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Unformatted text preview: Time Value of Money Chapter 5 Future Value Present Value Annuities Rates of Return Amortization 51 Time Lines Show the timing of cash flows. 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 CF 1 CF 3 CF 2 1 2 3 I% 52 Drawing Time Lines 53 100 100 100 1 2 3 I% 3 year $100 ordinary annuity 100 1 2 I% $100 lump sum due in 2 years Drawing Time Lines 54 100 50 75 1 2 3 I%50 Uneven cash flow stream What is the future value (FV) of an initial $100 after 3 years, if I/YR = 10%? Finding the FV of a cash flow or series of cash flows is called compounding. FV can be solved by using the stepbystep, financial calculator, and spreadsheet methods. FV = ? 1 2 3 10% 100 55 Solving for FV: The StepbyStep and Formula Methods After 1 year: FV 1 = PV(1 + I) = $100(1.10) = $110.00 After 2 years: FV 2 = PV(1 + I) 2 = $100(1.10) 2 = $121.00 After 3 years: FV 3 = PV(1 + I) 3 = $100(1.10) 3 = $133.10 After N years (general case): FV N = PV(1 + I) N 56 Solving for FV: The Calculator Method Solves the general FV equation. Requires 4 inputs into calculator, and will solve for the fifth. (Set to P/YR = 1 and END mode.) 57 INPUTS OUTPUT N I/YR PMT PV FV 3 10 133.10100 What is the present value (PV) of $100 due in 3 years, if I/YR = 10%? 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 terms of todays purchasing power. PV = ? 100 1 2 3 10% 58 Solving for PV: The Formula Method Solve the general FV equation for PV: PV = FV N /(1 + I) N PV = FV 3 /(1 + I) 3 = $100/(1.10) 3 = $75.13 59 Solving for PV: The Calculator Method Solves the general FV equation for PV. Exactly like solving for FV, except we have different input information and are solving for a different variable. 510 INPUTS OUTPUT N I/YR PMT PV FV 3 10 10075.13 Solving for I: What interest rate would cause $100 to grow to $125.97 in 3 years? Solves the general FV equation for I. Hard to solve without a financial calculator or spreadsheet. 511 INPUTS OUTPUT N I/YR PMT PV FV 3 8 125.97100 Solving for N: If sales grow at 20% per year, how long before sales double? Solves the general FV equation for N....
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 Spring '10
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