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Chapter 5

# Chapter 5 - CHAPTER5 TimeValueofMoney Futurevalue...

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6-1 CHAPTER 5 Time Value of Money Future value Present value Annuities Rates of return Amortization Note: Slides have been slightly revised from  those provided by the publisher.

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6-2 Time lines Show the  timing  of cash flows ( timing of cash flows  is important because a dollar in year 1 has a higher  value than a dollar in year 2) . 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%? Example: How much will you  have  in 3 years if you deposit \$100 today into  a banking account that pays 10% per year? The FV is equivalent to the amount of money you will have in your banking  account in 3 years 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  = Principal + Interest       = Principal + Principal * Interest Rate  = Principal * (1+ Interest Rate)  = PV ( 1 + i ) = \$100 (1.1) = \$110.00 After 2 years: FV 2  = ( Principal + Interest Rate) *  ( 1 + i )      = 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 (the general case): FV n  = PV ( 1 + i ) n
6-7 Solving for FV: The arithmetic method Mathematically, a \$100 deposited for three years will be  growing to \$133.10 in three years. FV = PV * (1 + Interest Rate) 3     = PV ( 1 + i )         = \$100 (1.10) 3  =\$133.10 Alternatively, FV = PV (FVIF i N      = \$100 (FVIF 10% 3 )        = \$100 * 1.3310 = \$133.10

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6-8 Solving for FV: The arithmetic method The mathematical formula for the FV:   FV N  = PV*(1+i) N Equivalently:    FV N  = PV* (FVIF i, N ) so    FV Interest Factor = (FVIF i, N ) = (1+i) N
6-9 Solving for FV: The calculator method Solves the general FV equation.

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