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The Time Value of Money
This topic review covers time value of money concepts and applications. Procedures are presented for calculating the future value and present value of a single cash flow, an annuity, and a series of uneven cash flows. The impact of different compounding periods is examined, along with the procedures for solving for other variables in time value of money problems. Your main objective in this chapter is to master time value of money mechanics (i.e., learn how to crunch the numbers). Work all the questions and problems found at the end of this review. Make sure you know how to grind out all the time value of money problems on your calculator. The more rapidly you can do them (correctly), the more time you will have for the more conceptual parts of the exam.
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Take-away Concepts
6a. An interest rate can be interpreted as the rate of return required in equilibrium for a particular investment, the discount rate for calculating the present value of future cash flows, or as the opportunity cost of consuming now, rather than saving and investing.
6b. The real risk-free rate is a theoretical rate on a single-period loan when there is no expectation of inflation. Nominal risk-free rate = real risk-free rate + expected inflation rate. Securities may have several risks, and each increases the required rate of return. These include default risk, liquidity risk, and maturity risk. The required rate of return on a security = real risk-free rate + expected inflation + default risk premium + liquidity premium + maturity risk premium.
6c. The effective annual rate is adjusted for different compounding periods.
6d. For non-annual time value of money problems, divide the stated annual interest rate by the number of compounding periods per year, m, and multiply the number of years by the number of compounding periods per year.
6e. Future value: FV = PV(1 + I/Y)^N ; Present value: PV = FV / (1 + I/Y)^N ; An annuity is a series of equal cash flows that occurs at evenly spaced intervals over time. Ordinary annuity cash flows occur at the end of each time period. Annuity due cash flows occur at the beginning of each time period. Perpetuities are annuities with infinite lives (perpetual annuities): PV = PMT/(I/Y) ; The present (future) value of any series of cash flows is equal to the sum of the present (future) values of the individual cash flows.
6f. Constructing a time line showing future cash flows will help in solving many types of TVM problems. Cash flows occur at the end of the period depicted on the time line. The end of one period is the same as the beginning of the next period. For example, a cash flow at the beginning of Year 3 appears at time t = 2 on the time line.
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