Cooperate Finance Chap 4 11e edition by Saram PDF

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Cooperate Finance Chap 4 11e edition by Saram...

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Cooperate Finance – Chap 4 Question & Problem 7,8,9,10,12,13,18,23,25,36,45,48

1. What is the relevant decision if NPV = 0? Explain It means that the profit expected (revenues - costs - initial investments) in the future from a project is zero -> that means that all your cash slows are likely 0 and there is no expectation of further growth at all => Thus the project is not particularly attractive itself to invest (at least from a financial point of view).

2. What if the payments are made at the beginning of the period? When payments are made at the beginning of each period, you will treat them as an annuity due -> the payer has enjoyed the benefits of the business/services for an entire period.

3. Upon retirement, your goal is to spend 5 years traveling around the world. To travel in style will require $250,000 per year at the beginning of each year. If you plan to retire in 30 years, what are the equal monthly payments necessary to achieve this goal? The funds in your retirement account will compound at 10% annually. PVAND30 = $250,000 (PVIFA.10,5) (1 + .10) = $250,000 (3.791) (1.1) = $1,042,525 ($1,042,466 by calculator)

7. Imprudential, Inc., has an unfunded pension liability of $550 million that must be paid in 20 years. To assess the value of the firm’s stock, financial analysts want to discount this liability back to the present. If the relevant discount rate is 6.4 percent, what is the present value of this liability? PV =

FV (1+r )t

PV =

550.000 .000 20 (1+6.4 % )

PV = $159,048,702.42

8. Although appealing to more refined tastes, art as a collectible has not always performed so profitably. During 2010, DeutscherMenzies sold Arkie under the Shower, a painting by renowned Australian painter Brett Whiteley, at auction for a price of $1,100,000. Unfortunately for the previous owner, he had purchased it three years earlier at a price of $1,680,000. What was his annual rate of return on this painting? PV = FV / (1 + r)t => r

=

1

FV t ) –1 ( PV

FV = $1,100,000; PV = $1,680,000; t = 3 => r = -0,1317 = -13.17%

9. An investor purchasing a British consol is entitled to receive annual payments from the British government forever. What is the price of a consol that pays $125 annually if the next payment occurs one year from today? The market interest rate is 3.9 percent. PV =

CF r

=

125 3.9 %

= $3.205,12

10. Compute the future value of $1,900 continuously compounded for Sử dụng công thức tính FV = PV x eR x T (hằng số e) a. 9 years at an APR of 12 percent = $5,594.89 b. 5 years at an APR of 8 percent = $2,834.47 c. 17 years at an APR of 5 percent = $4,445.33 d. 10 years at an APR of 9 percent = $4,673.25

12. Investment X offers to pay you $3,900 per year for nine years, whereas Investment Y offers to pay you $6,100 per year for five years. Which of these cash flow streams has the higher present value if the discount rate is 5 percent? If the discount rate is 22 percent? X = $3,900/per year (PV), t = 9 Y = $6,100/per year (PV), t = 5 r1 = 5%, r2 = 22%

PVA = CF x

1 (1+r ) ¿ ¿ ¿t 1 –¿ ¿

At an interest rate of 5 percent rate: X@5%: PVA = $3,900{[1 – (1/1.05)9 ] / .05 } = $27,720.50 Y@5%: PVA = $6,100{[1 – (1/1.05)5 ] / .05 } = $26,409.81 At an interest rate of 5 percent rate: X@22%: PVA = $3,900{[1 – (1/1.22)9 ] / .22 } = $14,766.51 Y@22%: PVA = $6,100{[1 – (1/1.22)5 ] / .22 } = $17,468.20

13. An investment offers $5,650 per year for 15 years, with the first payment occurring one year from now. If the required return is 8 percent, what is the value of the investment? What would the value be if the payments occurred for 40 years? For 75 years? Forever? 1 (1+r ) ¿ ¿ ¿t 1 –¿ ¿

PVA = CF x

CV = 5,650; r=8%

15y = $48,361.05 40y = $67,374.07 75y = $70,405.12 PV =

CF r

= $70,625

18. Well-known financial writer Andrew Tobias argues that he can earn 177 percent per year buying wine by the case. Specifically, he assumes that he will consume one $10 bottle of fine Bordeaux per week for the next 12 weeks. He can either pay $10 per week or buy a case of 12 bottles today. If he buys the case, he receives a 10 percent discount and, by doing so, earns the 177 percent. Assume he buys the wine and consumes the first bottle today. Do you agree with his analysis? Do you see a problem with his numbers?

23. You are planning to save for retirement over the next 30 years. To do this, you will invest $750 per month in a stock account and $250 per month in a bond account. The return of the stock account is expected to be 11 percent per year, and the bond account will earn 6 percent per year. When you retire, you will combine your money into an account with an annual return of 8 percent. How much can you withdraw each month from your account assuming a 25-year withdrawal period?

We need to find the annuity payment in retirement. Our retirement savings end at the same time the retirement withdrawals begin, so the PV of the retirement withdrawals will be the FV of the retirement savings. So, we find the FV of the stock account and the FV of the bond account and add the two FVs.

FVA = CF x

1 (1+r ) ¿ ¿ ¿t 1+¿ ¿

1

CF = $750; r = 11%; t=12month,

25. You’re trying to choose between two different investments, both of which have up-front costs of $75,000. Investment G returns $125,000 in six years. Investment H returns $185,000 in 10 years. Which of these investments has the higher return? PV1 =

FV 1 (1+r )t

 75,000 = PV2 =

125.000 6 (1+r )

=> r = 8.89%

185,000 10 (1+ r)

=> r = 9.45%

FV 2 (1+r )t

 75,000 =...