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Ch04 Show - Chapter 4 Time Value of Money 1 Time Value...

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1 Chapter 4 Time Value of Money
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2 Time Value Topics n Future value n Present value n Rates of return n Amortization
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Value =                         +                         +      + FCF1 FCF2 FCF (1 + WACC)1 (1 + WACC) (1 + WACC)2 Free cash  flow (FCF) Market interest rates Firm’s business risk Market risk aversion Firm’s debt/equity mix Cost of debt Cost of equity Weighted  average cost of capital (WACC) Net operating profit after taxes Required investments in operating capital = Determinants of Intrinsic Value: The Present Value Equation ...
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4 Time lines show timing of cash  flows. CF0 CF1 CF3 CF2 0 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.
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5 Time line for a $100 lump sum  due at the end of Year 2. 100 0 1 2 Year I%
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6 Time line for an ordinary  annuity of $100 for 3 years 100 100 100 0 1 2 3 I%
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7 Time line for uneven CFs 100 50 75 0 1 2 3 I% -50
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8 FV of an initial $100 after 3 years (I = 10%) FV = ? 0 1 2 3 10% Finding FVs (moving to the right on a time line) is called compounding. 100
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9 After 1 year FV1 = PV + INT1 = PV + PV (I) = PV(1 + I) = $100(1.10) = $110.00
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10 After 2 years FV2 = FV1(1+I) = PV(1 + I)(1+I) = PV(1+I)2 = $100(1.10)2 = $121.00
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11 After 3 years FV3 = FV2(1+I)=PV(1 + I)2(1+I) = PV(1+I)3 = $100(1.10)3 = $133.10 In general, FVN = PV(1 + I)N
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12 Four Ways to Find FVs n Step-by-step approach using time line  (as shown in Slides 7-10). n Solve the equation with a regular  calculator (formula approach). n Use a financial calculator. n Use a spreadsheet.
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13 Financial calculator: HP10BII n Adjust display brightness: hold down  ON and push + or –. n Set number of decimal places to  display: Orange Shift key, then DISP  key (in orange), then desired decimal  places (e.g., 3). n To temporarily show all digits, hit  Orange Shift key, then DISP, then =.
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14 HP10BII (Continued) n To permanently show all digits, hit  ORANGE shift, then DISP, then .  (period key). n Set decimal mode: Hit ORANGE shift,  then ./, key.  Note: many non-US  countries reverse the US use of  decimals and commas when writing a  number.
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15 HP10BII: Set Time Value  Parameters n To set END (for cash flows occurring at  the end of the year), hit ORANGE shift  key, then BEG/END. n To set 1 payment per period, hit 1, then  ORANGE shift key, then P/YR.
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16 Financial calculators solve this  equation: FVN + PV (1+I)N = 0. There are 4 variables.  If 3 are  known, the calculator will solve for  the 4th. Financial Calculator Solution
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3 10 -100 0 N I/YR PV PMT FV 133.10 INPUTS OUTPUT 17 Clearing automatically sets everything to 0,  but for safety enter PMT = 0.
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