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**Unformatted text preview: **Chapter 05 - Discounted Cash Flow Valuation CHAPTER 5 DISCOUNTED CASH FLOW VALUATION Answers to Concepts Review and Critical Thinking Questions 1. Assuming positive cash flows and a positive interest rate, both the present and the future value will rise. 2. Assuming positive cash flows and a positive interest rate, the present value will fall, and the future value will rise. 3. Its deceptive, but very common. The deception is particularly irritating given that such lotteries are usually government sponsored! 4. The most important consideration is the interest rate the lottery uses to calculate the lump sum option. If you can earn an interest rate that is higher than you are being offered, you can create larger annuity payments. Of course, taxes are also a consideration, as well as how badly you really need $5 million today. 5. If the total amount of 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 dont 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. 9. 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. 10. The problem is that the subsidy makes it easier to repay the loan, not obtain it. However, the ability to repay the loan depends on future employment, not current need. For example, consider a student who is currently needy, but is preparing for a career in a high-paying area (such as corporate finance!). Should this student receive the subsidy? How about a student who is currently not needy, but is preparing for a relatively low-paying job (such as becoming a college professor)? 5-1 Solutions to Questions and Problems NOTE: All end-of-chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to space and readability constraints, when these intermediate steps are included in this solutions manual, rounding may appear to have occurred. However, the final answer for each problem is found without rounding during any step in the problem. Basic 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 PV@10% = $950 / 1.10 + $730 / 1.10 2 + $1,420 / 1.10 3 + $1,780 / 1.10 4 = $3,749.57 PV@18% = $950 / 1.18 + $730 / 1.18 2 + $1,420 / 1.18 3 + $1,780 / 1.18 4 = $3,111.72 PV@24% = $950 / 1.24 + $730 / 1.24 2 + $1,420 / 1.24 3 + $1,780 / 1.24 4 = $2,738.56 2. To find the PVA, we use the equation: PVA = C ({1 [1/(1 + r ) t ]} / r ) At a 6 percent interest rate: X@6%: PVA = $4,300{[1 (1/1.06) 9 ] / .06 } = $29,247.28 Y@6%: PVA = $6,100{[1 (1/1.06)PVA = $6,100{[1 (1/1....

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