRR NPV @ 0% A: -$1,000,000 $0 $1,440,000 0.20 $440,000B: -2,000,000 2,400,000 0 0.20 400,000 In one particular case, the statement is true for equally risky projects. If the lives of thetwo projects are equal and in every time period the cash flows of the project B are twice the cash flows of project A, then the NPV of project B will be twice as great as the NPV of project A for any discount rate between 0% and 20%.6.14 a. NPVα = $756.57 - $500 = $256.57NPVβ = $2,492.11 - $2,000 = $492.11b. Choose project beta.6.15 Although the profitability index is higher for project B than for project A, the NPV is theincrease in the value of the company that will occur if a particular project is undertaken.Thus, the project with the higher NPV should be chosen because it increases the value of the firm the most. Only in the case of capital rationing could the pension fund manager be correct.6.16 a. PI A = ($70,000 / 1.12 + $70,000 / 1.122) / $100,000 = 1.183PI B = ($130,000 / 1.12 + $130,000 / 1.122) / $200,000 = 1.099PI C = ($75,000 / 1.12 + $60,000 / 1.122) / $100,000 = 1.148b. NPV A = -$100,000 + $118,303.57 = $18,303.57NPV B = -$200,000 + $219,706.63 = $19,706.63NPV C = -$100,000 + $114,795.92 = $14,795.92c. Accept all three projects because PIs of all the three projects are greater than one.d. Based on the PI rule, project C can be eliminated because its PI is less than the oneof project A, while both have the same amount of the investment. We can computethe PI of the incremental cash flows between the two projects,Project C0C1C2PIB - A -$100,000 $60,000 $60,000 1.014We should take project B since the PI of the incremental cash flows is greater thanone.e. Project B has the highest NPV, while A has the next highest NPV.Take both projects A and B.6.17 a. The payback period is the time it takes to recoup the initial investment of a project.Accept any project that has a payback period that is equal to or shorter than thecompany’s standard payback period. Reject all other projects.b. The average accounting return (AAR) is defined asAverage project earnings ÷ Average book value of the investment.Accept projects for which the AAR is equal to or greater than the firm’s standard.Reject all other projects.c. The internal rate of return (IRR) is the discount rate which makes the net presentvalue (NPV) of the project zero. The accept / reject criteria is:公司理财习题答案第六章If C0 < 0 and all future cash flows are positive, accept the project if IRR ≥discount rate.If C0 < 0 and all future cash flows are positive, reject the project if IRR <discount rate.If C0 > 0 and all future cash flows are negative, accept the project if IRR ≤discount rate.If C0 > 0 and all future cash flows are negative, reject the project if IRR >discount rate.If the project has cash flows that alternate in sign, there is likely to be more thanone positive IRR. In that situation, there is no valid IRR accept / reject rule.d. The profitability index (PI) is defined as:(The present value of the cash flows subsequent to the initial investment ÷The initial investment)Accept any project for which the profitability index is equal to or greater thanone. Reject project for which that is not true.e. The net present value (NPV) is the sum of the present values of all project cashflows. Accept those projects with NPVs which are equal to or greater than zero.Rejects p roposals with negative NPVs.6.18 Let project A represent New Sunday Early Edition; and let project B represent NewSaturday Late Edition.a. Payback period of project A = 2 + ($1,200 - $1,150) / $450 = 2.11 yearsPayback period of project B = 2 + ($2,100 - $1,900) / $800 = 2.25 yearsBased on the payback period rule, you should choose project A.b. Project A:Average investment = ($1,200 + $0) / 2 = $600Depreciation = $400 / yearAverage income = [($600 - $400) + ($550 - $400) + ($450 - $400)] / 3= $133.33AAR = $133.33 / $600 = 22.22%Project B:Average investment = ($2,100 + $0) / 2 = $1,050Depreciation = $700 / yearAverage income = [($1,000 - $700) + ($900 - $700) + ($800 - $700)] / 3= $200AAR = $200 / $1,050 = 19.05%c. IRR of project A:-$1,200 + $600 / (1 + r) + $550 / (1 + r)2 + $450 / (1 + r)3 = 0IRR = r = 16.76%IRR of project B:-$2,100 + $1,000 / (1 + r) + $900 / (1 + r)2 + $800 / (1 + r)3 = 0IRR = r = 14.29%Project A has a greater IRR.d. IRR of project B-A:Incremental cash flowsYear 0 1 2 3B - A -$900 $400 $350 $350-$900 + $400 / (1 + r) + $350 / (1 + r)2 + $350 / (1 + r)3 = 0Incremental IRR = r = 11.02%If the required rate of return is greater than 11.02%, then choose project A.If the required rate of return is less than 11.02%, then choose project B.6.19 Let project A be Deepwater Fishing; let project B be New Submarine Ride.a. Project A:Year Discounted CF Cumulative CF0 -$600,000 -$600,0001 234,783 -365,2172 264,650 -100,5673 197,255Discounted payback period of project A = 2 + $100,567 / $197,255= 2.51 yearsProject B:Year Discounted CF Cumulative CF0 -$1,800,000 -$1,800,0001 869,565 -930,4352 529,301 -401,1343 591,765Discounted payback period of project B = 2 + $401,134 / $591,765= 2.68 yearsProject A should be chosen.b. IRR of project A:-$600,000 + $270,000 / (1 + r) + $350,000 / (1 + r)2 + $300,000 / (1 + r)3 = 0IRR = r = 24.30%IRR of project B:-$1,800,000 + $1,000,000 /(1 + r) + $700,000 / (1 + r)2 + $900,000 / (1 + r)3= 0IRR = r = 21.46%Based on the IRR rule, project A should be chosen since it has a greater IRR.c. Incremental IRR:Year 0 1 2 3B - A -$1,200,000 $730,000 $350,000 $600,000-$1,200,000 + $730,000 / (1 + r) + $350,000 / (1 + r)2 + $600,000 / (1 + r)3 = 0Incremental IRR = r = 19.92%Since the incremental IRR is greater than the required rate of return, 15%, chooseproject B.d. NPV A = -$600,000 + $270,000 / 1.15 + $350,000 / 1.152 + $300,000 / 1.153= $96,687.76公司理财习题答案第六章NPV B = -$1,800,000 + $1,000,000 / 1.15 + $700,000 / 1.152 + $900,000 / 1.153= $190,630.39Since NPV B > NPV A , choose project B.Yes, the NPV rule is consistent with the incremental IRR rule. 6.20 a. The IRR is the discount rate at which the NPV = 0-$600,000 + ()0r 1000,50$r 1%811%)8r (000,100$1111=+-⎥⎥⎦⎤⎢⎢⎣⎡⎪⎭⎫ ⎝⎛++--IRR ≈18.56%b.Yes, the mine should be opened since its IRR exceeds its required return of 10%.。

罗斯《公司理财》英文习题答案DOCchap014公司理财习题答案第十四章Chapter 14: Long-T erm Financing: An Introduction14.1 a. C om m on Stock A ccountPar V alue$135,430$267,715 shares ==b. Net capital from the sale of shares = Common Stock + Capital SurplusNet capital = $135,430 + $203,145 = $338,575Therefore, the average price is $338,575 / 67,715 = $5 per shareAlternate solution:Average price = Par value + Average capital surplus= $2 + $203,145 / 67,715= $5 per sharec. Book value = Assets - Liabilities = Equity= Common stock + Capital surplus + Retained earnings= $2,708,600Therefore, book value per share is $2,708,600 / 67,715= $40.14.2 a. Common stock = (Shares outstanding ) x (Par value)= 500 x $1= $500Total = $150,500b.Common stock (1500 shares outstanding, $1 par) $1,500Capital surplus* 79,000Retained earnings 100,000Total $180,500* Capital Surplus = Old surplus + Surplus on sale= $50,000 + ($30 - $1) x 1,000=$79,00014.3 a. Shareholder s’ equityCommon stock ($5 par value; authorized 500,000shares; issued and outstanding 325,000 shares)$1,625,000 Capital in excess of par* 195,000Retained earnings** 3,794,600Total $5,614,600*Capital surplus = 12% of Common Stock= (0.12) ($1,625,000)= $195,000**Retained earnings = Old retained earnings + Net income - Dividends= $3,545,000 + $260,000 - ($260,000)(0.04)= 3,794,600b. Shareholders’ equity$1,750,000Common stock ($5 par value; authorized 500,000shares; issued and outstanding 350,000 shares)Capital in excess of par* 170,000Retained earnings 3,794,600Total $5,714,600*Capital surplus is reduced by the below par sale, i.e. $195,000 - ($1)(25,000) =$170,00014.4 a. Under straight voting, one share equals one vote. Thus, to ensure the election of onedirector you must hold a majority of the shares. Since two million shares areoutstanding, you must hold more than 1,000,000 shares to have a majority of votes.b. Cumulative voting is often more easily understood through a story. Remember thatyour goal is to elect one board member of the seven who will be chosen today.Suppose the firm has 28 shares outstanding. You own 4 of the shares and one otherperson owns the remaining 24 shares. Under cumulative voting, the total number ofvotes equals the number of shares times the number of directors being elected,(28)(7) = 196. Therefore, you have 28 votes and the other stockholder has 168 votes.Also, suppose the other shareholder does not wish to have your favorite candidateon the board. If that is true, the best you can do to try to ensure electing onemember is to place all of your votes on your favorite candidate. To keep yourcandidate off the board, the other shareholder must have enough votes to elect allseven members who will be chosen. If the other shareholder splits her votes evenlyacross her seven favorite candidates, then eight people, your one favorite and herseven favorites, will all have the same number of votes. There will be a tie! If shedoes not split her votes evenly (for example 29 28 28 28 28 28 27) then yourcandidate will win a seat. To avoid a tie and assure your candidate of victory, youmust have 29 votes which means you must own more than 4 shares.Notice what happened. If seven board members will be elected and you want to becertain that one of your favorite candidates will win, you must have more than one-eighth of the shares. That is, the percentage of the shares you must have to win ismore than1.(The num ber of m em bers being elected The num ber you w ant to select)Also notice that the number of shares you need does not change if more than oneperson owns the remaining shares. If several people owned the remaining 168shares they could form a coalition and vote together.Thus, in the Unicorn election, you will need more than 1/(7+1) = 12.5% of theshares to elect one board member. You will need more than (2,000,000) (0.125) =250,000 shares.Cumulative voting can be viewed more rigorously. Use the facts from the Unicornelection. Under cumulative voting, the total number of votesequals the number of公司理财习题答案第十四章shares times the number of directors being elected, 2,000,000 x 7 = 14,000,000. Let x be the number of shares you need. The number of shares necessary is7x14,000,0007x7x250,000.>-==>> You will need more than 250,000 shares.14.5 She can be certain to have one of her candidate friends be elected under the cumulativevoting rule. The lowest percentage of shares she needs to own to elect at least one out of 6candidates is higher than 1/7 = 14.3%. Her current ownership of 17.3% is more thanenough to ensure one seat. If the voting rule is staggered as described in the question, shewould need to own more than 1/4=25% of the shares to elect one out of the three candidatesfor certain. In this case, she will not have enough shares.14.6 a. You currently own 120 shares or 28.57% of the outstanding shares. You need to control 1/3 of the votes, which requires 140 shares. You need just over 20 additional shares to elect yourself to the board.b. You need just over 25% of the shares, which is 250,000 shares. At $5 a share it willcost you $2,500,000 to guarantee yourself a seat on the board.14.7 The differences between preferred stock and debt are:a. The dividends of preferred stock cannot be deducted as interest expenses whendetermining taxable corporate income. From the individual investor’s point of view,preferred dividends are ordinary income for tax purposes. From corporate investors,80% of the amount they receive as dividends from preferred stock are exempt fromincome taxes.b. In liquidation, the seniority of preferred stock follows that of the debt and leads thatof the common stock.c. There is no legal obligation for firms to pay out preferred dividends as opposed tothe obligated payment of interest on bonds. Therefore, firms cannot be forced intodefault if a preferred stock dividend is not paid in a given year. Preferred dividendscan be cumulative or non-cumulative, and they can also be deferred indefinitely.14.8 Some firms can benefit from issuing preferred stock. The reasons can be:a. Public utilities can pass the tax disadvantage of issuing preferred stock on to theircustomers, so there is substantial amount of straight preferred stock issued byutilities.b. Firms reporting losses to the IRS already don’t have positive income for taxdeduction, so they are not affected by the tax disadvantage of dividend vs. interestpayment. They may be willing to issue preferred stock.c. Firms that issue preferred stock can avoid the threat of bankruptcy that exists withdebt financing because preferred dividends are not legal obligation as interestpayment on corporate debt.14.9 a. The return on non-convertible preferred stock is lower than the return on corporatebond for two reasons:i. Corporate investors receive 80% tax deductibility on dividends if they hold thestock. Therefore, they are willing to pay more for the stock; that lowers its return.ii. Issuing corporations are willing and able to offer higher returns on debt since theinterest on the debt reduces their tax liabilities. Preferred dividends are paid outof net income, hence they provide no tax shield.b. Corporate investors are the primary holders of preferred stock since, unlikeindividual investors, they can deduct 80% of the dividend when computing their taxliability. Therefore, they are willing to accept the lower return which the stockgenerates.14.10 The following table summarizes the main differencebetween debt and equity.Debt EquityRepayment is an obligation of the firm Yes NoGrants ownership of the firm No YesProvides a tax shield Yes NoLiquidation will result if not paid Yes NoCompanies often issue hybrid securities because of the potential tax shield and thebankruptcy advantage. If the IRS accepts the security as debt, the firm can use it as a tax shield. If the security maintains the bankruptcy and ownership advantages of equity, the firm has the best of both worlds.14.11 The trends in long-term financing in the United States were presented in the text. If CableCompany follows the trends, it will probably use 80% internal financing, net income of the project plus depreciation less dividends, and 20% external financing, long term debt and equity.。

CHAPTER 8MAKING CAPITAL INVESTMENT DECISIONSAnswers to Concepts Review and Critical Thinking Questions1. In this context, an opportunity cost refers to the value of anasset or other input that will be used in a project. The relevant cost is what the asset or input is actually worth today, not, for example, what it cost to acquire.2. a.Yes, the reduction in the sales of the company’s otherproducts, referred to as erosion, and should be treated as an incremental cash flow. These lost sales are included because they are a cost (a revenue reduction) that the firm must bear if it chooses to produce the new product.b. Yes, expenditures on plant and equipment should be treatedas incremental cash flows. These are costs of the new product line. However, if these expenditures have already occurred, they are sunk costs and are not included as incremental cash flows.c. No, the research and development costs should not be treatedas incremental cash flows. The costs of research and development undertaken on the product during the past 3 years are sunk costs and should not be included in the evaluation of the project. Decisions made and costs incurred in the past cannot be changed. They should not affect the decision to accept or reject the project.d. Yes, the annual depreciation expense should be treated as anincremental cash flow. Depreciation expense must be taken into account when calculating the cash flows related to a given project. While depreciation is not a cash expense that directly affects c ash flow, it decreases a firm’s netincome and hence, lowers its tax bill for the year. Because of this depreciation tax shield, the firm has more cash on hand at the end of the year than it would have had without expensing depreciation.e.No, dividend payments should not be treated as incrementalcash flows. A firm’s decision to pay or not pay dividends is independent of the decision to accept or reject any given investment project. For this reason, it is not an incremental cash flow to a given project. Dividend policy is discussed in more detail in later chapters.f.Yes, the resale value of plant and equipment at the end of aproject’s life should be treated as an incremental cashflow. The price at which the firm sells the equipment is a cash inflow, and any difference between the book value ofthe equipment and its sale price will create gains or losses that result in either a tax credit or liability.g.Yes, salary and medical costs for production employees hiredfor a project should be treated as incremental cash flows.The salaries of all personnel connected to the project must be included as costs of that project.3.I tem I is a relevant cost because the opportunity to sell theland is lost if the new golf club is produced. Item II is also relevant because the firm must take into account the erosion of sales of existing products when a new product is introduced. If the firm produces the new club, the earnings from the existing clubs will decrease, effectively creating a cost that must be included in the decision. Item III is not relevant because the costs of Research and Development are sunk costs. Decisions made in the past cannot be changed. They are not relevant to the production of the new clubs.4. For tax purposes, a firm would choose MACRS because it providesfor larger depreciation deductions earlier. These larger deductions reduce taxes, but have no other cash consequences.Notice that the choice between MACRS and straight-line is purely a time value issue; the total depreciation is the same;only the timing differs.5.It’s probably only a mild over-simplification. Currentliabilities will all be paid, presumably. The cash portion of current assets will be retrieved. Some receivables won’t be collected, and some inventory will not be sold, of course.Counterbalancing these losses is the fact that inventory sold above cost (and not replaced at the end of the project’s life) acts to increase working capital. These effects tend to offset one another.6.Management’s discretion to set the firm’s capital structureis applicable at the firm level. Since any one particular project could be financed entirely with equity, another project could be financed with debt, and the firm’s overall capital structure remains unchanged, financing costs are not relevant in the analysis of a project’s incremental cash flows according to the stand-alone principle.7. The EAC approach is appropriate when comparing mutuallyexclusive projects with different lives that will be replaced when they wear out. This type of analysis is necessary so that the projects have a common life span over which they can be compared; in effect, each project is assumed to exist over an infinite horizon of N-year repeating projects. Assuming that this type of analysis is valid implies that the project cash flows remain the same forever, thus ignoring the possible effects of, among other things: (1) inflation, (2) changing economic conditions, (3) the increasing unreliability of cash flow estimates that occur far into the future, and (4) the possible effects of future technology improvement that could alter the project cash flows.8. Depreciation is a non-cash expense, but it is tax-deductible onthe income statement. Thus depreciation causes taxes paid, an actual cash outflow, to be reduced by an amount equal to the depreciation tax shield, t c D. A reduction in taxes that would otherwise be paid is the same thing as a cash inflow, so the effects of the depreciation tax shield must be added in to get the total incremental aftertax cash flows.9. There are two particularly important considerations. The firstis erosion. Will the “essentialized”book simply displace copies of the existing book that would have otherwise been sold?This is of special concern given the lower price. The second consideration is competition. Will other publishers step in and produce such a product? If so, then any erosion is much less relevant. A particular concern to book publishers (and producers of a variety of other product types) is that the publisher only makes money from the sale of new books. Thus, it is important to examine whether the new book would displace sales of used books (good from the publisher’s perspective) or new books (not good). The concern arises any time there is an active market for used product.10.D efinitely. The damage to Porsche’s reputation is definitely afactor the company needed to consider. If the reputation was damaged, the company would have lost sales of its existing car lines.11.O ne company may be able to produce at lower incremental cost ormarket better. Also, of course, one of the two may have made a mistake!12.P orsche would recognize that the outsized profits would dwindleas more products come to market and competition becomes more intense.Solutions to Questions and ProblemsNOTE: All end-of-chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to space and readability constraints, when these intermediate steps are included in this solutions manual, rounding may appear to have occurred. However, the final answer for each problem is found without rounding during any step in the problem.Basic1. Using the tax shield approach to calculating OCF, we get:OCF = (Sales – Costs)(1 – t C) + t C DepreciationOCF = [($5 × 2,000 –($2 × 2,000)](1 –0.35) +0.35($10,000/5)OCF = $4,600So, the NPV of the project is:NPV = –$10,000 + $4,600(PVIFA17%,5)NPV = $4,7172. We will use the bottom-up approach to calculate the operatingcash flow for each year. We also must be sure to include the net working capital cash flows each year. So, the total cash flow each year will be:Year 1 Year 2 Year 3 Year 4 Sales Rs.7,000 Rs.7,000 Rs.7,000 Rs.7,000Costs 2,000 2,000 2,000 2,000Depreciation 2,500 2,500 2,500 2,500EBT Rs.2,500 Rs.2,500 Rs.2,500 Rs.2,500Tax 850 850 850 850Net income Rs.1,650 Rs.1,650 Rs.1,650 Rs.1,650OCF 0 Rs.4,150 Rs.4,150 Rs.4,150 Rs.4,150Capital spending –Rs.10,000 0 0 0 0NWC –200 –250 –300 –200 950 Incremental cashflow –Rs.10,200 Rs.3,900 Rs.3,850 Rs.3,950 Rs.5,100The NPV for the project is:NPV = –Rs.10,200 + Rs.3,900 / 1.10 + Rs.3,850 / 1.102+ Rs.3,950 / 1.103 + Rs.5,100 / 1.104NPV = Rs.2,978.333. U sing the tax shield approach to calculating OCF, we get:OCF = (Sales – Costs)(1 – t C) + t C DepreciationOCF = (R2,400,000 – 960,000)(1 – 0.30) + 0.30(R2,700,000/3) OCF = R1,278,000So, the NPV of the project is:NPV = –R2,700,000 + R1,278,000(PVIFA15%,3)NPV = R217,961.704.T he cash outflow at the beginning of the project will increasebecause of the spending on NWC. At the end of the project, the company will recover the NWC, so it will be a cash inflow. The sale of the equipment will result in a cash inflow, but we also must account for the taxes which will be paid on this sale. So, the cash flows for each year of the project will be:Year Cash Flow0 – R3,000,000 = –R2.7M – 300K1 1,278,0002 1,278,0003 1,725,000 = R1,278,000 + 300,000 + 210,000 + (0 – 210,000)(.30)And the NPV of the project is:NPV = –R3,000,000 + R1,278,000(PVIFA15%,2) + (R1,725,000 / 1.153) NPV = R211,871.465. First we will calculate the annual depreciation for theequipment necessary for the project. The depreciation amount each year will be:Year 1 depreciation = R2.7M(0.3330) = R899,100Year 2 depreciation = R2.7M(0.4440) = R1,198,800Year 3 depreciation = R2.7M(0.1480) = R399,600So, the book value of the equipment at the end of three years, which will be the initial investment minus the accumulated depreciation, is:Book value in 3 years = R2.7M –(R899,100 + 1,198,800 + 399,600)Book value in 3 years = R202,500The asset is sold at a gain to book value, so this gain is taxable.Aftertax salvage value = R202,500 + (R202,500 – 210,000)(0.30) Aftertax salvage value = R207,750To calculate the OCF, we will use the tax shield approach, so the cash flow each year is:OCF = (Sales – Costs)(1 – t C) + t C DepreciationYear Cash Flow0 – R3,000,000 = –R2.7M – 300K1 1,277,730.00 = (R1,440,000)(.70) + 0.30(R899,100)2 1,367,640.00 = (R1,440,000)(.70) + 0.30(R1,198,800)3 1,635,630.00 = (R1,440,000)(.70) + 0.30(R399,600) + R207,750 + 300,000Remember to include the NWC cost in Year 0, and the recovery of the NWC at the end of the project. The NPV of the project with these assumptions is:NPV = – R3.0M + (R1,277,730/1.15) + (R1,367,640/1.152) +(R1,635,630/1.153)NPV = R220,655.206. First, we will calculate the annual depreciation of the newequipment. It will be:Annual depreciation charge = €925,000/5Annual depreciation charge = €185,000The aftertax salvage value of the equipment is:Aftertax salvage value = €90,000(1 – 0.35)Aftertax salvage value = €58,500Using the tax shield approach, the OCF is:OCF = €360,000(1 – 0.35) + 0.35(€185,000)OCF = €298,750Now we can find the project IRR. There is an unusual feature that is a part of this project. Accepting this project means that we will reduce NWC. This reduction in NWC is a cash inflow at Year 0. This reduction in NWC implies that when the project ends, we will have to increase NWC. So, at the end of theproject, we will have a cash outflow to restore the NWC to its level before the project. We also must include the aftertax salvage value at the end of the project. The IRR of the project is:NPV = 0 = –€925,000 + 125,000 + €298,750(PVIFA IRR%,5) + [(€58,500 – 125,000) / (1+IRR)5]IRR = 23.85%7. First, we will calculate the annual depreciation of the newequipment. It will be:Annual depreciation = £390,000/5Annual depreciation = £78,000Now, we calculate the aftertax salvage value. The aftertax salvage value is the market price minus (or plus) the taxes on the sale of the equipment, so:Aftertax salvage value = MV + (BV – MV)t cVery often, the book value of the equipment is zero as it is in this case. If the book value is zero, the equation for the aftertax salvage value becomes:Aftertax salvage value = MV + (0 – MV)t cAftertax salvage value = MV(1 – t c)We will use this equation to find the aftertax salvage value since we know the book value is zero. So, the aftertax salvage value is:Aftertax salvage value = £60,000(1 – 0.34)Aftertax salvage value = £39,600Using the tax shield approach, we find the OCF for the project is:OCF = £120,000(1 – 0.34) + 0.34(£78,000)OCF = £105,720Now we can find the project NPV. Notice that we include the NWC in the initial cash outlay. The recovery of the NWC occurs in Year 5, along with the aftertax salvage value.NPV = –£390,000 –28,000 + £105,720(PVIFA10%,5) + [(£39,600 + 28,000) / 1.15]NPV = £24,736.268. To find the BV at the end of four years, we need to find theaccumulated depreciation for the first four years. We could calculate a table with the depreciation each year, but an easier way is to add the MACRS depreciation amounts for each of the first four years and multiply this percentage times the cost of the asset. We can then subtract this from the asset cost. Doing so, we get:BV4 = $9,300,000 – 9,300,000(0.2000 + 0.3200 + 0.1920 + 0.1150) BV4 = $1,608,900The asset is sold at a gain to book value, so this gain is taxable.Aftertax salvage value = $2,100,000 + ($1,608,900 –2,100,000)(.40)Aftertax salvage value = $1,903,5609. We will begin by calculating the initial cash outlay, that is,the cash flow at Time 0. To undertake the project, we will have to purchase the equipment and increase net working capital. So, the cash outlay today for the project will be:Equipment –€2,000,000NWC –100,000Total –€2,100,000Using the bottom-up approach to calculating the operating cash flow, we find the operating cash flow each year will be:Sales €1,200,000Costs 300,000Depreciation 500,000EBT €400,000Tax 140,000Net income €260,000The operating cash flow is:OCF = Net income + DepreciationOCF = €260,000 + 500,000OCF = €760,000To find the NPV of the project, we add the present value of the project cash flows. We must be sure to add back the net working capital at the end of the project life, since we are assuming the net working capital will be recovered. So, the project NPV is:NPV = –€2,100,000 + €760,000(PVIFA14%,4) + €100,000 / 1.144NPV = €173,629.3810.W e will need the aftertax salvage value of the equipment tocompute the EAC. Even though the equipment for each product hasa different initial cost, both have the same salvage value. Theaftertax salvage value for both is:Both cases: aftertax salvage value = $20,000(1 –0.35) = $13,000To calculate the EAC, we first need the OCF and NPV of each option. The OCF and NPV for Techron I is:OCF = – $34,000(1 – 0.35) + 0.35($210,000/3) = $2,400NPV = –$210,000 + $2,400(PVIFA14%,3) + ($13,000/1.143) = –$195,653.45EAC = –$195,653.45 / (PVIFA14%,3) = –$84,274.10And the OCF and NPV for Techron II is:OCF = – $23,000(1 – 0.35) + 0.35($320,000/5) = $7,450NPV = –$320,000 + $7,450(PVIFA14%,5) + ($13,000/1.145) = –$287,671.75EAC = –$287,671.75 / (PVIFA14%,5) = –$83,794.05The two milling machines have unequal lives, so they can only be compared by expressing both on an equivalent annual basis, which is what the EAC method does. Thus, you prefer the Techron II because it has the lower (less negative) annual cost.Intermediate11.F irst, we will calculate the depreciation each year, which willbe:D1 = ¥480,000(0.2000) = ¥96,000D2 = ¥480,000(0.3200) = ¥153,600D3 = ¥480,000(0.1920) = ¥92,160D4 = ¥480,000(0.1150) = ¥55,200The book value of the equipment at the end of the project is:BV4= ¥480,000 –(¥96,000 + 153,600 + 92,160 + 55,200) = ¥83,040The asset is sold at a loss to book value, so this creates a tax refund.After-tax salvage value = ¥70,000 + (¥83,040 – 70,000)(0.35) = ¥74,564.00So, the OCF for each year will be:OCF1 = ¥160,000(1 – 0.35) + 0.35(¥96,000) = ¥137,600.00OCF2 = ¥160,000(1 – 0.35) + 0.35(¥153,600) = ¥157,760.00OCF3 = ¥160,000(1 – 0.35) + 0.35(¥92,160) = ¥136,256.00OCF4 = ¥160,000(1 – 0.35) + 0.35(¥55,200) = ¥123,320.00Now we have all the necessary information to calculate the project NPV. We need to be careful with the NWC in this project.Notice the project requires ¥20,000 of NWC at the beginning, and ¥3,000 more in NWC each successive year. We will subtract the ¥20,000 from the initial cash flow, and subtract ¥3,000 each year from the OCF to account for this spending. In Year 4, we will add back the total spent on NWC, which is ¥29,000. The ¥3,000 spent on NWC capital during Year 4 is irrelevant. Why?Well, during this year the project required an additional ¥3,000, but we would get the money back immediately. So, thenet cash flow for additional NWC would be zero. With all this, the equation for the NPV of the project is:NPV = –¥480,000 –20,000 + (¥137,600 –3,000)/1.14 + (¥157,760 – 3,000)/1.142+ (¥136,256 –3,000)/1.143+ (¥123,320 + 29,000 + 74,564)/1.144NPV = –¥38,569.4812.I f we are trying to decide between two projects that will notbe replaced when they wear out, the proper capital budgeting method to use is NPV. Both projects only have costs associated with them, not sales, so we will use these to calculate the NPV of each project. Using the tax shield approach to calculate the OCF, the NPV of System A is:OCF A = –元120,000(1 – 0.34) + 0.34(元430,000/4)OCF A = –元42,650NPV A = –元430,000 –元42,650(PVIFA20%,4)NPV A = –元540,409.53And the NPV of System B is:OCF B = –元80,000(1 – 0.34) + 0.34(元540,000/6)OCF B = –元22,200NPV B = –元540,000 –元22,200(PVIFA20%,6)NPV B = –元613,826.32If the system will not be replaced when it wears out, then System A should be chosen, because it has the more positive NPV.13.If the equipment will be replaced at the end of its useful life,the correct capital budgeting technique is EAC. Using the NPVs we calculated in the previous problem, the EAC for each system is:EAC A = –元540,409.53 / (PVIFA20%,4)EAC A = –元208,754.32EAC B = –元613,826.32 / (PVIFA20%,6)EAC B = –元184,581.10If the conveyor belt system will be continually replaced, we should choose System B since it has the more positive NPV.14.S ince we need to calculate the EAC for each machine, sales areirrelevant. EAC only uses the costs of operating the equipment, not the sales. Using the bottom up approach, or net income plus depreciation, method to calculate OCF, we get:Machine A Machine BVariable costs –₪3,150,000 –₪2,700,000Fixed costs –150,000 –100,000Depreciation –350,000 –500,000EBT –₪3,650,000 –₪3,300,000Tax 1,277,500 1,155,000Net income –₪2,372,500 –₪2,145,000+ Depreciation 350,000 500,000OCF –₪2,022,500 –₪1,645,000The NPV and EAC for Machine A is:NPV A = –₪2,100,000 –₪2,022,500(PVIFA10%,6) NPV A = –₪10,908,514.76EAC A = –₪10,908,514.76 / (PVIFA10%,6)EAC A = –₪2,504,675.50And the NPV and EAC for Machine B is:NPV B = –₪4,500,000 – 1,645,000(PVIFA10%,9)NPV B = –₪13,973,594.18EAC B = –₪13,973,594.18 / (PVIFA10%,9)EAC B = –₪2,426,382.43You should choose Machine B since it has a more positive EAC.15.W hen we are dealing with nominal cash flows, we must be carefulto discount cash flows at the nominal interest rate, and we must discount real cash flows using the real interest rate.Project A’s cash flows are in real terms, so we need to find the real interest rate. Using the Fisher equation, the real interest rate is:1 + R = (1 + r)(1 + h)1.15 = (1 + r)(1 + .04)r = .1058 or 10.58%So, the NPV of Project A’s real cash flows, discounting at the real interest rate, is:NPV = –฿40,000 + ฿20,000 / 1.1058 + ฿15,000 / 1.10582 + ฿15,000 / 1.10583NPV = ฿1,448.88Project B’s cash flow are in nominal terms, so the NPV discount at the nominal interest rate is:NPV = –฿50,000 + ฿10,000 / 1.15 + ฿20,000 / 1.152+ ฿40,000 /1.153NPV = ฿119.17We should accept Project A if the projects are mutually exclusive since it has the highest NPV.16.T o determine the value of a firm, we can simply find thepre sent value of the firm’s future cash flows. No depreciation is given, so we can assume depreciation is zero. Using the tax shield approach, we can find the present value of the aftertax revenues, and the present value of the aftertax costs. The required return, growth rates, price, and costs are all given in real terms. Subtracting the costs from the revenues will give us the value of the firm’s cash flows. We must calculate the present value of each separately since each is growing at a different rate. First, we will find the present value of the revenues. The revenues in year 1 will be the number of bottles sold, times the price per bottle, or:Aftertax revenue in year 1 in real terms = (2,000,000 ×$1.50)(1 – 0.34)Aftertax revenue in year 1 in real terms = $1,650,000Revenues will grow at six percent per year in real terms forever. Apply the growing perpetuity formula, we find the present value of the revenues is:PV of revenues = C1 / (R–g)PV of revenues = $1,650,000 / (0.10 – 0.06)PV of revenues = $41,250,000The real aftertax costs in year 1 will be:Aftertax costs in year 1 in real terms = (2,000,000 ×$0.65)(1 – 0.34)Aftertax costs in year 1 in real terms = $858,000Costs will grow at five percent per year in real terms forever.Applying the growing perpetuity formula, we find the present value of the costs is:PV of costs = C1 / (R–g)PV of costs = $858,000 / (0.10 – 0.05)PV of costs = $17,160,000Now we can find the value of the firm, which is:Value of the firm = PV of revenues – PV of costsValue of the firm = $41,250,000 – 17,160,000Value of the firm = $24,090,00017.To calculate the nominal cash flows, we simple increase eachitem in the income statement by the inflation rate, except for depreciation. Depreciation is a nominal cash flow, so it does not need to be adjusted for inflation in nominal cash flow analysis. Since the resale value is given in nominal terms as of the end of year 5, it does not need to be adjusted for inflation. Also, no inflation adjustment is needed for either the depreciation charge or the recovery of net working capital since these items are already expressed in nominal terms. Note that an increase in required net working capital is a negative cash flow whereas a decrease in required net working capital isa positive cash flow. The nominal aftertax salvage value is:Market price $30,000Tax on sale –10,200Aftertax salvage value $19,800Remember, to calculate the taxes paid (or tax credit) on the salvage value, we take the book value minus the market value, times the tax rate, which, in this case, would be:Taxes on salvage value = (BV – MV)t CTaxes on salvage value = ($0 – 30,000)(.34)Taxes on salvage value = –$10,200Now we can find the nominal cash flows each year using the income statement. Doing so, we find:Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Sales $200,000 $206,000 $212,180 $218,545 $225,102Expenses 50,000 51,500 53,045 54,636 56,275Depreciation 50,000 50,000 50,000 50,000 50,000EBT $100,000 $104,500 $109,135 $113,909 $118,826Tax 34,000 35,530 37,106 38,729 40,401Net income $66,000 $68,970 $72,029 $75,180 $78,425OCF $116,000 $118,970 $122,029 $125,180 $128,425Capital spending –$250,000 $19,800NWC –10,000 10,000Total cash flow –$260,000 $116,000 $118,970 $122,029 $125,180 $158,22518.T he present value of the company is the present value of thefuture cash flows generated by the company. Here we have real cash flows, a real interest rate, and a real growth rate. The cash flows are a growing perpetuity, with a negative growth rate. Using the growing perpetuity equation, the present value of the cash flows are:PV = C1 / (R–g)PV = $120,000 / [.11 – (–.07)]PV = $666,666.6719.T o find the EAC, we first need to calculate the NPV of theincremental cash flows. We will begin with the aftertax salvage value, which is:Taxes on salvage value = (BV – MV)t CTaxes on salvage value = (€0 – 10,000)(.34)Taxes on salvage value = –€3,400Market price €10,000Tax on sale –3,400Aftertax salvage value €6,600Now we can find the operating cash flows. Using the tax shield approach, the operating cash flow each year will be:OCF = –€5,000(1 – 0.34) + 0.34(€45,000/3)OCF = €1,800So, the NPV of the cost of the decision to buy is:NPV = –€45,000 + €1,800(PVIFA12%,3) + (€6,600/1.123)NPV = –€35,987.95In order to calculate the equivalent annual cost, set the NPV of the equipment equal to an annuity with the same economic life. Since the project has an economic life of three years and is discounted at 12 percent, set the NPV equal to a three-year annuity, discounted at 12 percent.EAC = –€35,987.95 / (PVIFA12%,3)EAC = –€14,979.8020.W e will find the EAC of the EVF first. There are no taxes sincethe university is tax-exempt, so the maintenance costs are the operating cash flows. The NPV of the decision to buy one EVF is:NPV = –₩8,000 –₩2,000(PVIFA14%,4)NPV = –₩13,827.42In order to calculate the equivalent annual cost, set the NPV of the equipment equal to an annuity with the same economic life. Since the project has an economic life of four years and is discounted at 14 percent, set the NPV equal to a three-year annuity, discounted at 14 percent. So, the EAC per unit is:EAC = –₩13,827.42 / (PVIFA14%,4)EAC = –₩4,745.64Since the university must buy 10 of the word processors, the total EAC of the decision to buy the EVF word processor is:Total EAC = 10(–₩4,745.64)Total EAC = –₩47,456.38Note, we could have found the total EAC for this decision by multiplying the initial cost by the number of word processors needed, and multiplying the annual maintenance cost of each by the same number. We would have arrived at the same EAC.We can find the EAC of the AEH word processors using the same method, but we need to include the salvage value as well. Thereare no taxes on the salvage value since the university is tax-exempt, so the NPV of buying one AEH will be:NPV = –₩5,000 –₩2,500(PVIFA14%,3) + (₩500/1.143)NPV = –₩10,466.59So, the EAC per machine is:EAC = –₩10,466.59 / (PVIFA14%,3)EAC = –₩4,508.29Since the university must buy 11 of the word processors, the total EAC of the decision to buy the AEH word processor is:Total EAC = 11(–₩4,508.29)Total EAC = –₩49,591.21The university should buy the EVF word processors since the EAC is lower. Notice that the EAC of the AEH is lower on a per machine basis, but because the university needs more of these word processors, the total EAC is higher.21.W e will calculate the aftertax salvage value first. Theaftertax salvage value of the equipment will be:Taxes on salvage value = (BV – MV)t CTaxes on salvage value = (₫0 – 100,000)(.34)Taxes on salvage value = –₫34,000Market price ₫100,000Tax on sale –34,000Aftertax salvage value ₫66,000Next, we will calculate the initial cash outlay, that is, the cash flow at Time 0. To undertake the project, we will have to purchase the equipment. The new project will decrease the net working capital, so this is a cash inflow at the beginning of the project. So, the cash outlay today for the project will be:Equipment –₫500,000NWC 100,000Total –₫400,000Now we can calculate the operating cash flow each year for the project. Using the bottom up approach, the operating cash flow will be:Saved salaries ₫120,000Depreciation 100,000EBT ₫20,000。

罗斯《公司理财》英⽂习题答案DOCchap022公司理财习题答案第⼆⼗⼆章Chapter 22: Options and Corporate Finance22.1 a. An option is a contract which gives its owner the right to buy or sell an underlyingasset at a fixed price on or before a given date.b. Exercise is the act of buying or selling the underlying asset under the terms of theoption contract.c. The strike price is the fixed price at which the option holder can buy or sell theunderlying asset. The strike price is also called the exercise price.d. The expiration date is the maturity date of the option. It is the last date on which anAmerican option can be exercised. It is the only date on which a European optioncan be exercised.e. A call is an option contract, which gives its owner the right to buy an underlyingasset at a fixed price on or before a given date.f. A put is an option contract, which gives its owner the right to sell an underlyingasset at a fixed price on or before a given date.22.2 American options can be exercised on any date up to and including the exercise date. A European option can be exercised only on the expiration date.22.3 The lower bound of the value of the put is Max {E - S, 0} = $40 - $35 = $5. Since theoption is selling for $4.5, the best strategy is (1) buy more put options at $4.5 and (2)exercise them to get arbitrage.22.4 a. It can be exercised on any date up to and including the expiration date.b. It can be exercised only on February 18 of next year.c. The option is not worthless.22.5 PayoffS < $80 S = $80 S > $80 Short 10 puts -10 ($80 - S) $0 0Long 5 calls $0 $0 5 (S - $80)Total payoff -10 ($80 - S) $0 5 (S - $80)22.6 a. Payoff = $55 - $50 = $5b. Payoff = max {$45 - $50, $0} = $0c.22.7 a. Payoff = $0b. Payoff = $50 - $45 = $5c22.8a. S = $65 S = $72 S = $80 Long 2 calls $0 200($72-$70)=$400 200($80-$70)=$2,000 Long 1 put 100($75-$65)=$1,000 100($75-$72)=$300 $0Total payoff$1,000 $700 $2,000b.PayoffValue of stock at expiration$50$0公司理财习题答案第⼆⼗⼆章S < $70 $70 < S < $75 S $75 Long 2 calls $0 200(S-$70) 200(S-$70)Long 1 put 100($75-S) 100($75-S) $0Total payoff 100($75-S) 100(S-$65) 200(S-$70)22.9 a. You would exercise the call option contract by paying the strike price of $100/share and receiving stock worth $130 / share. The total profit from the contract is ($130 - 100) x 100 = $3,000.b. If the stock price is lower than the strike price, the option will be expired unexercised.22.10 Assume the options will expire in one year, apply the put-call parity formula.S + P - C = PV(E)S = -$2 + $8 + $40 / 1.1= $42.3622.11 a. To eliminate the risk of the put, sell a call and buy stock. Buying stock makes stock available to you in the event that its price falls. If the price falls below the exercise price, the put will be exercised against you. The call provides additional income if the price of the stock rises above the exercise price. The combination,buy stock, buy a put and sell a call, ensures that the net payoff is the samewhether the stock price rises to $172 or falls to $138.b. Payoffs at expirationS = $172 S = $138 Buy stock $172 $138Buy put expires give up stock worth $138,receive $160 Sell call give up stock worth $172,receive $160Net payoff $160 $16022.12 a. You should buy the call and exercise it immediately.b.Profit = ($60 - $50) - $8 = $2c. The lower bound on the price of American calls is[Stock price - Exercise price].d. Upper bound = stock price because no one would be willing to pay more than the stock price for the right to receive the stock.21.13Factors determining the value of an American call:1.Strike price: The value of an American call must be at least the difference between the stock price and the exercise price [S - E]. For a given stock price, a higher exercise price will reduce the value of the call.2.Expiration date: The time to expiration of a call affects the price of the option. Compare two calls, which are identical except for the time to expiration. The longer-term option has all the rights and benefits of the shorter-term option, plus more. It has all of those benefits and rights for a longer period of time. Thus, asthe time to expiration increases, the value of the call increases.3.Stock price: The value of an American call must be at least the difference between the stock price and the exercise price [S - E]. For a given exercise price, a higher stock price will increase the value of the call.4.Variability of the price of the underlying asset: The higher the variability of the price of the underlying asset is, the higher is the probability that the call will be in the money at the expiration date. Thus, higher variability of the asset’s price will enhance the option’s value.5.Interest rate: If you buy a call, you do not have to pay the strike price until the expiration date. The delay in the payment has value. As interest rates rise, the delayed payment has more value. To convince yourself, consider what else you can do with the strike price until the expiration date (your opportunity cost). You can put that money in an account and earn interest on the amount until the expiration date. If the interest rate increases, you will earn more interest.21.14Factors determining the value of an American put:1.Strike price: The value of an American put must be at least the difference betweenthe exercise price and the stock price [E - S]. For a given stock price, a higherexercise price will increase the value of the put.公司理财习题答案第⼆⼗⼆章2.Expiration date: The time to expiration of a put affects the price of the option.Compare two puts which are identical except for the time to expiration. Thelonger-term option has all the rights and benefits of the shorter-term option, plusmore. It has all of those benefits and rights for a longer period of time. Thus, asthe time to expiration increases, the value of the put increases.3.Stock price: The value of an American put must be at least the difference betweenthe exercise price and the stock price [E - S]. For a given exercise price, a higherstock price will reduce the value of the put.4. Variability of the price of the underlying asset: The higher the variability of theprice of the underlying asset is, the higher is the probability that the put will be int he money at the expiration date. Thus, higher variability of the asset’s price willenhance the option’s value.5. Interest rate: If you buy a put, you have the right to sell the stock for a fixed pricein the future. The present value of the delayed receipt decreases as the interest raterises. Thus, if the interest rate rises, the value of the put will fall.22.15 a. An increase in the risk of the stock implies an increase in the volatility of the stockprice. As the volatility of the stock price rises, the value of a call increases. Callholders gain only if the stock price is greater than the exercise price. Call holdersdo not lose if the stock price is less than the exercise price. The volatility increasesthe probability that the call will be in the money.b.An increase in the risk of the stock implies an increase in the volatility of the stockprice. As the volatility of the stock price rises, the value of a put increases. Putholders gain only if the stock price is less than the exercise price. Put holders donot lose if the stock price is greater than the exercise price. The volatility increasesthe probability that the put will be in the money.22.16 Value the call by examining the value of the investment combination, which duplicates thepayoffs of the call. The investment strategy, which duplicates the payoffs of the call, is buy stock and borrow money. Payoffs of buying a call: S T = $120 S T = $95Call (A contract covers 100 shares) 100 ($120 - $112) ExpiresPayoff = $800 = $0Payoffs of the strategy:Buy 32 shares of the stock 32 ? $120 32 ? $95= $3,840 = $3,040 Borrow $3,012.26* -$3,040 -$3,040Net payoff $800 $0* The net payoffs of the duplicating strategy must be the same as the payoffs of the call.To have the payoff be $800 when the stock price is $120, the repayment of the loan and its interest must be $3,040. If the annual interest rate is 10%, then the interest rate applicable for the five week life of the call is (1.10)5/52 - 1 = 0.00921. Thus, the amount which youmust borrow to be sure you repay $3,040 is $3,012.26 [= $3,040 / 1.00921].To prevent arbitrage, the value of the call must be equal to the value of setting up thisstrategy. The cost today of purchasing 32 shares of stock is 32 ? $96 = $3,072. In addition you will borrow $3,012.26. The borrowing generates a cash inflow. The cost ofestablishing this strategy is $3,072 - $3,012.26 = $59.74. $59.74 is the cost of setting up a strategy, which duplicates the contract. Since the contract covers 100 shares, each call is worth $0.5974 [= $59.74 / 100].22.17Payoff at expiration S = $25 S = $351. Call $0 $3 ? 100 = $3002. Stock (N shares)Borrow ($25N/1.05) 25 N-25 N$35N-$25NNet payoff $0 $10NDuplicating amount = $25 N / 1.05where $10 N = $300N = 30 sharesBorrow $25 ? 30 shares / 1.05 = $714.29.Thus, buying one call contract= (1) buy 30 shares of stock $900(2) borrow $714.29 -$714.29$185.71Call option value = $185.71Call price per share = $1.857From put-call parity,P = C + PV(E) - S= $1.857 + $32 / 1.05 - $30 = $2.33322.18Payoff at expiration S T = $40 S T = $601. Call $0 100 ($60 - $50)= $1,0002. Buy N shares Borrow $40N-$40N$60N-$40NNet payoff $0 $20N To equate, $20N = $1,000N = 50 sharesThus, borrowing amount = $40 ? 50 / 1.09 = $1,834.86Call value = Value of 50 shares + Borrowing $1,834.86= 50 ? $55 - $1,834.86= $915.14Each call is worth $9.1514.公司理财习题答案第⼆⼗⼆章22.19 d1= [ ln ($62 / $70) + (0.05 + 0.35 / 2) ? (4 / 52)] / [0.35 ? (4 / 52)]0.5 = -0.6342d2= -0.6342 - [0.35 ? (4 / 52)]0.5= -0.7982N(d1) = 0.2643N(d2) = 0.2119C = [$62 ? N(d1)] - [$70 e-(0.05)(4/52)? N(d2)]= [$62 (0.2643)] - [$70 e-(0.05)(4/52) (0.2119)]= $1.6122.20 d1= [ ln ($52 / $48) + (0.05 + 0.02) ? (1 / 3)] / [0.04 ? (1 / 3)]0.5= 0.8953d2= 0.8953 - [0.04 ? (1 / 3)]0.5= 0.7798N(d1) = 0.8147N(d2) = 0.7822C = [$52 ? 0.8147] - [$48 e-(0.05)(1/3)? 0.7822] = $5.439422.21 a. d1= [ ln ($45 / $52) + (0.065 + 0.4 / 2) ? 0.5] / [0.4 ? 0.5]0.5= -0.0270d2= -0.0270 - [0.4 ? 0.5]0.5= -0.4742N(d1) = 0.4880N(d2) = 0.3192C = $45 ? 0.4880- $52 e-(0.065)(0.5)? 0.3192= $5.89b. Since the time period is only six months, the exponent used in the calculation of the PV of the exercise price is 0.5.P = C + PV(E) - S= $5.89 + $52 / (1 + 0.065)0.5 - $45= $11.2822.22 a. d1= [ ln ($70 / $90) + (0.06 + 0.25 / 2) ? 0.5] / [0.25 ? 0.5]0.5= -0.4492d2= -0.4492 - [0.25 ? 0.5]0.5= -0.8028N(d1) = 0.3267N(d2) = 0.2111C = $70 ? 0.3267 - $90 e-(0.06)(0.5)? 0.2111= $4.4315b. P = C + PV(E) - S= $4.4315 + $90 / (1 + 0.06)0.5 - $70= $21.847222.23 a. d1= [ ln ($37 / $35) + (0.07 + 0.004 / 2)] / 0.0632= 2.0185d2= 2.0185 - 0.0632= 1.9553N(d1) = 0.9782N(d2) = 0.9747C = $37 ? 0.9782 - $35 e-0.07? 0.9747= $4.3853b. d1= [ ln ($37 / $35) + (0.07 + 0.0064 / 2)] / 0.08= 1.6096d2= 1.6096 - 0.08= 1.5296N(d1) = 0.9463N(d2) = 0.9369C = $37 ? 0.9463 - $35 e-0.07? 0.9369c. d1= [$0 + (0.07 + 0.0064 / 2)] / 0.08= 0.915d2= 0.915 - 0.08= 0.835N(d1) = 0.8199N(d2) = 0.7981C = $35 ? 0.8199 - $35 e-0.07? 0.7981= $2.651522.24 S = $27E = $25t = 120 / 365σ2= 0.0576r f= 0.07d1= [ ln ($27 / $25) + (0.07 + 0.0576 / 2) ? (120 / 365)] / [0.0576 ? (120 / 365)]0.5 = 0.7953d2= 0.7953 - [0.0576 ? (120 / 365)]]0.5= 0.6577N(d1) = 0.7867N(d2) = 0.7447C = $27 ? 0.7867 - $25 e-(0.07)(120/365)? 0.7447= $3.047022.25 For a firm with debt, shares of stock can be thought of as call options on the assets of thefirm due to the limited liability of stock. If the value of the assets exceeds the value of the debt, the stockholders will pay the debt-holders and enjoy the benefits of ownership of the remaining assets. The stockholders have the property rights over the assets in excess of the debt.If the value of the assets of the firm is less than the value of the debt, the stockholders will simply give the bondholders the assets of the firm. The shareholders will walk awayowning nothing.Thus, the return to the shareholders at the end of a period is the maximum between zeroand the excess of assets over debt, [V - B] where V is the value of the assets of the firmand B is the value of the debt. This payoff is exactly the payoffs of a call where V isanalogous to the stock price and B is analogous to the exercise price.22.26 The equity of the firm is regarded as a call option.公司理财习题答案第⼆⼗⼆章Payoff at expiration (million) $250 $650 1. Call $0 $3502. Buy N shares Borrow $250N$650N-$250NNet payoff $0 $400N To equate, $400N = $350N = 0.875 shares of assets.Thus, borrowing amount = $250 ? 0.875 / 1.07 = $204.44 millionCall value = Value of 0.875 shares of the asset + Borrowing $204.44 million = $350 million - $204.44 million = $145.56 millionThe value of the equity= $145.56 millionThe value of the debt= $400 - $145.56= $254.44 million22.27Payoff at expiration (million) $100 $8001. Call $0 $5002. Buy N shares Borrow $100N-$100N$800N-$100NNet payoff $0 $700N To equate, $700N = $550N = (5 / 7) shares of assets.Thus, borrowing amount = $100 ? (5 / 7) / 1.07 = $66.76 millionCall value = Value of (5 / 7) shares of the asset + Borrowing $66.76 million = $285.71 million - $66.76 million = $218.95 millionThe value of the equity= $218.95 millionThe value of the debt= $400 - $218.95= $181.05 millionThus, bondholders prefer the less risky project.。

英文版罗斯公司理财习题答案Chap001CHAPTER 1INTRODUCTION TO CORPORATE FINANCEAnswers to Concept Questions1.The three basic forms are sole proprietorships, partnerships, and corporations. The advantages anddisadvantages of sole proprietorships and partnerships are: Disadvantages: unlimited liability, limited life, difficulty in transferring ownership, hard to raise capital funds. Some advantages: simpler, less regulation, the owners are also the managers, sometimes personal tax rates are better than corporate tax rates. The primary disadvantage of the corporate form is the double taxation to shareholders of distributed earnings and dividends. Some advantages include: limited liability, ease of transferability, ability to raise capital, and unlimited life. When a business is started, most take the form ofa sole proprietorship or partnership.2.To maximize the current market value (share price) of the equity of the firm (whether it’s publiclytraded or not).3. In the corporate form of ownership, the shareholders are the owners of the firm. The shareholderselect the directors of the corporation, who in turn appoint the firm’s management. This separation of ownership from control in the corporate form of organization is what causes agency problems to exist. Management may act in its own or someone else’s best interests, rather than those of the shareholders. If such events occur, they may contradict the goal of maximizing the share price of the equity of the firm.4.Such organizations frequently pursue social or political missions, so many different goals areconceivable. One goal that is often cited is revenue minimization; i.e., provide whatever goods and services are offered at the lowest possible cost to society. A better approach might be to observe that even a not-for-profit business has equity. Thus, one answer is that the appropriate goal is to maximize the value of the equity.5.Presumably, the current stock value reflects the risk, timing, and magnitude of all future cash flows,both short-term and long-term. If this is correct, then the statement is false.6.An argument can be made either way. At the one extreme, we could argue that in a market economy,all of these things are priced. There is thus an optimal level of, for example, ethical and/or illegal behavior, and the framework of stock valuation explicitly includes these. At the other extreme, we could argue that these are non-economic phenomena and are best handled through the political process.A classic (and highly relevant) thought question that illustrates this debate goes something like this: “A firm has estimated that the cost of improving the safety of one of its products is $30 million. However, the firm believes that improving the safety of the product will only save $20 million in product liability claims. Wha t should the firm do?”7.The goal will be the same, but the best course of action toward that goal may be different because ofdiffering social, political, and economic institutions.8.The goal of management should be to maximize the share price for the current shareholders. Ifmanagement believes that it can improve the profitability of the firm so that the share price will exceed $35, then they should fight the offer from the outside company. If management believes that this bidder or other unidentified bidders will actually pay more than $35 per share to acquire the company, then they should still fight the offer. However, if the current management cannot increase the value of the firm beyond the bid price, and no other higher bids come in, then management is not acting in the interests of the shareholders by fighting the offer. Since current managers often lose their jobs when the corporation is acquired, poorly monitored managers have an incentive to fight corporate takeovers in situations such as this.9.We would expect agency problems to be less severe in other countries, primarily due to the relativelysmall percentage of individual ownership. Fewer individual owners should reduce the number of diverse opinions concerning corporate goals. The high percentage of institutional ownership might lead to a higher degree of agreement between owners and managers on decisions concerning risky projects. In addition, institutions may be better able to implement effective monitoring mechanisms on managers th an can individual owners, based on the institutions’ deeper resources and experiences with their own management. The increase in institutional ownership of stock in the United States and the growing activism of these large shareholder groups may lead to a reduction in agency problems for U.S. corporations and a more efficient market for corporate control.10. How much is too much? Who is worth more, Jack Welch or Tiger Woods? The simplest answer isthat there is a market for executives just as there is for alltypes of labor. Executive compensation is the price that clears the market. The same is true for athletes and performers. Having said that, one aspect of executive compensation deserves comment.A primary reason that executive compensation has grown so dramatically is that companies have increasingly moved to stock-based compensation.Such movement is obviously consistent with the attempt to better align stockholder and management interests. In recent years, stock prices have soared, so management has cleaned up. It is sometimes argued that much of this reward is simply due to rising stock prices in general, not managerial performance. Perhaps in the future, executive compensation will be designed to reward only differential performance, i.e., stock price increases in excess of general market increases.。