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# newnansm7 - Chapter 7 Rate of Return Analysis 7-1 \$125 =...

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Unformatted text preview: Chapter 7: Rate of Return Analysis 7-1 \$125 = \$10 (P/A, i%, 6) + \$10 (P/G, i%, 6) at 12%, \$10 (4.111) + \$10 (8.930) = \$130.4 at 15%, \$10 (3.784) + \$10 (7.937) = \$117.2 i* = 12% + (3%) ((130.4 – 125).(130.4-117.2)) = 13.23% 7-2 The easiest solution is to solve one cycle of the repeating diagram: \$120 = \$80 (F/P, i%, 1) \$120 = \$80 (1 + i) (1 + i) = \$120/\$80 = 1.50 \$80 \$80 \$80 \$80 \$80 \$200 \$200 = \$80 \$80 \$80 \$20 \$12 \$12 \$10 \$20 \$30 \$40 \$50 \$60 i* = 0.50 = 50% Alternative Solution: EUAB = EUAC \$80 = [\$200 (P/F, i%, 2) + \$200 (P/F, i%, 4) + \$200 (P/F, i%, 6)] (A/P, i%, 6) Try i = 50% \$80 = [\$200 (0.4444) + \$200 (0.1975) + \$200 (0.0878)] (0.5481) = \$79.99 Therefore i* = 50%. 7-3 \$42.55 = \$5 (P/A, i%, 5) + \$5 (P/G, i%, 5) Try i = 15% , \$5 (3.352) + \$5 (5.775) = \$45.64 > \$42.55 Try i = 20%, \$5 (2.991) + \$5 (4.906) = \$39.49 < \$42.55 Rate of Return = 15% + (5%) [(\$45.64 - \$42.55)/(\$45.64 - \$39.49)] = 17.51% Exact Answer: 17.38% 7-4 For infinite series: A = Pi EUAC= EUAB \$3,810 (i) = \$250 + \$250 (F/P, i%, 1) (A/F, i%, 2)* Try i = 10% \$250 + \$250 (1.10) (0.4762) = \$381 \$3,810 (0.10) = \$381 i = 10% *Alternate Equations: \$3,810 (i) = \$250 + \$250 (P/F, i%, 1) (A/P, i%, 2) \$3,810 (j) = \$500 - \$250 (A/G, i%, 2) \$5 \$10 \$15 \$20 \$25 \$42.55 7-5 At Year 0, PW of Cost = PW of Benefits \$412 + \$5,000 (P/F, i%, 10) = (\$1000/i) (P/F, i%, 10) Try i = 15% \$412 + \$5,000 (0.2472) = (\$1,000/0.15) (0.2472) \$1,648 = \$1,648 ROR = 15% 7-6 The algebraic sum of the cash flows equals zero. Therefore, the rate of return is 0%. 7-7 Try i = 5% \$1,000 =(?) \$300 (3.546) (0.9524) =(?) \$1,013.16 Try i = 6% \$1,000 =(?) \$300 (3.465) (0.9434) =(?) \$980.66 Performing Linear Interpolation: i* = 5% + (1%) ((\$1,013.6 - \$1,000)/(\$1,013.6 - \$980.66)) = 5.4% …………. n = 10 \$41 Yr 0 \$5,000 P’ A = \$1,000 n = ∞ \$1,000 A = \$300 7-8 \$400 = [\$200 (P/A, i%, 4) - \$50 (P/G, i%, 4)] (P/F, i%, 1) Try i = 7% [\$200 (3.387) - \$50 (4.795)] (0.9346) = 409.03 Try i = 8% [\$200 (3.312) - \$50 (4.650)] (0.9259) = \$398.08 i* = 7% + (1%) [(\$409.03 - \$400)/(\$409.03 - \$398.04)] = 7.82% 7-9 \$100 = \$27 (P/A, i%, 10) (P/A, i%, 10) = 3.704 Performing Linear Interpolation: ( P/A , i %, 10) i 4.192 20% 3.571 25% Rate of Return = 20% + (5%) [(4.192 – 3.704)/(4.912 – 3.571)] = 23.9% 7-10 Year Cash Flow-\$500 1-\$100 2 +\$300 3 +\$300 4 +\$400 5 +\$500 \$500 + \$100 (P/F, i%, 1)= \$300 (P/A, i%, 2) (P/F, i%, 1) + \$400 (P/F, i%, 4) + \$500 (P/F, i%, 5) Try i = 30% \$500 + \$100 (0.7692) = \$576.92 \$300 (1.361) (0.7692) + \$400 (0.6501) + \$500 (0.2693)= \$588.75 ∆ = 11.83 Try i = 35% \$500 + \$100 (0.7407) = \$574.07 \$300 (1.289) (0.7407) + \$400 (0.3011) + \$500 (0.2230)= \$518.37 ∆ = 55.70 Rate of Return = 30% + (5%) [11.83/55.70) = 31.06% Exact Answer: 30.81% 7-11 Year Cash Flow-\$223 1-\$223 2-\$223 3-\$223 4-\$223 5-\$223 6 +\$1,000 7 +\$1,000 8 +\$1,000 9 +\$1,000 10 +\$1,000 The rate of return may be computed by any conventional means. On closer inspection one observes that each \$223 increases to \$1,000 in five years....
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## This note was uploaded on 08/13/2010 for the course IME IME 314 taught by Professor Freeman during the Spring '10 term at Cal Poly.

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newnansm7 - Chapter 7 Rate of Return Analysis 7-1 \$125 =...

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