Corporate Finance Test 2 - Ch. 5, 6, 7
Twenty-five years from now, you would like to give your child $100,000. How much money must you set aside today if you can earn 7.5 percent per year, compounded annually, on your investment?
$16,397.91 PV = $100,000/1.07525 PV = $16,397.91
A relative will support your education by paying you $500 a month for 50 months. If you can earn 7 percent on your money, what is this gift worth to you today?
$21,629.93 PVA = $500({1 - [1/(1 + .07/12)50]}/(.07/12)) PVA = $21,629.93
Assume you own a violin currently valued at $64,000. If the value increases by 2.5 percent annually, how much will the violin be worth 15 years from now?
$92,691.08 FV = $64,000(1.02515)FV = $92,691.08
Assume you currently earn a salary of $50,000 per year. What will be your annual salary 17 years from now if you receive annual raises of 3.75 percent?
$93,491 FV = $50,000(1.037517)FV = $93,491
Goldfarb Paints has 6.8 percent coupon bonds on the market with 11 years left to maturity. The bonds make semiannual payments and currently sell for 98.6 percent of par. What is the effective annual yield?
7.11%
Fifteen years ago, you invested $5,000. Today, it is worth $18,250. What annually compounded rate of interest did you earn?
9.01% $18,250 = $5,000(1 + r15)r = .0901, or 9.01%
Annalise will deposit into her investment account $4,500, $0, and $5,500 at the end of Years 1, 2, and 3, respectively. What will her account be worth at the end of the Year 3 if she earns an annual rate of 4.15 percent?
$10,381.25 FV = $4,500(1.04152) + $5,500 FV = $10,381.25
Aidan can afford $240 a month for five years for a car loan. If the interest rate is 8.5 percent, what is the most he can afford to borrow?
$11,697.88 PVA = $240({1 − [1/(1 + .085/12)(5)(12)]}/(.085/12)) PVA = $11,697.88
Carson expects to invest $50,000 at the end of Year 1, $28,000 at the end of Year 2, and $12,000 at the end of Year 3. If he can earn an average annual return of 10.5 percent, how much will he have saved in this account by the end of Year 25?
$1,033,545 FV = $50,000(1.10525) + $28,000(1.10524) + $12,000(1.10523) FV = $1,033,545
You just invested $49,000 that you received as an insurance settlement. How much more will this account be worth in 40 years if you earn an average return of 7.6 percent rather than 7.1 percent? (Assume annual compounding.)
$155,986.70 FV = $49,000(1.07640) FV = $917,670.84 FV = $49,000(1.07140) FV = $761,684.14 Difference = $917,670.84 − 761,684.14 Difference = $155,986.70
Mr. Rich arranged for a mortgage loan for 65 percent of the $2.5 million purchase price of a home. The monthly payment will be $10,400 and the mortgage term is 30 years. What is the EAR on this loan?
6.82% Loan amount = $2,500,000(.65) Loan amount = $1,625,000 PVA = $1,625,000 = $10,400[(1 − {1/[1 + (r/12)](30)(12)})/(r/12)] r = .0662, or 6.62% EAR = (1 + .0662/12)12− 1 EAR = .0682, or 6.82%
You hope to buy your dream car five years from now. Today, that car costs $62,500. You expect the price to increase by an average of 2.9 percent per year. How much will your dream car cost by the time you are ready to buy it?
$72,103.59 FV = $62,500(1.0295) FV = $72,103.59
A friend agreed to lend you money today. You must repay your friend by making payments of $30 per month for the next six months. The first payment must be paid today. In addition, you must pay 2 percent interest per month. How much total interest will you end up paying your friend?
$8.60 PVADue = $30{[1 − (1/1.026)]/.02(1.02)} PVADue = $171.40 Total payments = $30(6) Total payments = $180 Total interest = $180 − 171.40 Total interest = $8.60
At 5 percent annually compounded interest, how long would it take to triple your money?
22.52 years $3 = $1(1.05t)t = 22.52 years
Jacob invested $2,550 in an account that pays 5 percent simple interest. How much money will he have at the end of four years?
$3,060.00 FV = $2,550 + ($2,550)(.05)(4) FV = $3,060
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?
$33,338.44 PVADue = $2,500({1 − [1/(1.0475)20]}/.0475)(1.0475) PVADue = $33,338.44
Assume you own two coins, each of which is valued at $100 today. One coin is expected to appreciate by 5.2 percent annually while the other coin should appreciate by 5.7 percent annually. What will be the difference in the value of the two coins 50 years from now?
$337.43 FV = $100(1.05250)FV = $1,261.21FV = $100(1.05750)FV = $1,598.64Difference = $1,598.64 − 1,261.21Difference = $337.43
Assume the average price of a new vehicle in the United States last year was $36,420. The average price five years earlier was $31,208. What was the annual increase in the price over this time period?
$36,420 = $31,208[(1 + r)5]r = .0314, or 3.14%
You have a savings account valued at $1,500 today that earns an annual interest rate of 8.7 percent. How much more would this account be worth if you wait to spend the entire balance in 25 years rather than in 20 years? (Assume annual compounding.)
$4,117.64 FV = $1,500(1.08725) FV = $12,073.41 FV = $1,500(1.08720) FV = $7,955.77 Difference = $12,073.41 − 7,955.77 Difference = $4,117.64
Excellent Yachting is considering acquiring Turquoise Tours. Management believes Turquoise Tours 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 Excellent Yachting should pay today to acquire Turquoise Coast?
$519,799.59 PVA = $218,000/1.145 + $224,000/1.1452 + $238,000/1.1453 PV = $519,799.59
A scholarship will pay 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?
$6,682.99 PVA = $150({1 − [1/(1 + .037/12)(4)(12)]}/(.037/12)) PVA = $6,682.99
The Friendly Bank wants to earn an EAR of 12 percent on its consumer loans. The bank uses daily compounding. What rate is the bank most apt to quote on these loans?
11.33% APR = 365(1.121/365− 1) APR = .1133, or 11.33%
A 3.25 percent Treasury bond is quoted at a price of 99.04. The bond pays interest semiannually. What is the current yield?
3.28% Current yield = .0325/.9904 Current yield = .0328, or 3.28%
Aidan deposited $8,500 in an account today. If the account earns 8.5 percent per year, compounded annually, how many years will it take for the account to reach a balance of $138,720?
34.23 years $138,720 = $8,500(1.085t)t = 34.23 years
A corporate bond is quoted at a price of 98.96 and has a coupon rate of 4.8 percent, paid semiannually. What is the current yield?
4.85% Current yield = .048/.9896 Current yield = .0485, or 4.85%
Which one of the following premiums is compensation for the possibility that a bond issuer may not pay a bond's interest or principal payments as expected?
Default risk
A sinking fund is managed by a trustee for which one of the following purposes?
Early bond redemption
Assume you are investing $100 today in a savings account. Which one of the following terms refers to the total value of this investment one year from now?
Future value
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?
Option B: It has the largest value today. Option A:PVA = $1,500({1 − [1/(1 + .068/12)(6)(12)]}/(.068/12)) PVA = $88,479.23 Option B:PVA = $1,025({1 − [1/(1 + .068/12)(10)(12)]}/(.068/12)) PVA = $89,068.22 Option C: PV = $85,000 Your decision should be based on present value.
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?
You should accept the $200,000 because the payments are only worth $195,413 to you today. PVA = $1,400({1 − [1/(1 + .06/12)(20)(12)]}/(.06/12)) PVA = $195,413
A bond that has only one payment, which occurs at maturity, defines which one of these types of bonds?
Zero coupon
Bonds issued by the U.S. government:
are considered to be free of default risk.
The interest rate risk premium is the:
compensation investors demand for accepting interest rate risk.
Cullen invested $5,000 five years ago and earns 6 percent annual interest. By leaving his interest earnings in her account, he increases the amount of interest he earns each year. His investment is best described as benefitting from:
compounding.
A discount bond's coupon rate is equal to the annual interest divided by the:
face value.
A 13-year, 6 percent coupon bond pays interest semiannually. The bond has a face value of $1,000. What is the percentage change in the price of this bond if the market yield to maturity rises to 5.7 percent from the current rate of 5.5 percent?
−1.79% Bond price = $30({1 − [1/(1 + .055/2)(13)(2)]}/(.055/2)) + $1,000/(1 + .055/2)(13)(2) Bond price = $1,046.01 Bond price = $30({1 − [1/(1 + .057/2)(13)(2)]}/(.057/2)) + $1,000/(1 +.057/2)(13)(2) Bond price = $1,027.28 % change in price = ($1,027.28 − 1,046.01)/$1,046.01 % change in price = −.0179, or −1.79%
Elena receives $450 on the first of each month. Harley receives $450 on the last day of each month. Both Elena and Harley will receive four years of payments. If the discount rate is 9.5 percent, what is the difference in the present value of these two sets of payments?
$141.80 PVADue = $450[(1 − {1/[1 + (.095/12)](4)(12)})/(.095/12)][1 + (.095/12)] PVADue = $18,053.58 PVA = $450[(1 − {1/[1 + (.095/12)](4)(12)})/(.095/12)] PVA = $17,911.78 Difference = $18,053.58 − 17,911.78 Difference = $141.80
Grace is retiring today and has $300,000 in her retirement savings. She expects to earn 8.5 percent per year compounded monthly. How much can she withdraw from her retirement savings each month if she plans to spend her last penny 17 years from now?
$2,784.88 PVA = $300,000 = C[(1 − {1/[1 + (.085/12)](17)(12)})/(.085/12)] C = $2,784.88
Al obtained a mortgage of $195,000 at 5.25 percent for 15 years. How much of the second monthly payment is applied to interest?
$850.00 $195,000 = C({1 - [1/(1 + .0525/12)(15)(12)]}/(.0525/12)) C = $1,567.56 InterestMonth 1 = $195,000(.0525/12) InterestMonth 1 = $853.13 PrincipalMonth 1 = $1,567.56 − 853.13 PrincipalMonth 1 = $714.43 InterestMonth 2 = ($195,000 − 714.43)(.0525/12) InterestMonth 2 = $850.00
Caston's zero coupon bonds have a market price of $318.46, a face value of $1,000, and a yield to maturity of 6.69 percent. How many years is it until these bonds mature? Assume semiannual compounding.
17.39 years Bond price = $318.46 = $1,000/(1 + .0669/2)^t t = 34.78 semiannual periods = 17.39 years
The Art Gallery is notoriously known as a slow payer. The firm currently needs to borrow $25,000 and only one company will loan to them. The terms of the loan call for weekly payments of $500 at a weekly interest rate of .45 percent. What is the loan term?
56.77 weeks PVA = $25,000 = $500{[1 − (1/1.0045t)]/.0045} t = 56.77 weeks
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?
6.64 years PVA = $3,200 = $60[(1 − {1/[1 + (.129/12)]t })/(.129/12)] t = 79.66 months, or 6.64 years
First City Bank offers an APR of 7.65 percent on its loans. What is the maximum effective annual rate the bank can earn based on the quoted rate?
7.95% EAR = e.0765− 1 EAR = .0795, or 7.95%
A new sports coupe costs $41,750 and the finance office has quoted you an APR of 7.7 compounded monthly for 36 months. What is the EAR?
7.98% EAR = (1 + .077/12)12− 1 EAR = .0798, or 7.98%
Coronel Corporation wants to issue new 20-year bonds. The company currently has 8.5 percent bonds on the market that sell for $994, make semiannual payments, and mature in seven years. What should the coupon rate be on the new bonds if the firm wants to sell them at par?
8.62%
Stoessel, Incorporated, issued 20-year bonds 3 years ago at a coupon rate of 8.5 percent. The bonds make semiannual payments. If these bonds currently sell for 91.4 percent of par value, what is the YTM?
9.53%
Your aunt has promised to give you $5,000 when you graduate from college. You expect to graduate three years from now. If you speed up your plans to enable you to graduate two years from now, the present value of the promised gift will:
increase.
Hayley won a lottery and will receive $1,000 each year for the next 30 years. The current value of these winnings is called the:
present value.
With an interest-only loan the principal is:
repaid in one lump sum at the end of the loan period.
Assume your mother invested a lump sum 28 years ago at 4.05 percent interest, compounded annually. Today, she gave you the proceeds of that investment, totaling $48,613.24. How much did your mother originally invest?
$15,994.70 PV = $48,613.24/1.040528PV = $15,994.70
Twelve years ago, your parents set aside $8,000 to help fund your college education. Today, that fund is valued at $23,902. What annually compounded rate of interest is being earned on this account?
9.55% $23,902 = $8,000[(1 + r)12] r = .0955, or 9.55%
The bond market requires a return of 6.2 percent on the 15-year bonds issued by Mingwei Manufacturing. The 6.2 percent is referred to as the:
yield to maturity.
A bond has a coupon rate of 8 percent, seven years to maturity, semiannual interest payments, and a YTM of 7 percent. If interest rates suddenly rise by 1.5 percent, what will be the percentage change in the bond price?
−7.64% Bond price = $40({1 − [1/(1 + .07/2)(7)(2)]}/(.07/2)) + $1,000/(1 + .07/2)(7)(2) Bond price = $1,054.60 Bond price = $40({1 − [1/(1 + .085/2)(7)(2)]}/(.085/2)) + $1,000/(1 + .085/2)(7)(2) Bond price = $974.02 %Δ price = ($974.02 − 1,054.60)/$1,054.60 %Δ price = −.0764, or −7.64%