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# chap004 with additions - Chapter 4 Introduction to...

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1 Chapter 4 - Introduction to Valuation: The Time Value of Money Future Value and Compounding Present Value and Discounting More on Present and Future Values

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2 Basic Definitions Present Value – PV – earlier money on a time line Future Value – FV – later money on a time line Number of Periods – N or T – number of periods between timing of PV and FV Interest rate – R or I – “exchange rate” between earlier money and later money Discount rate Cost of capital Opportunity cost of capital Required return
3 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 If money is left invested 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 Notice the pattern: FV = PV (1 + r) N

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4 Future Values: General Formula FV = PV(1 + r) t FV = future value PV = present value r = period interest rate, expressed as a decimal (expressed as I or I/Y on calculators) T or N = number of periods Future value interest factor = (1 + r) t Can use financial calculator, spreadsheet or formula NOTE: We do not use the “PMT” time value of money value in Chapter 4 questions – only Chapter 5!
5 Effects of Compounding Simple interest (interest is earned only on the original principal) Compound interest (interest is earned on principal and on interest received) FV = PV growing with compound interest 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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6 Figure 4.1
7 Calculator Keys Texas Instruments BA-II Plus FV = future value PV = present value I/Y = period interest rate ( = R) 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 ( = T ) Remember to clear the registers (CLR TVM) before (and after) each problem Other calculators are similar in format Understand what “sign” (positive/negative) means.

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8 Future Values – Example 2 Suppose you invest the \$1000 from the previous example for 5 years. How much would you have?
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chap004 with additions - Chapter 4 Introduction to...

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