罗斯《公司理财》英文习题答案DOCchap004

公司理财习题答案

第四章

Chapter 4: Net Present Value

4.1 a. $1,000 ? 1.0510 = $1,628.89 b. $1,000 ? 1.0710 = $1,967.15 c. $1,000 ? 1.0520 = $2,653.30 d. Interest compounds on the I nterest already earned. Therefore, the interest earned in part c, $1,653.30, is more than double the amount earned in part a, $628.89.

4.2 a. $1,000 / 1.17 = $513.16 b. $2,000 / 1.1 = $1,818.18 c. $500 / 1.18 = $233.25

4.3 You can make your decision by computing either the present value of the $2,000 that you

can receive in ten years, or the future value of the $1,000 that you can receive now. Present value: $2,000 / 1.0810 = $926.39 Future value: $1,000 ? 1.0810 = $2,158.93 Either calculation indicates you should take the $1,000 now.

4.4 Since 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 = $92.30

4.5 PV = $1,500,000 / 1.0827 = $187,780.23

4.6 a. 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 = $9,090.91 Option two: $20,000 / 1.15 = $12,418.43 Choose the second option. c. Option one: $10,000 / 1.2 = $8,333.33 Option two: $20,000 / 1.25 = $8,037.55 Choose the first option.

d. You are indifferent at the rate that equates the PVs of the two alternatives. You

know that rate must fall between 10% and 20% because the option you would choose differs at these rates. Let r be the discount rate that makes you indifferent between the options.

$10,000 / (1 + r) = $20,000 / (1 + r)5 (1 + r)4 = $20,000 / $10,000 = 2 1 + r = 1.18921 r = 0.18921 = 18.921%

4.7 PV of Joneses’ offer = $150,000 / (1.1)3 = $112,697.22 Since the PV of Joneses’ offer is less than Smiths’ offer, $115,000, you should choose

Smiths’ offer.

4.8 a. P0 = $1,000 / 1.0820 = $214.55 b. P10 = P0 (1.08)10 = $463.20

Answers to End-of-Chapter Problems

B-49

4.9 4.10 4.11 4.12 4.13 4.14 4.15

c. P15 = P0 (1.08)15 = $680.59

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 = $6,714.61 PV = $5,000,000 / 1.1210 = $1,609,866.18 a. b. c.

The cost of investment is $900,000.

PV of cash inflows = $120,000 / 1.12 + $250,000 / 1.122 + $800,000 / 1.123 = $875,865.52

Since the PV of cash inflows is less than the cost of investment, you should not make the investment.

NPV = -$900,000 + $875,865.52 = -$24,134.48

NPV = -$900,000 + $120,000 / 1.11 + $250,000 / 1.112 + $800,000 / 1.113 = $-4,033.18

Since the NPV is still negative, you should not make the investment.

NPV = -($340,000 + $10,000) + ($100,000 - $10,000) / 1.1

+ $90,000 / 1.12 + $90,000 / 1.13 + $90,000 / 1.14 + $100,000 / 1.15 = -$2,619.98

Since the NPV is negative, you should not buy it.

If the relevant cost of capital is 9 percent, NPV = -$350,000 + $90,000 / 1.09 + $90,000 / 1.092 + $90,000 / 1.093 + $90,000 / 1.094 + $100,000 / 1.095 = $6,567.93 Since the NPV is positive, you should buy it. a. b.

Profit = PV of revenue - Cost = NPV

NPV = $90,000 / 1.15 - $60,000 = -$4,117.08 No, the firm will not make a profit. Find r that makes zero NPV. $90,000 / (1+r)5 - $60,000 = $0 (1+r)5 = 1.5

r = 0.08447 = 8.447%

The future value of the decision to own your car for one year is the sum of the trade-in value and the benefit from owning the car. Therefore, the PV of the decision to own the car for one year is $3,000 / 1.12 + $1,000 / 1.12 = $3,571.43

Since the PV of the roommate’s offer, $3,500, is lower than the aunt’s offer, you should accept aunt’s offer. a. b. c. d.

$1.000 (1.08)3 = $1,259.71

$1,000 [1 + (0.08 / 2)]2 ? 3 = $1,000 (1.04)6 = $1,265.32

$1,000 [1 + (0.08 / 12)]12 ? 3 = $1,000 (1.00667)36 = $1,270.24 $1,000 e0.08 ? 3 = $1,271.25

B-50 Answers to End-of-Chapter Problems

公司理财习题答案

第四章

e. 4.16 4.17 4.18

a. b. c. d.

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 end 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. $1,000 e0.12 ? 5 = $1,822.12 $1,000 e0.1 ? 3 = $1,349.86 $1,000 e0.05 ? 10 = $1,648.72 $1,000 e0.07 ? 8 = $1,750.67

PV = $5,000 / [1+ (0.1 / 4)]4 ? 12 = $1,528.36 Effective annual interest rate of Bank America = [1 + (0.041 / 4)]4 - 1 = 0.0416 = 4.16% Effective annual interest rate of Bank USA = [1 + (0.0405 / 12)]12 - 1 = 0.0413 = 4.13% You should deposit your money in Bank America.

4.19 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 = $800

4.20 Quarterly interest rate = 12% / 4 = 3% = 0.03 Therefore, the price of the security = $10 / 0.03 = $333.33

4.21 The price at the end of 19 quarters (or 4.75 years) from today = $1 / (0.15 ? 4) = $26.67 The current price = $26.67 / [1+ (.15 / 4)]19 = $13.25

4.22 a. $1,000 / 0.1 = $10,000

b. $500 / 0.1 = $5,000 is the value one year from now of the perpetual stream. Thus,

the value of the perpetuity 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.

4.23 The value at t = 8 is $120 / 0.1 = $1,200. Thus, the value at t = 5 is $1,200 / 1.13 = $901.58.

4.24 P = $3 (1.05) / (0.12 - 0.05) = $45.00

4.25 P = $1 / (0.1 - 0.04) = $16.67

4.26 The first cash flow will be generated 2 years from today. The value at the end of 1 year from today = $200,000 / (0.1 - 0.05) = $4,000,000. Thus, PV = $4,000,000 / 1.1 = $3,636,363.64.

4.27 A zero NPV

- $100,000 + $50,000 / r = 0 - r = 0.5

Answers to End-of-Chapter Problems B-51

4.28 Apply the NPV technique. Since the inflows are an annuity you can use the present value

of an annuity factor. NPV = -$6,200 + $1,200 ?80.1 = -$6,200 + $1,200 (5.3349) = $201.88 Yes, you should buy the asset.

4.29 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

20stream of payments. Value at the end of year two = $2,000 ?0 .08 = $2,000 (9.8181) = $19,636.20 The present value is simply that amount discounted back two years. PV = $19,636.20 / 1.082 = $16,834.88

4.30 The value of annuity at the end of year five = $500 ?150.15 = $500 (5.84737) = $2,923.69 The present value = $2,923.69 / 1.125 = $1,658.98

4.31 The 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 Atr. 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 ? b c ? 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%.

B-52 Answers to End-of-Chapter Problems

公司理财习题答案

第四章

4.32 a. The annuity amount can be computed by first calculating the PV of the $25,000

which you need in five years. That amount is $17,824.65 [= $25,000 / 1.075]. Next compute the annuity which has the same present value. $17,824.65 = C ?50.07 $17,824.65 = C (4.1002) C = $4,347.26 Thus, 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 = $17,824.65 The formula for future value of any annuity can be used to solve the problem (see

footnote 14 of the text).

4.33 The amount of loan is $120,000 ? 0.85 = $102,000.

20C?0.10 = $102,000 The amount of equal installments is

20 C = $102,000 / ?0.10 = $102,000 / 8.513564 = $11,980.88

4.34 The present value of salary is $5,000 ?360.01 = $150,537.53 4.35 4.36

The present value of bonus is $10,000 ?30.1268 = $23,740.42 (EAR = 12.68% is used since bonuses are paid annually.)

The present value of the contract = $150,537.53 + $23,740.42 = $174,277.94 The amount of loan is $15,000 ? 0.8 = $12,000.

48C ?0.0067 = $12,000

The amount of monthly installments is

48C = $12,000 / ?0.0067 = $12,000 / 40.96191 = $292.96

Option one: This cash flow is an annuity due. To value it, you must use the after-tax amounts. The after-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. Value = $115,200 + $115,200 ?300.10 = $115,200 + $115,200 (9.4269) = $1,201,178.88 Option 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)]. Value = $446,000 + $72,759.60 ?300.10 = $446,000 + $72,759.60 (9.4269) = $1,131,897.47

Since option one has a higher PV, you should choose it.

Answers to End-of-Chapter Problems B-53

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