FM2010 Topic 1a Time Value of Money [Compatibility Mode]

# FM2010 Topic 1a Time Value of Money [Compatibility Mode] -...

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2010 Topic 1 Time Value of Money 2-1 s Future value s Present value s Annuities s Rates of return s Amortization

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Time lines 0 1 2 3 I% 2-2 s Show the timing of cash flows. s 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. CF 0 CF 1 CF 3 CF 2
Drawing time lines 0 1 2 \$100 lump sum due in 2 years 2-3 100 100 100 0 1 2 3 I% 3 year \$100 ordinary annuity 100 I%

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Drawing time lines 0 1 2 3 Uneven cash flow stream 2-4 100 50 75 I% -50
What is the future value (FV) of an initial \$100 after 3 years, if I/YR = 10%? s Finding the FV of a cash flow or series of cash flows is called compounding. s FV can be solved by using the step-by-step, nancial calculator, and spreadsheet methods. 2-5 financial calculator, and spreadsheet methods. FV = ? 0 1 2 3 10% 100

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3 Solution methods 1. step-by-step 2-6 2. financial calculator 3. spreadsheet methods
Solving for FV: The step-by-step and formula methods s After 1 year: s FV 1 = PV (1 + I) = \$100 (1.10) = \$110.00 s After 2 years: 2-7 s FV 2 = PV (1 + I) 2 = \$100 (1.10) 2 =\$121.00 s After 3 years: s FV 3 = PV (1 + I) 3 = \$100 (1.10) 3 =\$133.10 s After N years (general case): s FV N = PV (1 + I) N

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Solving for FV: The calculator method s Solves the general FV equation. s Requires 4 inputs into calculator, and will solve for the fifth. (Set to P/YR = 1 and 2-8 END mode.) INPUTS OUTPUT N I/YR PMT PV FV 3 10 0 133.10 -100
Calculator Keys s Texas Instruments BA-II Plus s FV = future value s PV = present value 2-9 s I/Y = period interest rate s P/Y must equal 1 for the I/Y to be the period rate s Interest is entered as a percent, not a decimal s N = number of periods s Remember to clear the registers (CLR TVM) before (and after) each problem s Other calculators are similar in format

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Figure 4.1 2-10
Figure 4.2 2-11

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What is the present value (PV) of \$100 due in 3 years, if I/YR = 10%? s Finding the PV of a cash flow or series of cash flows is called discounting (the reverse of compounding). 2-12 PV = ? 100 s The PV shows the value of cash flows in terms of today’s purchasing power. 0 1 2 3 10%
Solving for PV: The formula method s Solve the general FV equation for PV: s PV = FV N / (1 + I) N 2-13 s PV = FV 3 / (1 + I) 3 = \$100 / (1.10) 3 = \$75.13

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Solving for PV: The calculator method s Solves the general FV equation for PV. s
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## This note was uploaded on 06/28/2010 for the course FINANCE FIN3410 taught by Professor On9 during the Spring '10 term at New England Conservatory.

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FM2010 Topic 1a Time Value of Money [Compatibility Mode] -...

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