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Answers to Problem Set 5 1. (5.24) Determine the capitalized cost of an expenditure of \$200,000 at time 0, \$25,000 in years 2 through 5, and \$40,000 per year from year 6 on. Use an interest rate of 12% per year. CC = -200,000 – 25,000(P/A,12%,4)(P/F,12%,1) – [40,000/0.12](P/F,12%,5) = -200,000 – 25,000(3.0373)(0.8929) – [40,000/0.12])(0.5674) = \$-456,933 2. (5.27) If you want to be able to withdraw 80,000 per year forever beginning 30 years from now, how much will you have to have in your retirement account (that earns 8% per year interest) in (a) year 29 and (b) year 0? (a) P 29 = 80,000/0.08 = \$1,000,000 (b) P 0 = 1,000,000(P/F,8%,29) = 1,000,000(0.1073) = \$107,300 3. (5.30) Compare the following alternatives on the basis of their capitalized cost at an interest rate of 10% per year. Petroleum- Based Feedstock Inorganic- Based Feedstock First cost, \$ –250,000 –110,000 Annual operating cost, –130,000 –65,000 \$/year Annual revenues, 400,000 270,000 \$/year Salvage value, \$ 50,000 20,000 Life, years 6 4 CC petroleum = [-250,000(A/P,10%,6) –130,000 + 400,000 + 50,000(A/F,10%,6)]/0.10 = [-250,000(0.22961) –130,000 + 400,000 + 50,000(0.12961)]/0.10 = \$2,190,780 CC inorganic = [-110,000(A/P,10%,4) – 65,000 + 270,000 + 20,000(A/F,10%,4)]/0.10 = [-110,000(0.31547) – 65,000 + 270,000 + 20,000(0.21547)]/0.10 = \$1,746,077 Petroleum-based alternative has a larger profit. SO CLEARLY CAPITALIZED COST IS NOT ABOUT “COSTS” ONLY. IF THERE ARE REVENUES WHOSE PRESENT VALUE EXCEEDS THAT OF COSTS, CC VALUE WILL BE POSITIVE.

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14. (5.33) Compare the alternatives shown below on the basis of their capitalized costs, using an interest rate 12% per year, compounded quarterly. Alternative E
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