CHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY Learning Objectives LO1 How to determine the future value of an investment made today. LO2 How to determine the present value of cash to be received at a future date. LO3 How to find the return on an investment. LO4 How long it takes for an investment to reach a desired value. Answers to Concepts Review and Critical Thinking Questions 1. (LO2) The four parts are the present value (PV), the future value (FV), the discount rate (r), and the number of payments or periods (t). 2. (LO1, 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. (LO1, 2) Future values grow (assuming a positive rate of return); present values shrink. 4. (LO1, 2) The future value rises (assuming it's positive); the present value falls. 5. (LO2) It's a reflection of the time value of money. The Province of Ontario gets to use the $76.04 immediately. As payment for deferring his own use of that money, the investor receives one interest payment of $23.96 plus return of the principal amount of $76.04 on the maturity date. 6. (LO2) 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. As the province of Ontario had an AA- credit rating in 2015 from S&P, we are very likely to see payment of the $10,000. The $500 investment would thus have a an over 10% annualized rate of return-an excellent return given the low risk. 7. (LO2) The Province of Alberta security would have a somewhat higher price because Alberta is a stronger borrower than Ontario, as reflected in a AAA credit rating for Alberta and a lower AA- credit rating for Ontario. 8. (LO2) 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 the future, the price will probably be higher for the same reason. We cannot be sure, however, because interest rates could be much higher, or Ontario's financial position could deteriorate. Either event would tend to depress the security's price. 301
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,