# ch06 - CHAPTER6 TimeValueofMoney Futurevalue Presentvalue...

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6-1 CHAPTER 6 Time Value of Money Future value Present value Annuities Rates of return Amortization

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6-2 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%
6-3 Drawing time lines: \$100 lump sum due in 2 years; 3-year \$100 ordinary annuity 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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6-4 Drawing time lines: Uneven cash flow stream;  CF 0  = -\$50,  CF 1  = \$100, CF 2  = \$75, and CF 3  = \$50  100 50 75 0 1 2 3 i% -50 Uneven cash flow stream
6-5 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 when compound interest is  applied is called compounding. FV can be solved by using the arithmetic,  financial calculator, and spreadsheet  methods. FV = ? 0 1 2 3 10% 100

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6-6 Solving for FV: The arithmetic method 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
6-7 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.) INPUTS OUTPUT N I/YR PMT PV FV 3 10 0 133.10 -100

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6-8 PV = ? 100 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 when compound interest is  applied is called discounting (the reverse of  compounding). The PV shows the value of cash flows in  terms of today’s purchasing power. 0 1 2 3 10%
6-9 Solving for PV: The arithmetic 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

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6-10 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. INPUTS OUTPUT N I/YR PMT PV FV 3 10 0 100 -75.13
6-11 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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