REVISED_ch06_v1_052405

# REVISED_ch06_v1_052405 - CHAPTER6 TimeValueofMoney...

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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 Value of Money Future Value Present Value Mixed Flows Ordinary Annuity Single Amounts Mixed Flows Ordinary Annuity Single Amounts 1 (1 ) o n n PV FV i = + ) n n o FV PV i = + (1 ) 1 n n i FVA R i   + - =     1 1 (1 ) n n i PVA R i   -   +   =       1 ) n j o n j R PV i = = + 1 ) n n n j j FV R i = = + (1 ) 1 n n n n o i FV FV FVA PV i R i   + -   = + = + +       Annuity Due 1 1 n n i PVAD R i i   -   +   = +       Annuity Due (1 ) 1 n n i FVAD R i i   + - = +    
6-3 Time Value of Money Effective Annual Interest Rate Periodic Present Value Periodic* Future Value Compounding Continuous Periodic (1 ) mn n o i FV PV m   = +     1 ) o n mn PV FV i m = + Continuous Present Value 1 o n in PV FV e   =     Continuous Present Value in n o FV PV e = *Periodic means m discrete periods, e.g., monthly, quarterly, semiannual, daily 1 1 m i m + - 1 i e -

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6-4 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%
6-5 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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6-6 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
6-7 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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6-8 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
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## This note was uploaded on 09/05/2011 for the course FIN 4405 taught by Professor Cowan during the Spring '11 term at Fairleigh Dickinson.

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REVISED_ch06_v1_052405 - CHAPTER6 TimeValueofMoney...

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