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# ch4 - Chapter 4 Net Present Value 4.1 a Future Value = C0(1...

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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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ch4 - Chapter 4 Net Present Value 4.1 a Future Value = C0(1...

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