Ch6Solutions

# Ch6Solutions - Chapter 6 6.1 The lowest rate of return is...

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Chapter 6  6.1 The lowest rate of return is –100%. 6.2 For an investment that doubles every 6 months when interest is compounded semiannually, the effective rate of return per 6-months is 100%. Therefore, the nominal return per year is 2*100 = 200%. 6.3 For interest on principal , interest each month is 0.005(100,000,000) = \$500,000 For interest on unrecovered balance , monthly payment is: A = 100,000,000(A/P,0.5,60) = 100,000,000(0.01933) = 1,933,333 Amt owed after 1 st month is 100,000,000 – 1,933,333 = \$98,067,000 Interest in month 2 = \$98,067,000(0.005) = \$490,335 Difference = 500,000 – 490,335 = \$9665 6.4 Amount due after 1 month = 300,000(1.007) = \$302,100 Balance after \$50,000 payment = 302,100 – 50,000 = \$252,100 6.5 Solve equation by trial and error or Excel: 0 = -50,000 + 15,000(P/A,i,4) + 9000(P/F,i,4) Try i = 12%: -50,000 + 15,000(3.0373) + 9000(0.6355) = \$1279 i too low Try i = 14%: -50,000 + 15,000(2.9137) + 9000(0.5921) = \$-965.60 i too high By interpolation, i = 13.14% 6.6 Move all cash flow to year 1: 0 = -80,000 – 9000(P/F,i,1) + 40,000(P/F,i,2) + 70,000(P/F,i,3) Solve for i by trial and error or excel: i = 8.74% (Excel) 6.7 0 = -24,000 + (27,000 – 17,000)(P/A,i,5) (P/A,i,5) = 2.4000 i = 30.77% (Excel) 6.8 0 = -2000 + 7000(P/F,i,2) (P/F,i,2) = 0.28571 Solve by equation or spreadsheet i = 87.1% per year 6- 1

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6.9 0 = -65,220(P/A,i,4) + (57,925 – 35,220)(P/A,i,31)(P/F,i,4) 0 = -65,220(P/A,i,4) + (22,705)(P/A,i,31)(P/F,i,4) Solve by trial and error: Try 6%: 0 = -225,994 + 250,510 = \$24,516 i too low Try 7%: 0 = -220,913 + 217,071 = -\$3842 i too high i = 6.86% per year (spreadsheet) 6.10 0 = -1537(P/A,i,48) + (2057 – 1537)(P/A,i,240)(P/F,i,48) 0 = -1537(P/A,i,48) + (520)(P/A,i,240)(P/F,i,48) Solve by trial and error or spreadsheet: (a) i = 0.39% per month (spreadsheet) (b) i = 0.39*12 = nominal 4.68% per year 6.11 0 = -100 – 400(100,000) + 20(P/A,i,10) (millions) 0 = -140 + 20(P/A,i,10) (P/A,i,10) = 7.000 From 7% and 8% tables, i is slightly over 7% i = 7.07% per year (spreadsheet) 6.12 0 = -5(6000) + 600(P/A,i,156) (P/A,i,156) = 50.0000 Solve for i by trial and error or spreadsheet: (a) i = 1.89% per week (spreadsheet) (b) i = 1.89*52 = nominal 98.3% per year 6.13 Spending \$60,000 now will result in savings of \$28,000 in years 0, 3 and 6. The rate of return equation is : 0 = -60,000 + 28,000 + 28,000[(P/F,i,3) + (P/F,i,+6)] 0 = -32,000 + 28,000[(P/F,i,3) + (P/F,i,+6)] Solve for i by trial and error or spreadsheet: i = 13.7% per year (spreadsheet) 6.14 0 = -500 + 0.18(2500)(P/F,i,2) + 500(1.62)(P/A,i,5)(P/F,i,5) – 10(P/A,i,10) 0 = -500 + 450(P/F,i,2) + 810(P/A,i,5)(P/F,i,5) – 10(P/A,i,10) Solve for i by trial and error or spreadsheet: i = 42% per year (spreadsheet) 6- 2
6.15 (a) 0 = -4.97 + + 1.3(P/A,i,10) (P/A,i,10) = 3.8231 Solve for i by trial and error or spreadsheet: i = 22.8% per year (spreadsheet) (b) Cost of guardrail = 72,000(113) = \$8.136 million 0 = -8.136 + 1.1(P/A,i,10) (P/A,i,10) = 7.39636 Solve for i by trial and error or spreadsheet:

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## This note was uploaded on 03/24/2011 for the course ISEN 302 taught by Professor Ko during the Spring '08 term at Texas A&M.

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Ch6Solutions - Chapter 6 6.1 The lowest rate of return is...

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