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**Unformatted text preview: **CHAPTER 4 DISCOUNTED CASH FLOW VALUATION Answers to Concepts Review and Critical Thinking Questions 1. Assuming positive cash flows and interest rates, the future value increases and the present value decreases. 2. Assuming positive cash flows and interest rates, the present value will fall and the future value will rise. 3. The better deal is the one with equal installments. 4. 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 im- portant. 5. A freshman does. The reason is that the freshman gets to use the money for much longer before interest starts to accrue. 6. Its a reflection of the time value of money. GMAC gets to use the $500 immediately. If GMAC uses it wisely, it will be worth more than $10,000 in thirty years. 7. Oddly enough, it actually makes it more desirable since GMAC only has the right to pay the full $10,000 before it is due. This is an example of a call feature. Such features are discussed at length in a later chapter. 8. The key considerations would be: (1) Is the rate of return implicit in the offer attractive relative to other, similar risk investments? and (2) How risky is the investment; i.e., how certain are we that we will actually get the $10,000? Thus, our answer does depend on who is making the prom- ise to repay. 9. The Treasury security would have a somewhat higher price because the Treasury is the strongest of all borrowers. 10. The price would be higher because, as time passes, the price of the security will tend to rise toward $10,000. This rise is just a reflection of the time value of money. As time passes, the time until receipt of the $10,000 grows shorter, and the present value rises. In 2010, the price will probably be higher for the same reason. We cannot be sure, however, because interest rates could be much higher, or GMACs financial position could deteriorate. Either event would tend to de- press the securitys price. B-48 SOLUTIONS 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 read- ability 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. The simple interest per year is: $5,000 .07 = $350 So, after 10 years, you will have: $350 10 = $3,500 in interest. The total balance will be $5,000 + 3,500 = $8,500 With compound interest, we use the future value formula: FV = PV(1 + r ) t FV = $5,000(1.07) 10 = $9,835.76 The difference is: $9,835.76 8,500 = $1,335.76 2. To find the FV of a lump sum, we use: FV = PV(1 + r ) t a. FV = $1,000(1.05) 10 = $1,628.89 b. FV = $1,000(1.07) 10 = $1,967.15 c. FV = $1,000(1.05) 20 = $2,653.30 d. Because interest compounds on the interest already earned, the future value in part...

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