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Unformatted text preview: 1 Chapter 4 Time Value of Money 2 Time Value Topics Future value Present value Rates of return Amortization 4 Time lines show timing of cash flows. CF CF 1 CF 3 CF 2 1 2 3 I% Tick marks at ends of periods, so Time 0 is today; Time 1 is the end of Period 1; or the beginning of Period 2. 5 Time line for a $100 lump sum due at the end of Year 2. 100 1 2 Year I% 6 Time line for an ordinary annuity of $100 for 3 years 100 100 100 1 2 3 I% 7 Time line for uneven CFs 100 50 75 1 2 3 I%50 8 FV of an initial $100 after 3 years (I = 10%) FV = ? 1 2 3 10% Finding FVs (moving to the right on a time line) is called compounding. 100 9 After 1 year FV 1 = PV + INT 1 = PV + PV (I) = PV(1 + I) = $100(1.10) = $110.00 10 After 2 years FV 2 = FV 1 (1+I) = PV(1 + I)(1+I) = PV(1+I) 2 = $100(1.10) 2 = $121.00 11 After 3 years FV 3 = FV 2 (1+I)=PV(1 + I) 2 (1+I) = PV(1+I) 3 = $100(1.10) 3 = $133.10 In general, FV N = PV(1 + I) N 12 Four Ways to Find FVs Stepbystep approach using time line (as shown in Slides 710). Solve the equation with a regular calculator (formula approach). Use a financial calculator. Use a spreadsheet. 13 Financial calculator: HP10BII Adjust display brightness: hold down ON and push + or . Set number of decimal places to display: Orange Shift key, then DISP key (in orange), then desired decimal places (e.g., 3). To temporarily show all digits, hit Orange Shift key, then DISP, then =. 14 HP10BII (Continued) To permanently show all digits, hit ORANGE shift, then DISP, then . (period key). Set decimal mode: Hit ORANGE shift, then ./, key. Note: many nonUS countries reverse the US use of decimals and commas when writing a number. 15 HP10BII: Set Time Value Parameters To set END (for cash flows occurring at the end of the year), hit ORANGE shift key, then BEG/END. To set 1 payment per period, hit 1, then ORANGE shift key, then P/YR. 16 Financial calculators solve this equation: FV N + PV (1+I) N = 0. There are 4 variables. If 3 are known, the calculator will solve for the 4th. Financial Calculator Solution 3 10100 N I/YR PV PMT FV 133.10 INPUTS OUTPUT 17 Clearing automatically sets everything to 0, but for safety enter PMT = 0. Set: P/YR = 1, END. Heres the setup to find FV 18 Spreadsheet Solution Use the FV function: see spreadsheet in Ch04 Mini Case.xls = FV(I, N, PMT, PV) = FV(0.10, 3, 0, 100) = 133.10 19 Whats the PV of $100 due in 3 years if I/YR = 10%?...
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This note was uploaded on 02/02/2011 for the course FINC 350 taught by Professor Johnson during the Spring '11 term at UCLA.
 Spring '11
 Johnson

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