Corporate Finance 第7版 答案Ch004Word格式文档下载.docx

1、 PV（C10） = C10 / （1+r）10= $2,000 / （1.08）10 = $926.39Since the present value of the cash flow occurring today is higher than the present value of the cash flow occurring in year 10, you should take the $1,000 now. 4.4 Since the bond has no interim coupon payments, its present value is simply the pre

2、sent value of the $1,000 that will be received in 25 years. Note that the price of a bond is the present value of its cash flows. P0 = PV（C25）= C25 / （1+r）25= $1,000 / （1.10）25 = $92.30 The price of the bond is $92.30.4.5 The future value, FV, of the firms investment must equal the $1.5 million pens

3、ion liability. FV = C0 （1+r）27To solve for the initial investment, C0, discount the future pension liability （$1,500,000） back 27 years at eight percent, （1.08）27. $1,500,000 / （1.08）27 = C0 = $187,780.23 The firm must invest $187,708.23 today to be able to make the $1.5 million payment.4.6 The deci

4、sion involves comparing the present value, PV, of each option. Choose the option with the highest PV. a. At a discount rate of zero, the future value and present value of a cash flow are always the same. There is no need to discount the two choices to calculate the PV. PV（Alternative 1） = $10,000,00

5、0 PV（Alternative 2） = $20,000,000Choose Alternative 2 since its PV, $20,000,000, is greater than that of Alternative 1, $10,000,000.b. Discount the cash flows at 10 percent. Discount Alternative 1 back one year and Alternative 2, five years. PV（Alternative 1） = C / （1+r） = $10,000,000 / （1.10）1 = $9

6、,090,909.10 PV（Alternative 2） = $20,000,000 / （1.10）5 = $12,418,426.46Choose Alternative 2 since its PV, $12,418,426.46, is greater than that of Alternative 1, $9,090,909.10.c. Discount the cash flows at 20 percent. Discount Alternative 1 back one year and Alternative 2, five years. = $10,000,000 /

7、（1.20）1 = $8,333,333.33 PV（Alternative 2） = $20,000,000 / （1.20）5 = $8,037,551.44Choose Alternative 1 since its PV, $8,333,333.33, is greater than that of Alternative 2, $8,037,551.44.d. You are indifferent when the PVs of the two alternatives are equal. Alternative 1, discounted at r = Alternative

8、2, discounted at r$10,000,000 / （1+r）1 = $20,000,000 / （1+r）5Solve for the discount rate, r, at which the two alternatives are equally attractive. 1 / （1+r）1 （1+r）5 = $20,000,000 / $10,000,000（1+r）4 = 21+r = 1.18921r = 0.18921 = 18.921%The two alternatives are equally attractive when discounted at 1

9、8.921 percent. 4.7 The decision involves comparing the present value, PV, of each offer. Choose the offer with the highest PV. Since the Smiths payment occurs immediately, its present value does not need to be adjusted.PV（Smith） = $115,000The Joneses offer occurs three years from today. Therefore, t

10、he payment must be discounted back three periods at 10 percent. PV（Jones） = C3 / （1+r）3 = $150,000 / （1.10）3 = $112,697.22Since the PV of the Joneses offer, $112,697.22, is less than the Smiths offer, $115,000, you should choose the Smiths offer. 4.8 a. Since the bond has no interim coupon payments,

11、 its present value is simply the present value of the $1,000 that will be received in 20 years. Note that the price of the bond is this present value. P0 = PV（C20）= C20 / （1+r）20= $1,000 / （1.08）20 = $214.55 The current price of the bond is $214.55.b. To find the bonds price 10 years from today, fin

12、d the future value of the current price. P10 = FV10 = C0 （1+r）10 = $214.55 （1.08）10 = $463.20The bonds price 10 years from today will be $463.20.c. To find the bonds price 15 years from today, find the future value of the current price. P15 = FV15 = C0 （1+r）15 = $214.55 （1.08）15 = $680.59The bonds p

13、rice 15 years from today will be $680.59. 4.9 Ann Woodhouse would be willing to pay the present value of its resale value. PV = $5,000,000 / （1.12）10 = $1,609,866.18 The most she would be willing to pay for the property is $1,609,866.18. 4.10 a. Compare the cost of the investment to the present valu

14、e of the cash inflows. You should make the investment only if the present value of the cash inflows is greater than the cost of the investment. Since the investment occurs today （year 0）, it does not need to be discounted. PV（Investment） = $900,000PV（Cash Inflows） = $120,000 / （1.12） + $250,000 / （1

15、.12）2 + $800,000 / （1.12）3 = $875,865.52Since the PV of the cash inflows, $875,865.52, is less than the cost of the investment, $900,000, you should not make the investment. b. The net present value, NPV, is the present value of the cash inflows minus the cost of the investment. NPV = PV（Cash Inflow

16、s） Cost of Investment = $875,865.52 $900,000 = -$24,134.48The NPV is -$24,134.48.c. Calculate the PV of the cash inflows, discounted at 11 percent, minus the cost of the investment. If the NPV is positive, you should invest. If the NPV is negative, you should not invest. = $120,000 / （1.11） + $250,0

17、00 / （1.11）2 + $800,000 / （1.11）3 $900,000 = -$4,033.18Since the NPV is still negative, -$4,033.18, you should not make the investment. 4.11 Calculate the NPV of the machine. Purchase the machine if it has a positive NPV. Do not purchase the machine if it has a negative NPV. Since the initial invest

18、ment occurs today （year 0）, it does not need to be discounted. PV（Investment） = -$340,000 Discount the annual revenues at 10 percent. PV（Revenues） = $100,000 / （1.10） + $100,000 / （1.10）2 + $100,000 / （1.10）3 + $100,000 / （1.10）4 + $100,000 / （1.10）5 = $379,078.68Since the maintenance costs occur at

19、 the beginning of each year, the first payment is not discounted. Each year thereafter, the maintenance cost is discounted at an annual rate of 10 percent.PV（Maintenance） = -$10,000 - $10,000 / （1.10） - $10,000 / （1.10）2 - $10,000 / （1.10）3 $10,000 / （1.10）4= -$41,698.65 NPV = PV（Investment） + PV（Ca

20、sh Flows） + PV（Maintenance） = -$340,000 + $379,078.68 - $41,698.65 = -$2,619.97 Since the NPV is negative, -$2,619.97, you should not buy the machine. To find the NPV of the machine when the relevant discount rate is nine percent, repeat the above calculations, with a discount rate of nine percent.

21、Discount the annual revenues at nine percent. PV（Revenues） = $100,000 / （1.09） + $100,000 / （1.09）2 + $100,000 / （1.09）3 + $100,000 / （1.09）4 + $100,000 / （1.09）5 = $388,965.13Since the maintenance costs occur at the beginning of each year, the first payment is not discounted. Each year thereafter,

22、the maintenance cost is discounted at an annual rate of nine percent.PV（Maintenance） = -$10,000 - $10,000 / （1.09） - $10,000 / （1.09）2 - $10,000 / （1.09）3 $10,000 / （1.09）4= -$42,397.20 = -$340,000 + $388,965.13 - $42,397.20 = $6,567.93 Since the NPV is positive, $6,567.93, you should buy the machin

23、e. 4.12 a. The NPV of the contract is the PV of the items revenue minus its cost. PV（Revenue） = C5 / （1+r）5 = $90,000 / （1.10）5 = $55,882.92NPV = PV（Revenue） Cost = $55,882.92 - $60,000 = -$4,117.08The NPV of the item is -$4,117.08. b. The firm will break even when the items NPV is equal to zero. NP

24、V = PV（Revenues） Cost = C5 / （1+r）5 Cost$0 = $90,000 / （1+r）5 - $60,000 r = 0.08447 = 8.447%The firm will break even on the item with an 8.447 percent discount rate. 4.13 Compare the PV of your aunts offer with your roommates offer. Choose the offer with the highest PV. The PV of your aunts offer is

25、 the sum of her payment to you and the benefit from owning the car an additional year. PV（Aunt） = PV（Trade-In） + PV（Benefit of Ownership） = $3,000 / （1.12） + $1,000 / （1.12） = $3,571.43 Since your roommates offer occurs today （year 0）, it does not need to be discounted. PV（Roommate） = $3,500Since th

26、e PV of your aunts offer, $3,571.43, is higher than your roommates offer, $3,500, you should accept your aunts offer. 4.14 The cost of the car 12 years from today will be $80,000. To find the rate of interest such that your $10,000 investment will pay for the car, set the FV of your investment equal

27、 to $80,000. FV = C0 （1+r）12$80,000 = $10,000 （1+r）12Solve for the interest rate, r. 8 = （1+r）12 0.18921 = r The interest rate required is 18.921%. 4.15 The deposit at the end of the first year will earn interest for six years, from the end of year 1 to the end of year 7. FV = $1,000 （1.12）6 = $1,973.82The deposit at the end of the second year will earn interest for five years. FV = $1,000 （1.12）5 = $1,762.34The depo