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1.Chapter 05&amp;06(1)

# 1.Chapter 05&amp;06(1) - Chapter 5 The Time Value of...

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Chapter 5: The Time Value of Money

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Basic Definitions Present Value – earlier money on a time line Future Value – later money on a time line Interest rate – “exchange rate” between earlier money and later money Discount rate Cost of capital Opportunity cost of capital Required return
Future Values Suppose you invest \$1000 for one year at 5% per year. What is the future value in one year? Interest = 1,000(.05) = 50 Value in one year = principal + interest = 1,000 + 50 = 1050 Future Value (FV) = 1,000(1 + .05) = 1,050 Suppose you leave the money in for another year. How much will you have two years from now? FV = 1,000(1.05)(1.05) = 1,000(1.05) 2 = 1,102.50

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Future Values: General Formula 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
Effects of Compounding Simple interest (interest is earned only on the original principal) Compound interest (interest is earned on principal and on interest received) Consider the previous example FV with simple interest = 1,000 + 50 + 50 = 1,100 FV with compound interest = 1,102.50 The extra 2.50 comes from the interest of . 05(50) = 2.50 earned on the first interest payment

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Calculator Keys Texas Instruments BA-II Plus FV = future value PV = present value I/Y = period interest rate P/Y must equal 1 for the I/Y to be the period rate Interest is entered as a percent, not a decimal N = number of periods Other calculators are similar in format
Future Values – Example 1 Suppose you invest the \$1000 from the previous example for 5 years. How much would you have? FV = 1,000(1.05) 5 = 1,276.28 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 \$1,250, for a difference of \$26.28.)

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Future Values – Example 2 Suppose you had a small deposit of \$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 + 10(200)(.055) = 120 Compounding added \$447,069.84 to the value of the investment
Present Values 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. When we talk about the “value” of something, we are talking about the present value unless we specifically indicate that we want the future value.

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PV – One Period Example Suppose you need \$10,000 in one year for the down payment on a new car. If you can earn 7% annually, how much do you need to invest today?
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