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 square6 Future value square6 Present value square6 Annuities square6 Rates of return square6 Amortization

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Time lines CF CF CF CF 0 1 2 3 I% 2-2 square6 Show the timing of cash flows. square6 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. 0 1 3 2
Drawing time lines 0 1 2 I% \$100 lump sum due in 2 years 2-3 100 100 100 0 1 2 3 I% 3 year \$100 ordinary annuity 100

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Drawing time lines 0 1 2 3 I% Uneven cash flow stream 2-4 100 50 75 -50
What is the future value (FV) of an initial \$100 after 3 years, if I/YR = 10%? square6 Finding the FV of a cash flow or series of cash flows is called compounding. square6 FV can be solved by using the step-by-step, financial calculator, and spreadsheet methods. 2-5 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 square6 After 1 year: square6 FV 1 = PV (1 + I) = \$100 (1.10) = \$110.00 square6 After 2 years: 2-7 square6 FV 2 = PV (1 + I) 2 = \$100 (1.10) 2 =\$121.00 square6 After 3 years: square6 FV 3 = PV (1 + I) 3 = \$100 (1.10) 3 =\$133.10 square6 After N years (general case): square6 FV N = PV (1 + I) N

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Solving for FV: The calculator method square6 Solves the general FV equation. square6 Requires 4 inputs into calculator, and will solve for the fifth. (Set to P/YR = 1 and END mode.) 2-8 INPUTS OUTPUT N I/YR PMT PV FV 3 10 0 133.10 -100
Calculator Keys square6 Texas Instruments BA-II Plus square6 FV = future value square6 PV = present value I/Y = period interest rate 2-9 square6 square6 P/Y must equal 1 for the I/Y to be the period rate square6 Interest is entered as a percent, not a decimal square6 N = number of periods square6 Remember to clear the registers (CLR TVM) before (and after) each problem square6 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%? square6 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 2-12 PV = ? 100 square6 terms of today’s purchasing power. 0 1 2 3 10%
Solving for PV: The formula method square6 Solve the general FV equation for PV: square6 PV = FV N / (1 + I) N 2-13 square6 PV = FV 3 / (1 + I) 3 = \$100 / (1.10) 3 = \$75.13

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Solving for PV: The calculator method square6 Solves the general FV equation for PV.
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