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IFM10 Ch28 Lecture

# IFM10 Ch28 Lecture - Chapter28 TimeValueofMoney 1...

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1 Chapter 28 Time Value of Money

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2 Time Value Topics Future value Present value Rates of return Amortization
3 Time lines show timing of  cash flows. CF 0 CF 1 CF 3 CF 2 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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4 Time line for a \$100 lump  sum due at the end of Year 2. 100 0 1 2   Year I%
5 Time line for an ordinary  annuity of \$100 for 3 years 100 100 100 0 1 2 3 I%

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6 Time line for uneven CFs 100  50  75 0 1 2 3 I% -50
7 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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8 After 1 year FV 1 = PV + INT = PV + PV (I) = PV(1 + I) = \$100(1.10) = \$110.00.
9 After 2 years FV 2 = FV 1 (1+I) = PV(1 + I)(1+I) = PV(1+I) 2 = \$100(1.10) 2 = \$121.00.

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10 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 .
11 Three Ways to Find FVs Solve the equation with a regular  calculator. Use a financial calculator. Use a spreadsheet.

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12 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 =
13 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 non-US  countries reverse the US use of  decimals and commas when writing a  number.

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14 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
15 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

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16 3 10 -100 0 N I/YR PV PMT FV 133.10 Clearing automatically sets everything to 0,  but for safety enter PMT = 0. Set: P/YR = 1, END. INPUTS OUTPUT Here’s the setup to find FV
17 Spreadsheet Solution Use the FV function: see spreadsheet in  IFM10 Ch28 Mini Case.xls  = FV(I, N, PMT, PV)  = FV(0.10, 3, 0, -100) = 133.10

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18 What’s the PV of \$100 due in  3 years if i = 10%? 10% Finding PVs is discounting, and it’s the  reverse of compounding.
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