rw6ech05_sol - CHAPTER 5 INTRODUCTION TO VALUATION: THE...

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CHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY Answers to Concepts Review and Critical Thinking Questions 1. The four parts are the present value (PV), the future value (FV), the discount rate ( r ), and the life of the investment ( t ). 2. Compounding refers to the growth of a dollar amount through time via reinvestment of interest earned. It is also the process of determining the future value of an investment. Discounting is the process of determining the value today of an amount to be received in the future. 3. Future values grow (assuming a positive rate of return); present values shrink. 4. The future value rises (assuming it’s positive); the present value falls. 5. It’s a reflection of the time value of money. ScotiaMcLeod gets to use the $29.19 immediately. If Scotia uses it wisely, it will be worth more than $100 in twenty years. 6. 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 promise to repay. 7. The Government of Canada security would have a somewhat higher price because the Government of Canada is the strongest of all borrowers. 8. The price would be higher because, as time passes, the price of the security will tend to rise toward $100. This rise is just a reflection of the time value of money. As time passes, the time until receipt of the $100 grows shorter, and the present value rises. In 2007, the price will probably be higher for the same reason. We cannot be sure, however, because interest rates could be much higher, or Canada’s financial position could deteriorate. Either event would tend to depress the security’s price. 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. 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: 45
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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 FV = $2,250(1.10) 19 = $ 13,760.80 FV = $9,310(1.08) 13 = $ 25,319.70 FV = $76,355(1.22) 4 = $169,151.87 FV = $183,796(1.07) 8 = $315,795.75 3.
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rw6ech05_sol - CHAPTER 5 INTRODUCTION TO VALUATION: THE...

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