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Unformatted text preview: 21CHAPTER 2Time Value of MoneyFuture valuePresent valueAnnuitiesRates of returnAmortization22Which would you rather have?Today In One Year Int. Rate$100$1000%$100$1m 999,900%$100$1,000900%$100$500400%$100$200100%$100$15050%$100?$110?10%$100?$105?5%23Time linesShow the timing of cash flows.Tick marks occur at the end of periods, so Time 0 is today; Time 1 is the end of the first period (year, month, etc.) or the beginning of the second period.CFCF1CF3CF2123I%24General Assumption:Cash Flows (CFs) occur at the END of the period, unless stated otherwise. Payments (PMTs) occur at the END of the period (ordinary annuity), unless stated otherwise (annuity due).Calculator: Orange Key, BEG/END25CFs can either be: a) Lump Sum ($1000 to received in 1 year or 5 years, or $1000 invested today), or b) recurring CFs (nonconstant CFs), e.g. $100 in YR1, $200 in YR 2, $300 in YR) 3) or PMTs (constant CFs, e.g. $100 per year for 3 years). Calculator: CFj key vs. PMT key26Drawing time lines100100100123I%3 year $100 ordinary annuity10012I%$100 lump sum due in 2 years27Drawing time lines100 50 75123I%50Uneven cash flow stream28What is the future value (FV) of an initial $100 after 3 years, if I/YR = 10%?Finding the FV of a cash flow or series of cash flows is called compounding.FV can be solved by using the stepbystep, financial calculator, and spreadsheet methods.FV = ?12310%10029Solving for FV:The stepbystep and formula methodsAfter 1 year:FV1 = PV (1 + I) = $100 (1.10) = $110.00After 2 years:FV2 = PV (1 + I)2 = $100 (1.10)2 =$121.00After 3 years:FV3 = PV (1 + I)3 = $100 (1.10)3 =$133.10After N years (general case):FVN = PV (1 + I)N210See graph on p. 31. Note that FV grows geometrically, or exponentially, because of the compounding process. Why isnt it a straight line? 211Solving for FV:The calculator methodSolves the general FV equation.Requires 4 inputs into calculator, and will solve for the fifth. (Set to P/YR = 1 and END mode.)INPUTSOUTPUTNI/YRPMTPVFV310133.10100212PV = ?100What is the present value (PV) of $100 due in 3 years, if I/YR = 10%?Finding the PV of a cash flow or series of cash flows is called discounting (the reverse of compounding).The PV shows the value of cash flows in terms of todays purchasing power....
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This note was uploaded on 01/23/2012 for the course BUS 361 taught by Professor Staff during the Fall '11 term at University of Michigan.
 Fall '11
 STAFF
 Amortization

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