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# ch 05 - Chapter 5 Time Value of Money Future Value Present...

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Time Value of Money Chapter 5 Future Value Present Value Annuities Rates of Return Amortization 5-1

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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 0 CF 1 CF 3 CF 2 0 1 2 3 I% 5-2
Drawing Time Lines 5-3 100 100 100 0 1 2 3 I% 3 year \$100 ordinary annuity 100 0 1 2 I% \$100 lump sum due in 2 years

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Drawing Time Lines 5-4 100  50  75 0 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 step-by-step,  financial calculator, and spreadsheet  methods. FV = ? 0 1 2 3 10% 100 5-5

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Solving for FV: The Step-by-Step and Formula Methods After 1 year: FV 1 = PV(1 + I) = \$100(1.10) = \$110.00 After 2 years: FV 2 = PV(1 + I) = \$100(1.10) 2  = \$121.00 After 3 years: FV 3 = PV(1 + I) = \$100(1.10) 3  = \$133.10 After N years (general case): FV N = PV(1 + I) N 5-6
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.) 5-7 INPUTS OUTPUT N I/YR PMT PV FV 3 10 0 133.10 -100

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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 today’s purchasing power. PV = ? 100 0 1 2 3 10% 5-8
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 5-9

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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. 5-10 INPUTS OUTPUT N I/YR PMT PV FV 3 10 0 100 -75.13
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. 5-11 INPUTS OUTPUT N I/YR PMT PV FV 3 8 0 125.97 -100

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Solving for N:  If sales grow at 20% per year,  how long before sales double? Solves the general FV equation for N. Hard to solve without a financial calculator or  spreadsheet. 5-12 INPUTS OUTPUT N I/YR PMT PV FV 3.8 20 0 2 -1
What is the difference between an ordinary  annuity and an annuity due?

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