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**Unformatted text preview: **Chapter 2: Time Value of Money Learning Objectives 7 Chapter 2 Time Value of Money Learning Objectives After reading this chapter, students should be able to: Convert time value of money (TVM) problems from words to time lines. Explain the relationship between compounding and discounting, between future and present value. Calculate the future value of some beginning amount, and find the present value of a single payment to be received in the future. Solve for interest rate or time, given the other three variables in the TVM equation. Find the future value of a series of equal, periodic payments (an annuity) and the present value of such an annuity. Explain the difference between an ordinary annuity and an annuity due, and calculate the difference in their values — both on a present value and future value basis. Solve for annuity payments, periods, and interest rates, given the other four variables in the TVM equation. Calculate the value of a perpetuity. Demonstrate how to find the present and future values of an uneven series of cash flows and how to solve for the interest rate of an uneven series of cash flows. Solve TVM problems for non-annual compounding. Distinguish among the following interest rates: Nominal (or Quoted) rate, Periodic rate, Annual Percentage Rate (APR), and Effective (or Equivalent) Annual Rate; and properly choose among securities with different compounding periods. Solve time value of money problems that involve fractional time periods. Construct loan amortization schedules for fully-amortized loans. 8 Integrated Case Chapter 2: Time Value of Money Answers to End-of-Chapter Questions 2-1 The opportunity cost is the rate of interest one could earn on an alternative investment with a risk equal to the risk of the investment in question. This is the value of I in the TVM equations, and it is shown on the top of a time line, between the first and second tick marks. It is not a single rate — the opportunity cost rate varies depending on the riskiness and maturity of an investment, and it also varies from year to year depending on inflationary expectations (see Chapter 6). 2-2 True. The second series is an uneven cash flow stream, but it contains an annuity of $400 for 8 years. The series could also be thought of as a $100 annuity for 10 years plus an additional payment of $100 in Year 2, plus additional payments of $300 in Years 3 through 10. 2-3 True, because of compounding effects — growth on growth. The following example demonstrates the point. The annual growth rate is I in the following equation: $1(1 + I) 10 = $2. We can find I in the equation above as follows: Using a financial calculator input N = 10, PV = -1, PMT = 0, FV = 2, and I/YR = ? Solving for I/YR you obtain 7.18%....

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