ch4 - Chapter 4: Net Present Value 4.1 a. Future Value = C0...

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Chapter 4: Net Present Value 4.1 a. Future Value = C 0 (1+r) T = $1,000 (1.05) 10 = $1,628.89 b. Future Value = $1,000 (1.07) 10 = $1,967.15 c. Future Value = $1,000 (1.05) 20 = $2,653.30 d. Because interest compounds on interest already earned, the interest earned in part ( c ), $1,653.30 (=$2,653.30 - $1,000) is more than double the amount earned in part ( a ), $628.89 (=$1,628.89). 4.2 The present value, PV, of each cash flow is simply the amount of that cash flow discounted back from the date of payment to the present. For example in part ( a ), discount the cash flow in year 7 by seven periods, (1.10) 7 . a. PV(C 7 ) = C 7 / (1+r) 7 = $1,000 / (1.10) 7 = $513.16 b. PV(C 1 ) = $2,000 / 1.10 = $1,818.18 c. PV(C 8 ) = $500 / (1.10) 8 = $233.25 4.3 The decision involves comparing the present value, PV, of each option. Choose the option with the highest PV. Since the first cash flow occurs 0 years in the future, or today, it does not need to be adjusted. PV(C 0 ) = $1,000 Since the second cash flow occurs 10 years in the future, it must be discounted back 10 years at eight percent. PV(C 10 ) = C 10 / (1+r) 10 = $2,000 / (1.08) 10 = $926.39 Since 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 present 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. P 0 = PV(C 25 ) = C 25 / (1+r) 25 = $1,000 / (1.10) 25 = $92.30 The price of the bond is $92.30. B-49
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4.5 The future value, FV, of the firm’s investment must equal the $1.5 million pension liability. FV = C 0 (1+r) 27 To solve for the initial investment, C 0 , discount the future pension liability ($1,500,000) back 27 years at eight percent, (1.08) 27 . $1,500,000 / (1.08) 27 = C 0 = $187,780.23 The firm must invest $187,708.23 today to be able to make the $1.5 million payment. 4.6 The decision 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) = $10,000,000 PV(Alternative 2) = $20,000,000 Choose 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 = $9,090,909.10 PV(Alternative 2) = $20,000,000 / (1.10) 5 = $12,418,426.46 Choose Alternative 2 since its PV, $12,418,426.46, is greater than that of Alternative 1, $9,090,909.10. c.
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This note was uploaded on 06/22/2009 for the course ECON 134a taught by Professor Lim during the Spring '08 term at UCSB.

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ch4 - Chapter 4: Net Present Value 4.1 a. Future Value = C0...

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