Fundamentals of Corporate Finance, 12e (Ross)
Chapter 6 Discounted Cash Flow Valuation
1) Which one of the following statements correctly defines a time value of money relationship?
A) Time and future values are inversely related, all else held constant.
B) Interest rates and time are positively related, all else held constant.
C) An increase in a positive discount rate increases the present value.
D) An increase in time increases the future value given a zero rate of interest.
E) Time and present value are inversely related, all else held constant.
2) Project X has cash flows of $8,500, $8,000, $7,500, and $7,000 for Years 1 to 4, respectively. Project Y has cash flows of $7,000, $7,500, $8,000, and $8,500 for Years 1 to 4, respectively. Which one of the following statements is true concerning these two projects given a positive discount rate? (No calculations needed)
A) Both projects have the same future value at the end of Year 4.
B) Both projects have the same value at Time 0.
C) Both projects are ordinary annuities.
D) Project Y has a higher present value than Project X.
E) Project X has both a higher present and a higher future value than Project Y.
3) Project A has cash flows of $4,000, $3,000, $0, and $3,000 for Years 1 to 4, respectively. Project B has cash flows of $2,000, $3,000, $2,000, and $3,000 for Years 1 to 4, respectively. Which one of the following statements is correct assuming the discount rate is positive? (No calculations needed)
A) The cash flows for Project B are an annuity, but those of Project A are not.
B) Both sets of cash flows have equal present values as of Time 0.
C) The present value at Time 0 of the final cash flow for Project A will be discounted using an exponent of three.
D) Both projects have equal values at any point in time since they both pay the same total amount.
E) Project B is worth less today than Project A.
4) You are comparing two investment options that each pay 6 percent interest, compounded annually. Both options will provide you with $12,000 of income. Option A pays $2,000 the first year followed by two annual payments of $5,000 each. Option B pays three annual payments of $4,000 each. Which one of the following statements is correct given these two investment options? Assume a positive discount rate. (No calculations needed.)
A) Both options are of equal value since they both provide $12,000 of income.
B) Option A has the higher future value at the end of Year 3.
C) Option B has a higher present value at Time 0.
D) Option B is a perpetuity.
E) Option A is an annuity.
5) Which one of the following statements related to annuities and perpetuities is correct?
A) An ordinary annuity is worth more than an annuity due given equal annual cash flows for 10 years at 7 percent interest, compounded annually.
B) A perpetuity comprised of $100 monthly payments is worth more than an annuity of $100 monthly payments provided the discount rates are equal.
C) Most loans are a form of a perpetuity.
D) The present value of a perpetuity cannot be computed but the future value can.
E) Perpetuities are finite but annuities are not.
6) Which one of these statements related to growing annuities and perpetuities is correct?
A) You can compute the present value of a growing annuity but not a growing perpetuity.
B) In computing the present value of a growing annuity, you discount the cash flows using the growth rate as the discount rate.
C) The future value of an annuity will decrease if the growth rate is increased.
D) An increase in the rate of growth will decrease the present value of an annuity.
E) The present value of a growing perpetuity will decrease if the discount rate is increased.
7) You are comparing two annuities that offer regular payments of $2,500 for five years and pay .75 percent interest per month. You will purchase one of these today with a single lump sum payment. Annuity A will pay you monthly, starting today, while annuity B will pay monthly, starting one month from today. Which one of the following statements is correct concerning these two annuities?
A) These annuities have equal present values but unequal future values.
B) These two annuities have both equal present and equal future values.
C) Annuity B is an annuity due.
D) Annuity A has a smaller future value than annuity B.
E) Annuity B has a smaller present value than annuity A.
8) An ordinary annuity is best defined as:
A) increasing payments paid for a definitive period of time.
B) increasing payments paid forever.
C) equal payments paid at the end of regular intervals over a stated time period.
D) equal payments paid at the beginning of regular intervals for a limited time period.
E) equal payments that occur at set intervals for an unlimited period of time.
9) A perpetuity is defined as:
A) a limited number of equal payments paid in even time increments.
B) payments of equal amounts that are paid irregularly but indefinitely.
C) varying amounts that are paid at even intervals forever.
D) unending equal payments paid at equal time intervals.
E) unending equal payments paid at either equal or unequal time intervals.
10) A Canadian consol is best categorized as a(n):
A) ordinary annuity.
B) amortized cash flow.
C) annuity due.
D) discounted loan.
E) perpetuity.
11) The interest rate that is most commonly quoted by a lender is referred to as the:
A) annual percentage rate.
B) compound rate.
C) effective annual rate.
D) simple rate.
E) common rate.
12) The actual interest rate on a loan that is compounded monthly but expressed as an annual rate is referred to as the ________ rate.
A) stated
B) discounted annual
C) effective annual
D) periodic monthly
E) consolidated monthly
13) Your credit card charges you .85 percent interest per month. This rate when multiplied by
12 is called the ________ rate.
A) effective annual
B) annual percentage
C) periodic interest
D) compound interest
E) episodic interest
14) Which one of the following statements related to loan interest rates is correct?
A) The annual percentage rate considers the compounding of interest.
B) When comparing loans you should compare the effective annual rates.
C) Lenders are most apt to quote the effective annual rate.
D) Regardless of the compounding period, the effective annual rate will always be higher than the annual percentage rate.
E) The more frequent the compounding period, the lower the effective annual rate given a fixed annual percentage rate.
15) Which one of the following statements concerning interest rates is correct?
A) Savers would prefer annual compounding over monthly compounding given the same annual percentage rate.
B) The effective annual rate decreases as the number of compounding periods per year increases.
C) The effective annual rate equals the annual percentage rate when interest is compounded annually.
D) Borrowers would prefer monthly compounding over annual compounding given the same annual percentage rate.
E) For any positive rate of interest, the annual percentage rate will always exceed the effective annual rate.
16) Which one of the following compounding periods will yield the lowest effective annual rate given a stated future value at Year 5 and an annual percentage rate of 10 percent?
A) Annual
B) Semi-annual
C) Monthly
D) Daily
E) Continuous
17) A loan where the borrower receives money today and repays a single lump sum on a future date is called a(n) ________ loan.
A) amortized
B) continuous
C) balloon
D) pure discount
E) interest-only
18) A loan that calls for periodic interest payments and a lump sum principal payment is referred to as a(n) ________ loan.
A) amortized
B) modified
C) balloon
D) pure discount
E) interest-only
19) Amortized loans must have which one of these characteristics over its life?
A) Either equal or unequal principal payments
B) One lump-sum principal payment
C) Increasing payments
D) Equal interest payments
E) Declining periodic payments
20) A(n) ________ loan has regular payments that include both principal and interest but these payments are insufficient to pay off the loan.
A) perpetual
B) continuing
C) balloon
D) pure discount
E) interest-only
21) The entire repayment of a(n) ________ loan is computed simply by computing one single future value.
A) interest-only
B) balloon
C) amortized
D) pure discount
E) bullet
22) With an interest-only loan the principal is:
A) forgiven over the loan period; thus it does not have to be repaid.
B) repaid in decreasing increments and included in each loan payment.
C) repaid in one lump sum at the end of the loan period.
D) repaid in equal annual payments.
E) repaid in increasing increments through regular monthly payments.
23) An amortized loan:
A) requires the principal amount to be repaid in even increments over the life of the loan.
B) may have equal or increasing amounts applied to the principal from each loan payment.
C) requires that all interest be repaid on a monthly basis while the principal is repaid at the end of the loan term.
D) requires that all payments be equal in amount and include both principal and interest.
E) repays both the principal and the interest in one lump sum at the end of the loan term.
24) You need $25,000 today and have decided to take out a loan at 7 percent interest for five years. Which one of the following loans would be the least expensive for you? Assume all loans require monthly payments and that interest is compounded on a monthly basis.
A) Interest-only loan
B) Amortized loan with equal principal payments
C) Amortized loan with equal loan payments
D) Discount loan
E) Balloon loan where 50 percent of the principal is repaid as a balloon payment
25) Southern Tours is considering acquiring Holiday Vacations. Management believes Holiday Vacations can generate cash flows of $218,000, $224,000, and $238,000 over the next three years, respectively. After that time, they feel the business will be worthless. If the desired rate of return is 14.5 percent, what is the maximum Southern Tours should pay today to acquire Holiday Vacations?
A) $519,799.59
B) $538,615.08
C) $545,920.61
D) $595,170.53
E) $538,407.71
26) You are considering two savings options. Both options offer a rate of return of 7.6 percent. The first option is to save $2,500, $2,500, and $3,000 at the end of each year for the next three years, respectively. The other option is to save one lump sum amount today. You want to have the same balance in your savings account at the end of the three years, regardless of the savings method you select. If you select the lump sum method, how much do you need to save today?
A) $7,414.59
B) $6,289.74
C) $6,660.00
D) $6,890.89
E) $6,784.20
27) Your parents have made you two offers. The first offer includes annual gifts of $5,000, $6,000, and $8,000 at the end of each of the next three years, respectively. The other offer is the payment of one lump sum amount today. You are trying to decide which offer to accept given the fact that your discount rate is 6.2 percent. What is the minimum amount that you will accept today if you are to select the lump sum offer?
A) $16,707.06
B) $16,407.78
C) $16,360.42
D) $17,709.48
E) $17,856.42
28) You want to start a business that you believe can produce cash flows of $5,600, $48,200, and $125,000 at the end of each of the next three years, respectively. At the end of three years you think you can sell the business for $250,000. At a discount rate of 16 percent, what is this business worth today?
A) $258,803.02
B) $314,011.33
C) $280,894.67
D) $325,837.81
E) $297,077.17
29) You are considering a project with cash flows of $16,500, $25,700, and $18,000 at the end of each year for the next three years, respectively. What is the present value of these cash flows, given a discount rate of 7.9 percent?
A) $54,877.02
B) $51,695.15
C) $55,429.08
D) $46,388.78
E) $53,566.67
30) You just signed a consulting contract that will pay you $38,000, $42,000, and $45,000 annually at the end of the next three years, respectively. What is the present value of this contract given a discount rate of 10.5?
A) $102,138.76
B) $108,307.67
C) $112,860.33
D) $92,433.27
E) $96,422.15
31) You have some property for sale and have received two offers. The first offer is for $89,500 today in cash. The second offer is the payment of $35,000 today and an additional guaranteed $70,000 two years from today. If the applicable discount rate is 11.5 percent, which offer should you accept and why?
A) You should accept the $89,500 today because it has the higher net present value.
B) You should accept the $89,500 today because it has the lower future value.
C) You should accept the first offer as it is a lump sum payment.
D) You should accept the second offer because it has the larger net present value.
E) It does not matter which offer you accept as they are equally valuable.
32) Your anticipated wedding is three years from today. You don't know who your spouse will be but you do know that you are saving $10,000 today and $17,000 one year from today for this purpose. You also plan to pay the final $12,000 of anticipated costs on your wedding day. At a discount rate of 5.5 percent, what is the current cost of your upcoming wedding?
A) $36,333.11
B) $41,065.25
C) $36,895.17
D) $38,411.08
E) $35,248.16
33) One year ago, JK Mfg. deposited $12,000 in an investment account for the purpose of buying new equipment four years from today. Today, it is adding another $15,000 to this account. The company plans on making a final deposit of $10,000 to the account one year from today. How much cash will be available when the company is ready to buy the equipment assuming an interest rate of 5.5 percent?
A) $43,609.77
B) $45,208.61
C) $44,007.50
D) $46,008.30
E) $47,138.09
34) Troy will receive $7,500 at the end of Year 2. At the end of the following two years, he will receive $9,000 and $12,500, respectively. What is the future value of these cash flows at the end of Year 6 if the interest rate is 8 percent?
A) $38,418.80
B) $32,907.67
C) $36,121.08
D) $39,010.77
E) $33,445.44
35) Sue plans to save $4,500, $0, and $5,500 at the end of Years 1 to 3, respectively. What will her investment account be worth at the end of the Year 3 if she earns an annual rate of 4.15 percent?
A) $10,583.82
B) $10,381.25
C) $10,609.50
D) $11,526.50
E) $10,812.07
36) A proposed project has cash flows of $2,000, $?, $1,750, and $1,250 at the end of Years 1 to 4. The discount rate is 7.2 percent and the present value of the four cash flows is $6,669.25. What is the value of the Year 2 cash flow?
A) $2,450
B) $2,750
C) $2,500
D) $2,250
E) $2,800
37) Waldo expects to save the following amounts: Year 1 = $50,000; Year 2 = $28,000; Year 3 = $12,000. If he can earn an average annual return of 10.5 percent, how much will he have saved in this account exactly 25 years from the time of the first deposit?
A) $1,172,373
B) $935,334
C) $806,311
D) $947,509
E) $1,033,545
38) A charity plans to invest annual payments of $60,000, $70,000, $75,000, and $50,000, respectively, over the next four years. The first payment will be invested one year from
today. Assuming the investment earns 5.5 percent annually, how much will the charity have available four years from now?
A) $263,025
B) $236,875
C) $277,491
D) $328,572
E) $285,737
39) Your broker is offering 1.2 percent compounded daily on its money market account. If you deposit $7,500 today, how much will you have in your account 15 years from now?
A) $8,979.10
B) $9,714.06
C) $8,204.50
D) $9,336.81
E) $9,414.14
40) Your grandmother will be gifting you $150 at the end of each month for four years while you attend college. At a discount rate of 3.7 percent, what are these payments worth to you on the day you enter college?
A) $6,201.16
B) $6,682.99
C) $6,539.14
D) $6,608.87
E) $6,870.23
41) You just won the grand prize in a national writing contest! As your prize, you will receive $500 a month for 50 months. If you can earn 7 percent on your money, what is this prize worth to you today?
A) $21,629.93
B) $18,411.06
C) $21,338.40
D) $20,333.33
E) $19,450.25
42) Phil can afford $240 a month for five years for a car loan. If the interest rate is 8.5 percent, how much can he afford to borrow to purchase a car?
A) $11,750.00
B) $12,348.03
C) $11,697.88
D) $10,266.67
E) $10,400.00
43) As the beneficiary of a life insurance policy, you have two options for receiving the insurance proceeds. You can receive a lump sum of $200,000 today or receive payments of $1,400 a month for 20 years. If you can earn 6 percent on your money, which option should you take and why?
A) You should accept the payments because they are worth $202,414 to you today.
B) You should accept the payments because they are worth $201,846 to you today.
C) You should accept the payments because they are worth $201,210 to you today.
D) You should accept the $200,000 because the payments are only worth $189,311 to you today.
E) You should accept the $200,000 because the payments are only worth $195,413 to you today.
44) Assume you work for an employer who will contribute $60 a week for the next 20 years into
a retirement plan for your benefit. At a discount rate of 9 percent, what is this employee benefit worth to you today?
A) $28,927.38
B) $27,618.46
C) $29,211.11
D) $25,306.16
E) $25,987.74
45) The Distribution Point plans to save $2,000 a month for the next 3 years for future emergencies. The interest rate is 4.5 percent compounded monthly. The first monthly deposit will be made today. What would today's deposit amount have to be if the firm opted for one lump sum deposit that would yield the same amount of savings as the monthly deposits after 3 years?
A) $70,459.07
B) $67,485.97
C) $69,068.18
D) $69,333.33
E) $67,233.84
46) You need some money today and the only friend you have that has any is a miser. He agrees to loan you the money you need, if you make payments of $30 a month for the next six months. In keeping with his reputation, he requires that the first payment be paid today. He also charges you 2 percent interest per month. How much total interest is he charging?
A) $4.50
B) $3.60
C) $9.50
D) $4.68
E) $8.60
47) Sue just purchased an annuity that will pay $24,000 a year for 25 years, starting today. What was the purchase price if the discount rate is 8.5 percent?
A) $241,309
B) $245,621
C) $251,409
D) $258,319
E) $266,498
48) Marcus is scheduled to receive annual payments of $3,600 for each of the next 12 years. The discount rate is 8 percent. What is the difference in the present value if these payments are paid at the beginning of each year rather than at the end of each year?
A) $2,170.39
B) $2,511.07
C) $2,021.18
D) $2,027.94
E) $2,304.96
49) Two annuities have equal present values and an applicable discount rate of 7.25 percent. One annuity pays $2,500 on the first day of each year for 15 years. How much does the second annuity pay each year for 15 years if it pays at the end of each year?
A) $2,331.00
B) $2,266.67
C) $2,500.00
D) $2,390.50
E) $2,681.25
50) Trish receives $450 on the first of each month. Josh receives $450 on the last day of each month. Both Trish and Josh will receive payments for next four years. At a discount rate of 9.5 percent, what is the difference in the present value of these two sets of payments?
A) $141.80
B) $151.06
C) $154.30
D) $159.08
E) $162.50
51) What is the future value of $1,575 a year for 25 years at 6.3 percent interest, compounded annually?
A) $76,919.04
B) $72,545.78
C) $90,152.04
D) $92,006.08
E) $91,315.09
52) What is the future value of $8,500 a year for 40 years at 10.8 percent interest, compounded annually?
A) $3,278,406.16
B) $4,681,062.12
C) $2,711,414.14
D) $3,989,476.67
E) $4,021,223.33
53) Rosina plans on saving $2,000 a year and expects to earn an annual rate of 6.9 percent. How much will she have in her account at the end of 37 years?
A) $406,429.10
B) $338,369.09
C) $297,407.17
D) $313,274.38
E) $308,316.67
54) Theresa adds $1,500 to her savings account on the first day of each year. Marcus adds $1,500 to his savings account on the last day of each year. They both earn 6.5 percent annual interest. What is the difference in their savings account balances at the end of 35 years?
A) $12,093.38
B) $12,113.33
C) $12,127.04
D) $12,211.12
E) $12,219.46
55) You just obtained a loan of $16,700 with monthly payments for four years at 6.35 percent interest, compounded monthly. What is the amount of each payment?
A) $387.71
B) $391.40
C) $401.12
D) $419.76
E) $394.89
56) You borrowed $185,000 for 30 years to buy a house. The interest rate is 4.35 percent, compounded monthly. If you pay all of your monthly payments as agreed, how much total interest will you pay on this mortgage? (Round the monthly payment to the nearest whole cent.)
A) $150,408
B) $147,027
C) $146,542
D) $154,319
E) $141,406
57) Travis International has a one-time expense of $1.13 million that must be paid two years from today. The firm can earn 4.3 percent, compounded monthly, on its savings. How much must the firm save each month to fund this expense if the firm starts investing equal amounts each month starting at the end of this month?
A) $38,416.20
B) $45,172.02
C) $51,300.05
D) $47,411.08
E) $53,901.15
58) Nadine is retiring today and has $96,000 in her retirement savings. She expects to earn 5.5 percent, compounded monthly. How much can she withdraw from her retirement savings each month if she plans to spend her last penny 18 years from now?
A) $809.92
B) $847.78
C) $919.46
D) $616.08
E) $701.10
59) Island News purchased a piece of property for $1.79 million. The firm paid a down payment of 20 percent in cash and financed the balance. The loan terms require monthly payments for 20 years at an APR of 4.75 percent, compounded monthly. What is the amount of each mortgage payment?
A) $9,253.92
B) $10,419.97
C) $8,607.11
D) $11,567.40
E) $12,301.16
60) You estimate that you will owe $40,200 in student loans by the time you graduate. If you want to have this debt paid in full within 10 years, how much must you pay each month if the interest rate is 4.35 percent, compounded monthly?
A) $411.09
B) $413.73
C) $414.28
D) $436.05
E) $442.50
61) Phil purchased a car today at a price of $8,500. He paid $300 down in cash and financed the balance for 36 months at 5.75 percent, compounded monthly. What is the amount of each monthly loan payment?
A) $248.53
B) $270.23
C) $318.47
D) $305.37
E) $257.62
62) An insurance annuity offers to pay you $1,000 per quarter for 20 years. If you want to earn a
rate of return of 6.5 percent, compounded quarterly, what is the most you are willing to pay as a lump sum today to obtain this annuity?
A) $32,008.24
B) $34,208.16
C) $44,591.11
D) $43,008.80
E) $38,927.59
63) Your car dealer is willing to lease you a new car for $190 a month for 36 months. Payments are due on the first day of each month starting with the day you sign the lease contract. If your cost of money is 6.5 percent, what is the current value of the lease?
A) $10,331.03
B) $6,232.80
C) $9,197.74
D) $7,203.14
E) $11,008.31
64) Your great aunt left you an inheritance in the form of a trust. The trust agreement states that you are to receive $2,500 on the first day of each year, starting immediately and continuing for 20 years. What is the value of this inheritance today if the applicable discount rate is 4.75 percent?
A) $24,890.88
B) $31,311.16
C) $33,338.44
D) $28,909.29
E) $29,333.33
65) Chris has three options for settling an insurance claim. Option A will provide $1,500 a month for 6 years. Option B will pay $1,025 a month for 10 years. Option C offers $85,000 as a lump sum payment today. The applicable discount rate is 6.8 percent, compounded monthly. Which option should Chris select, and why, if he is only concerned with the financial aspects of the offers?
A) Option A: It provides the largest monthly payment.
B) Option B: It pays the largest total amount.
C) Option C: It is all paid today.
D) Option B: It pays the greatest number of payments.
E) Option B: It has the largest value today.
66) Racing Motors wants to save $825,000 to buy some new equipment three years from now. The plan is to set aside an equal amount of money on the first day of each quarter starting today. How much does the company need to save each quarter to achieve its goal if it can earn 4.45 percent on its savings?
A) $63,932.91
B) $62,969.70
C) $63,192.05
D) $62,925.00
E) $64,644.17
67) Stephanie is going to contribute $160 on the first of each month, starting today, to her retirement account. Her employer will provide a match of 50 percent. In other words, her employer will add $80 to the amount Stephanie saves. If both Stephanie and her employer continue to do this and she can earn a monthly interest rate of .45 percent, how much will she have in her retirement account 35 years from now?
A) $336,264.14
B) $204,286.67
C) $199,312.04
D) $268,418.78
E) $299,547.97
68) An annuity that pays $12,500 a year at an annual interest rate of 5.45 percent costs $150,000 today. What is the length of the annuity time period?
A) 25 years
B) 18 years
C) 15 years
D) 20 years
E) 22 years
69) You want to be a millionaire when you retire in 30 years and expect to earn 8.5 percent, compounded monthly. How much more will you have to save each month if you wait 10 years to start saving versus if you start saving at the end of this month?
A) $947.22
B) $1,046.80
C) $808.47
D) $841.15
E) $989.10
70) You are the recipient of a gift that will pay you $25,000 one year from now and every year thereafter for the following 24 years. The payments will increase in value by 2.5 percent each year. If the appropriate discount rate is 8.5 percent, what is the present value of this gift?
A) $416,667
B) $316,172
C) $409,613
D) $311,406
E) $386,101
71) You are preparing to make monthly payments of $100, beginning at the end of this month, into an account that pays 5 percent interest, compounded monthly. How many payments will you
have made when your account balance reaches $10,000?
A) 97.30
B) 83.77
C) 89.46
D) 100.00
E) 91.12
72) You want to borrow $27,500 and can afford monthly payments of $650 for 48 months, but no more. Assume monthly compounding. What is the highest APR rate you can afford?
A) 6.33 percent
B) 6.67 percent
C) 5.82 percent
D) 7.01 percent
E) 7.18 percent
73) Today, you borrowed $3,200 on a credit card that charges an interest rate of 12.9 percent, compounded monthly. How long will it take you to pay off this debt assuming that you do not charge anything else and make regular monthly payments of $60?
A) 6.87 years
B) 6.28 years
C) 6.64 years
D) 7.23 years
E) 7.31 years
74) The Rodriquez family is determined to purchase a $250,000 home without incurring any debt. The family plans to save $2,500 a quarter for this purpose and expects to earn 6.65 percent, compounded quarterly. How long will it be until the family can purchase a home?
A) 23.09 years
B) 14.85 years
C) 35.46 years
D) 48.82 years
E) 59.39 years
75) Today, you are retiring. You have a total of $289,416 in your retirement savings. You want to withdraw $2,500 at the beginning of every month, starting today and expect to earn 4.6 percent, compounded monthly. How long will it be until you run out of money?
A) 29.97 years
B) 8.56 years
C) 22.03 years
D) 12.71 years
E) 18.99 years。
