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RW5eCh06RR

# RW5eCh06RR - CHAPTER 6 DISCOUNTED CASH FLOW VALUATION...

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CHAPTER 6 DISCOUNTED CASH FLOW VALUATION Answers to Concepts Review and Critical Thinking Questions 1. The four pieces are the present value (PV), the periodic cash flow ( C ), the discount rate ( r ), and the number of payments, or the life of the annuity, t . 2. Assuming positive cash flows, both the present and the future values will rise. 3. Assuming positive cash flows, the present value will fall, and the future value will rise. 4. It’s deceptive, but very common. The deception is particularly irritating given that such lotteries are usually government sponsored! 5. If the total money is fixed, you want as much as possible as soon as possible. The team (or, more accurately, the team owner) wants just the opposite. 6. The better deal is the one with equal installments. Solutions to Questions and Problems Basic 1. [email protected]% = \$1,300 / 1.10 + \$500 / 1.10 2 + \$700 / 1.10 3 + 1,620 / 1.10 4 = \$3,227.44 [email protected]% = \$1,300 / 1.18 + \$500 / 1.18 2 + \$700 / 1.18 3 + 1,620 / 1.18 4 = \$2,722.41 [email protected]% = \$1,300 / 1.24 + \$500 / 1.24 2 + \$700 / 1.24 3 + 1,620 / 1.24 4 = \$2,425.93 2. PVA = \$3,000{[1 – (1/1.05) 8 ] / .05 } = \$19,389.64 PVA = \$5,000{[1 – (1/1.05) 4 ] / .05 } = \$17,729.75 PVA = \$3,000{[1 – (1/1.22) 8 ] / .22 } = \$10,857.80 PVA = \$5,000{[1 – (1/1.22) 4 ] / .22 } = \$12,468.20 3. = \$900(1.08) 3 + \$1,000(1.08) 2 + \$1,100(1.08) + 1,200 = \$4,688.14 = \$900(1.11) 3 + \$1,000(1.11) 2 + \$1,100(1.11) + 1,200 = \$4,883.97 = \$900(1.24) 3 + \$1,000(1.24) 2 + \$1,100(1.24) + 1,200 = \$5,817.56 4. PVA = \$4,100{[1 – (1/1.10) 15 ] / .10} = \$31,184.93 PVA = \$4,100{[1 – (1/1.10) 40 ] / .10} = \$40,094.11 PVA = \$4,100{[1 – (1/1.10) 75 ] / .10} = \$40,967.76 PVA = \$4,100 / .10 = \$41,000.00 5. PVA = \$20,000 = \$ C {[1 – (1/1.0825) 12 ] / .0825}; C = \$20,000 / 7.4394 = \$2,688.38 6. PVA = \$75,000{[1 – (1/1.075) 8 ] / .075} = \$439,297.77; can afford the system. 7. FVA = \$50,000 = \$ C [(1.062 5 – 1) / .062]; C = \$50,000 / 5.65965 = \$8,834.47 8. PV = \$5,000 / .09 = \$55,555.56 9. PV = \$58,000 = \$5,000 / r ; r = \$5,000 / \$58,000 = 8.62% 10. EAR = [1 + (.12 / 4)] 4 – 1 = 12.55% 51

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EAR = [1 + (.08 / 12)] 12 – 1 = 8.30% EAR = [1 + (.07 / 365)] 365 – 1 = 7.25% EAR = e .16 – 1 = 17.35% 11. EAR = .072 = [1 + (APR / 2)] 2 – 1; APR = 2[(1.072) 1/2 – 1] = 7.07% EAR = .091 = [1 + (APR / 12)] 12 – 1; APR = 12[(1.091) 1/12 – 1] = 8.74% EAR = .185 = [1 + (APR / 52)] 52 – 1; APR = 52[(1.185) 1/52 – 1] = 17.00% EAR = .283 = e APR – 1; APR = ln 1.283 = 24.92% 12. Royal Canadian: EAR = [1 + (.091 / 12)] 12 – 1 = 9.49% First Royal: EAR = [1 + (.092 / 2)] 2 – 1 = 9.41% 13. EAR = .14 = [1 + (APR / 365)] 365 – 1; APR = 365[(1.14) 1/365 – 1] = 13.11% The borrower is actually paying annualized interest of 14% per year, not the 13.11% reported on the loan contract. 14. FV in 5 years = \$5,000[1 + (.063/365)] 5(365) = \$6,851.11 FV in 10 years = \$5,000[1 + (.063/365)] 10(365) = \$9,387.55 FV in 20 years = \$5,000[1 + (.063/365)] 20(365) = \$17,625.22 15. PV = \$19,000 / (1 + .12/365) 6(365) = \$9,249.39 16. APR = 12(25%) = 300%; EAR = (1 + .25) 12 – 1 = 1,355.19% 17. PVA = \$48,250 = \$ C [1 – {1 / [1 + (.098/12)] 60 } / (.098/12)]; C = \$48,250 / 47.284 = \$1,020.43 EAR = [1 + (.098/12)] 12 – 1 = 10.25% 18. PVA = \$17,805.69 = \$400{ [1 – (1/1.015) t ] / .015}; 1/1.015 t = 1 – [(\$17,805.69)(.015) / (\$400)] 1.015 t = 1/(0.33229) = 3.0094; t = ln 3.0094 / ln 1.015 = 74 months 19. \$3(1 + r ) = \$4; r = 4/3 – 1 = 33.33% per week APR = (52)33.33% = 1,733.33%; EAR = [1 + (1/3)] 52 – 1 = 313,916,512% 20. PV = \$75,000 = \$1,050 / r ; r = \$1,050 / \$75,000 = 1.40% per month Nominal return = 12(1.40%) = 16.80% per year; Effective return = [1.0140] 12 – 1 = 18.16% per year 21. FVA = \$100[{[1 + (.11/12) ] 240 – 1} / (.11/12)] = \$86,563.80 22. EAR = [1 + (.11/12)] 12 – 1 = 11.571884% FVA = \$1,200[(1.11571884 20 – 1) / .11571884] = \$82,285.82 23. PVA = \$1,000{[1 – (1/1.0075) 16 ] / .0075} = \$15,024.31 24. EAR = [1 + (.14/4)] 4 – 1 = 14.7523% PV = \$800 / 1.147523 + \$700 / 1.147523 2 + \$1,200 / 1.147523 4 = \$1,920.79 Intermediate 25. (.06)(10) = (1 + r ) 10 – 1 ; r = 1.6 1/10 – 1 = 4.81% 26. EAR = .14 = (1 + r ) 2 – 1; r = (1.14) 1/2 – 1 = 6.77% per 6 months EAR = .14 = (1 + r ) 4 – 1; r = (1.14) 1/4 – 1 = 3.33% per quarter EAR = .14 = (1 + r ) 12 – 1; r = (1.14) 1/12 – 1 = 1.10% per month 27. FV = \$3,000 [1 + (.029/12)] 6 [1 + (.15/12)] 6 = \$3,279.30 52
Interest = \$3,279.30 – \$3,000.00 = \$279.30 28. First: \$95,000(.05) = \$4,750 per year (\$150,000 – 95,000) / \$4,750 = 11.58 years Second: \$150,000 = \$95,000 [1 + (.05/12)] t t = 109.85 months = 9.15 years 29. FV = \$1(1.0172) 12 = \$1.23 FV = \$1(1.0172) 24 = \$1.51 30. FV = \$2,000 = \$1,100(1 + .01) t ; t = 60.08 months 31. FV = \$4 = \$1(1 + r ) (12/3) ; r = 41.42% 32. EAR = [1 + (.10 / 12)] 12 – 1 = 10.4713% PVA 1 = \$75,000 {[1 – (1 / 1.104713) 2 ] / .104713} = \$129,346.66 PVA 2 = \$30,000 + \$55,000{[1 – (1/1.104713) 2 ] / .104713} = \$124,854.22 33. PVA = \$10,000 [1 – (1/1.095) 20 / .095] = \$88,123.82 34. G: PV = –\$30,000 + [\$55,000 / (1 + r ) 6 ] = 0; (1 + r ) 6 = 55/30; r = (1.833) 1/6 – 1 = 10.63% H: PV = –\$30,000 + [\$90,000 / (1 + r ) 11 ] = 0; (1 + r ) 11 = 90/30; r = (3.000) 1/11 – 1 = 10.50% 35. PVA falls as r increases, and PVA rises as r decreases

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RW5eCh06RR - CHAPTER 6 DISCOUNTED CASH FLOW VALUATION...

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