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**Unformatted text preview: **FINS 5514: W EEK 02 Mark Humphery-Jenner T HE T IME V ALUE OF M ONEY Future Value and Compounding Present Value and Discounting Future and Present Values of Multiple Cash Flows Valuing Level Cash Flows: Annuities and Perpetuities Comparing Rates: The Effect of Compounding 5-1 B ASIC D EFINITIONS Present Value earlier money on a time line (ie value today) Future Value later money on a time line (ie value at some time in the future) Interest rate exchange rate between earlier money and later money Discount rate Cost of capital Opportunity cost of capital Required return 5-2 F UTURE V ALUES : G ENERAL F ORMULA FV = PV(1 + r) t FV = future value PV = present value r = period interest rate, expressed as a decimal T = number of periods Future value interest factor = (1 + r) t 5-3 F UTURE V ALUES Suppose you invest $1000 for one year at 5% per year. What is the future value in one year? Interest = 1000(.05) = 50 Value in one year = principal + interest = 1000 + 50 = 1050 Future Value (FV) = 1000(1 + .05) = 1050 Suppose you leave the money in for another year. How much will you have two years from now? FV = 1050 (1.05) = 1102.50 ie 1000(1.05)(1.05) = 1000(1.05) 2 = 1102.50 5-4 E FFECTS OF C OMPOUNDING Simple interest assumes that interest rate paid is a flat percentage of the principal (P) each period Compound interest interest is earned/paid on the principal plus any accumulated interest determined since the start of the deposit/loan. Consider the previous example FV with simple interest = 1000 + 50 + 50 = 1100 FV with compound interest = 1102.50 The extra 2.50 comes from the interest of .05(50) = 2.50 earned on the first interest payment 5-5 F UTURE V ALUES E XAMPLE 2 Suppose you invest the $1000 from the previous example for 5 years. How much would you have? FV = 1000(1.05) 5 = 1276.28 The effect of compounding is small for a small number of periods, but increases as the number of periods increases. (Simple interest would have a future value of $1250, for a difference of $26.28.) 5-6 F UTURE V ALUES E XAMPLE 3 Suppose you had a relative deposit $10 at 5.5% interest 200 years ago. How much would the investment be worth today? FV = 10(1.055) 200 = 447,189.84 What is the effect of compounding? Simple interest = 10 + 200(10)(.055) = 120.00 Compounding added $447,069.84 to the value of the investment 5-7 P RESENT V ALUES How much do I have to invest today to have some amount in the future? FV = PV(1 + r) t Rearrange to solve for PV = FV / (1 + r) t When we talk about discounting, we mean finding the present value of some future amount....

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