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Unformatted text preview: Note 1 : Unless otherwise stated, all cash flows given in the problems represent after tax cash flows in actual dollars. The MARR also represents a market interest rate, which considers any inflationary effects in the cash flows. Note 2 : Unless otherwise stated, all interest rates presented in this set of problems assume annual compounding. 6.1 Consider the following cash flows and compute the equivalent annual worth at i = 12%: A n n Investment Revenue$10,000 1 $2,000 2 $2,000 3 $3,000 4 $3,000 5 $1,000 6 $2,000 $500 Answer AE (12%) = [$10,000 + $2,000(P/F, 12%, 1) + +$2,500(P/F, 12%, 6)] (A/P, 12%, 6) = $180.96 1 6.2 (A) The following investment has a net present value of zero at i = 8%: X X X X $400 $400 0 1 2 3 4 5 6 Years $2,145 Which of the following is the net equivalent annual worth at 8% interest? (a) $400 (b) $0 (c) $500 (d) $450 Answer (b) NEAW = NPW * (A/P, 8, 6) 0 = 2145 + 400 * (P/F, 8, 1) + 400 * (P/F, 8, 4) + X * (P/A, 8, 2) (P/F, 8, 1) + X * (P/A, 8, 2) (P/F, 8, 4) = 2145 + 400 * [(P/F, 8, 1) + (P/F, 8, 4)] + X * (P/A, 8, 2) [(P/F, 8, 1) + (P/F, 8, 4)] = 2145 + 400 * [.9259 + .7350] + X * 1.7833 * [9259 + .7350] = 2145 + 400 * 1.6609 + X * 2.9619 1475.64 / 2.9619 = X = 498.21 2 6.3 Consider the following sets of investment projects: Projects Cash Flow n A B C D 0 $2,000 $4,000 $3,000 $9,000 1 $400 $3,000 $2,000 $2,000 2 $500 $2,000 $4,000 $4,000 3 $600 $1,000 $2,000 $8,000 4 $700 $500 $4,000 $8,000 5 $800 $500 $2,000 $4,000 Compute the equivalent annual worth of each project at i = 10%, and determine the acceptability of each project. Answer AE (10%) A = $2,000(A/P, 10%, 5) + $400 +$100(A/G, 10%, 5) = $53.42 (Accept) AE (10%) B = $4,000(A/P, 10%, 5) + $500 + [$2,500(P/F, 10%, 1) + $1,500(P/F, 10%, 2) + $500(P/F, 10%, 3)] (A/P, 10%, 5) = $470.47 (Accept) AE (10%) C = [$3,000  $2,000(P/F, 10%, 1) + + $2,000(P/F, 10%, 5)] (A/P, 10%, 5) = $1,045.73 (Accept) AE (10%) D = [$9,000 + $2,000(P/F, 10%, 1) + + $4,000(P/F, 10%, 5)] (A/P, 10%, 5) = $2,659.68 (Accept) 3 6.4 (A) What is the annualequivalence amount for the following infinite series at i = 12%? $1,200 $700 0 1 2 3 4 5 6 7 8 9 10 11 12 13 Years (a) $950 (b) $866 (c) $926 (d) None of the above Answer (a) AE (12%) = $700 + [($500/0.12) (P/F, 12%, 6)] (0.12) = $700 + [($500/0.12) (.50663)] (0.12) = $953 NB AE (12%) = $700 +$500 * (P/F, 12%, 6) 4 6.5 Consider the following sets of investment projects: Period Projects Cash Flow (n) A B C D 0 $3,500 $3,000 $3,000 $3,600 1 $0 $1,500 $3,000 $1,800 2 $0 $1,800 $2,000 $1,800 3 $5,500 $2,100 $1,000 $1,800 Compute the equivalent annual worth of each project at i = 13%, and determine the acceptability of each project....
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 Spring '11
 bardis
 Inflation

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