Chapter05

# Chapter05 - Outline L06-1 Chapter 5 The Time Value of Money...

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L06-1 Outline Chapter 5. The Time Value of Money Future Value and Compounding of Single Cash Flow Present Value and Discounting of Single Cash Flow More on Present and Future Values of Single Cash Flow Summary and Conclusions

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L06-2 One of the basic problems faced by the financial manager is how to determine the value today of cash flows expected in the future. For example, the jackpot in a PowerBall lottery drawing was \$110 million. Does this mean the winning ticket was worth \$110 million? The answer is no because the jackpot was actually going to pay out over a 20-year period at a rate of \$5.5 million per year. Then, how much was the ticket worth? The answer depends on the time value of money . Time value of money refers to the fact that a dollar in hand today is worth more than a dollar promised at some time in future. This is mainly due to the fact that a dollar today earns interest as time goes on. Future value for a single cash flow
L06-3 Future value refers to the amount of money an investment will grow to over some period of time at some given interest rate. Suppose you invest \$100 in a savings account that pays 10% per year. 1. How much will you have in one year? Year 0 Year 1 Principal \$ 100 \$ 100 Interest earned \$ 10 Total \$ 110 2. How much will you have in two years assuming the interest rate doesn’t change? Year 0 Year 1 Year2 Principal \$ 100 \$ 100 \$ 100 Interest on principal \$ 10 Interest of year 1 \$ 10 \$ 10 Interest on interest \$ 1 Total \$ 110 \$ 121 Future value for a single cash flow (continued)

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L06-4 The process of leaving your money and any accumulated interest in an investment for more than one period, thereby reinvesting the interest, is called compounding . Compounding the interest means earning interest on interest , so we call the result compound interest . With simple interest , the interest is not reinvested, so interest is earned each period only on the original principal. For one year period: Simple interest = \$ 10 = Compound interest For two year periods: Simple interest = \$ 20 Compound interest = \$ 21 Future value : One year period : \$110 [ = 100 x (1 + 0.1)] Two year periods: \$121 [ = 110 x (1 + 0.1) = 100 X (1+0.1) 2 ] Future value for a single cash flow (continued)
L06-5 In general, the future value , FV t , of \$1 invested today at r% for t periods is FV t = \$1 × (1 + r) t The expression (1 + r) t is the future value interest factor ( or future value factor) and can be abbreviated as FVIF(r,t). Table A-1 in the appendix gives the future value factor. These days, we use a financial calculator Future value for a single cash flow (continued) Figure 5.2 illustrates this relationship by plotting the growth of \$1 for different rates and lengths of time. Notice that the future

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Chapter05 - Outline L06-1 Chapter 5 The Time Value of Money...

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