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# chap5 - Chapter 5 The Time Value of Money FIN 3716 5-1 Key...

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5 -1 FIN 3716 Chapter 5 The Time Value of Money

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5 -2 FIN 3716 Key Concepts and Skills Key Concepts and Skills Be able to compute the future value of an investment made today Be able to compute the present value of cash to be received at some future date Be able to compute the return on an investment Be able to compute the number of periods that equates a present value and a future value given an interest rate Be able to use a financial calculator and/or a spreadsheet to solve time value of money problems
5 -3 FIN 3716 Chapter Outline Chapter Outline Future Value and Compounding Present Value and Discounting More on Present and Future Values

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5 -4 FIN 3716 Basic Definitions 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 Other terms for interest rate Discount rate Cost of capital Opportunity cost of capital Required return
5 -5 FIN 3716 Future Values Future Values Suppose you invest \$1,000 (principal) 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 + 1,000(0.05) = 1,050 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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5 -6 FIN 3716 Future Values: General Formula 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
5 -7 FIN 3716 Effects of Compounding Effects of Compounding Simple interest (no reinvestment of interest) 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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5 -8 FIN 3716 Calculator Keys 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 Remember to clear the registers (CLR TVM) after each problem Other calculators are similar in format
FIN 3716 Future Values – Example 2 Future Values – Example 2 Suppose you invest the \$1,000 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

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chap5 - Chapter 5 The Time Value of Money FIN 3716 5-1 Key...

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