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# newnansm5 - Chapter 5 Present Worth Analysis 5-1 P =...

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Unformatted text preview: Chapter 5: Present Worth Analysis 5-1 P = \$50 (P/A, 10%, 4) + \$50 (P/G, 10%, 4) = \$50 (3.170) + \$50 (4.378) = \$377.40 5-2 P = \$30 + \$20 (P/A, 15%, 2) + \$30 (P/F, 15%, 3) = \$30 + \$20 (1.626) + \$30 (0.6575) = \$82.25 5-3 P = \$300 (P/A, 12%, 3) - \$100 (P/G, 12%, 3) = \$300 (2.402) - \$100 (2.221) = \$498.50 \$50 \$10 \$15 \$200 P \$30 \$30 \$20 P P \$30 \$20 \$10 5-4 Q = \$50 (P/A, 12%, 6) (F/P, 12%, 2) = \$50 (4.111) (1.254) = \$257.76 5-5` P = \$50 (P/A, 10%, 6) (P/F, 10%, 3) + \$70 (P/F, 10%, 5) + \$70 (P/F, 10%, 7) + \$70 (P/F, 10%, 9) = \$50 (4.355) (0.7513) + \$70 (0.6209 + 0.5132 + 0.4241) = \$272.67 Alternative Solution P = [\$50 (P/A, 10%, 6) + \$70(P/F, 10%, 2) + \$70 (P/F, 10%, 4) + \$70 (P/F, 10%, 6)](P/F, 10%, 3) = [\$50 (4.355) + \$70 (0.8264 + 0.6830 + 0.5645)] (0.7513) = \$272.66 \$50 \$50 \$50 \$50 \$50 Q P \$120 \$120 \$50 \$50 \$50 5-6 P = \$60 + \$60 (P/A, 10%, 4) + \$120 (P/F, 10%, 5) = \$60 + \$60 (3.170) + \$120 (0.6209) = \$324.71 5-7 P = A 1 (P/A, q, i, n) = A 1 [(1 – (1.10) 4 (1.15)-4 )/(0.15 – 0.10)] = \$200 (3.258) = \$651.60 5-8 P^ = B/0.10 = 10 B P = P^ (P/F, 10%, 3) = 10 B (0.7513) = 7.51 B ………... P P^ B B B ………..... \$60 \$60 \$60 \$60 \$120 P 5-9 P* = G (P/G, i %, 6) P = P* (F/P, i %, 1) Thus: P = G (P/G, i %, 6) (F/P, i %, 1) 5-10 P = F e-rn + F* [(e r – 1)/(re rn )] = \$500 (0.951229) + \$500 [0.051271/0.058092] = \$475.61 + 441.29 = \$916.90 5-11 The cycle repeats with a cash flow as below: P* G 2G 3G 4G 5G P* P G 2G 3G 4G 5G Carved Equation Carved 1 2 3 \$50 \$500 P P = {[\$400 - \$100 (A/G, 8%, 4) + \$900 (A/F, 8%, 4)]/0.08 + \$1,000} {P/F, 8%, 5} = {[\$400 - \$100 (1.404) + \$900 (0.2219)]/0.08 + \$1,000} {0.6806} = \$4,588 Alternative Solution: An alternate solution may be appropriate if one assumes that the \$1,000 cash flow is a repeating annuity from time 13 to infinity (rather than indicating the repeating decreasing gradient series cycles). In this case P is calculated as: P = [\$500 - \$100 (A/G, 8%, 4)](P/A, 8%, 8)(P/F, 8%, 4) + \$500 (P/F, 8%, 5) + \$500 (P/F, 8%, 9) + \$1,000 (P/A, 8%, ∞) (P/F, 8%, 12) = \$7,073 5-12 P = \$9,000 (P/A, 18%, 10) + \$145,000 (P/F, 18%, 10) = \$9,000 (4.494) + \$145,000 (0.1911) = \$68,155.50 5-13 P = \$100 (P/A, 6%, 6) + \$100 (P/G, 6%, 6) = \$100 (4.917) + \$100 (11.459) = \$1,637.60 A = \$9,000 \$145,000 P \$40 \$300 \$20 \$1,000 5-14 PW of Cost = PW of Benefits P = \$750 (P/A, 7%, 20) + 0.1P (P/F, 7%, 20) = \$750 (10.594) + 0.1P (0.2584) = \$7945 + 0.02584P P = \$7945/(1-0.02584) = \$7945/0.97416 = \$8156 5-15 Determine the cash flow: Year Cash Flow-\$4,400 1 \$220 2 \$1,320 3 \$1,980 4 \$1,540 NPW = PW of Benefits – PW of Cost = \$220 (P/F, 6%, 1) + \$1,320 (P/F, 6%, 2) + \$1,980 (P/F, 6%, 3) + \$1,540 (P/F, 6%, 4) - \$4,400 = \$220 (0.9434) + \$1,320 (0.8900) + \$1,980 (0.8396) + \$1,540 (0.7921) - \$4,400 = -\$135.41 NPW is negative. Do not purchase equipment....
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newnansm5 - Chapter 5 Present Worth Analysis 5-1 P =...

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