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Unformatted text preview: Chapter 2 Chapter 2 Time Value of Money (TVOM) Focus Items: Annual Worth/Uniform Series Gradient Series Geometric Series Uniform Series “Uniform” – implies a cash flow occurs every period. no skipped periods Sometimes called an annuity Regular payments – car, house, loan A=a single payment, in a series of n equal payments, made at the end of each interest period. How would we do these problems? We could use what we already know….. Uniform Series UNIFORM CASH FLOW SERIES (A or AW) a measure of worth where all cash flows are spread equally across the “life” or planning horizon in a uniform series. Where A is the magnitude of an individual cash flow in the series Sometimes termed AW for Annual Worth. Uniform Series Uniform Series 4 Scenarios we consider (first two): • If you have a uniform or equal series of cash flows over a time horizon then you can: Use the uniform series, PW factor to find the PW of a uniform cash flow profile. Find P given A . Use the uniform series, PW factor to find the uniform series for a given Present Worth amount of money (this is termed capital recovery factor since you recover an equal amount of money each period). Find A given P . Uniform Series and Present Worth • Uniform Series Formulas: A represents the uniform cash flow amounts over the horizon n ; P represents the Present Worth Find the Present Worth given a uniform series A or find the uniform series A given the Present Worth for some interest rate P = A[(1+i) n1]/[i(1+i) n ] P = A(PA i%,n) A = Pi(1+i) n /[(1+i) n1] A = P(AP i%,n) Appendix Aa Appendix Aa Note: Appendix Aa (pp 825849 in text) contains the notation values for various interest rates (i) and periods (n) Formula Formula When finding P given A, P occurs before the first A Example 2.17 Troy Long deposits a single sum of money in a savings account that pays 5% compounded annually. How much must he deposit in order to withdraw $2,000/yr for 5 years, with the first withdrawal occurring 1 year after the deposit? P = $2,000(PA 5%,5) P = $2,000(4.32948) = $8,658.96 P = PV(5%,5,2000) P = $8,658.95 Excel Version Example 2.18 Troy Long deposits a single sum of money in a savings account that pays 5% compounded annually. How much must he deposit in order to withdraw $2,000/yr for 5 years, with the first withdrawal occurring 3 years after the deposit? P = $2,000(PA 5%,5)(PF 5%,2) P = $2,000(4.32948)(0.90703) = $7,853.94 P =PV(5%,2,,PV(5%,5,2000)) P = $7,853.93 Excel Version Example 2.19 Rachel Townsley invests $10,000 in a fund that pays 8% compounded annually. If she makes 10 equal annual withdrawals from the fund, how much can she withdraw if the first withdrawal occurs 1 year after her investment?...
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 Spring '07
 Deyong
 Time Value Of Money

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