Chapter6solutions

Chapter6solutions - CHAPTER 6 DISCOUNTED CASH FLOW...

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CHAPTER 6 DISCOUNTED CASH FLOW VALUATION Answers to Concepts Review and Critical Thinking Questions 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 basic concept of time value of money is that a dollar today is not worth the same as a dollar tomorrow. 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. 7. Yes, they should. APRs generally don’t provide the relevant rate. The only advantage is that they are easier to compute, but, with modern computing equipment, that advantage is not very important. 8. A freshman does. The reason is that the freshman gets to use the money for much longer before interest starts to accrue. The subsidy is the present value (on the day the loan is made) of the interest that would have accrued up until the time it actually begins to accrue. Solutions to Questions and Problems 1. To solve this problem, we must find the PV of each cash flow and add them. To find the PV of a lump sum, we use: PV = FV / (1 + r) t [email protected]% = $950 / 1.10 + $1,040 / 1.10 2 + $1,130 / 1.10 3 + $1,075 / 1.10 4 = $3,306.37 [email protected]% = $950 / 1.18 + $1,040 / 1.18 2 + $1,130 / 1.18 3 + $1,075 / 1.18 4 = $2,794.22 [email protected]% = $950 / 1.24 + $1,040 / 1.24 2 + $1,130 / 1.24 3 + $1,075 / 1.24 4 = $2,489.88 3. To solve this problem, we must find the FV of each cash flow and add them. To find the FV of a lump sum, we use: FV = PV(1 + r) t [email protected]% = $940(1.08) 3 + $1,090(1.08) 2 + $1,340(1.08) + $1,405 = $5,307.71
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[email protected]% = $940(1.11) 3 + $1,090(1.11) 2 + $1,340(1.11) + $1,405 = $5,520.96 [email protected]% = $940(1.24) 3 + $1,090(1.24) 2 + $1,340(1.24) + $1,405 = $6,534.81 Notice we are finding the value at Year 4, the cash flow at Year 4 is simply added to the FV of the other cash flows. In other words, we do not need to compound this cash flow. 4. To find the PVA, we use the equation: PVA = C ({1 – [1/(1 + r) ] t } / r ) [email protected] yrs: PVA = $5,300{[1 – (1/1.07) 15 ] / .07} = $48,271.94 [email protected] yrs: PVA = $5,300{[1 – (1/1.07) 40 ] / .07} = $70,658.06 [email protected] yrs: PVA = $5,300{[1 – (1/1.07) 75 ] / .07} = $75,240.70 To find the PV of a perpetuity, we use the equation: PV = C / r PV = $5,300 / .07 = $75,714.29 Notice that as the length of the annuity payments increases, the present value of the annuity approaches the present value of the perpetuity. The present value of the 75 year annuity and the present value of the perpetuity imply that the value today of all perpetuity payments beyond 75 years is only $473.59.
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This note was uploaded on 07/01/2010 for the course ECON 393 taught by Professor D during the Summer '10 term at Rutgers.

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Chapter6solutions - CHAPTER 6 DISCOUNTED CASH FLOW...

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