Chapter 02

# Chapter 02 - CHAPTER2 TimeValueofMoney Futurevalue...

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2-1 CHAPTER 2 Time Value of Money Future value Present value Annuities Rates of return Amortization

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2-2 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%
2-3 Drawing time lines 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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2-4 Drawing time lines 100  50  75 0 1 2 3 I% -50 Uneven cash flow stream
2-5 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 is called compounding. FV can be solved by using the step-by-step  arithmetic, financial calculator, and spreadsheet  methods. FV = ? 0 1 2 3 10% 100

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2-6 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
2-7 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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2-8 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 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%
2-9 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

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2-10 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
2-11 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. INPUTS OUTPUT N I/YR PMT PV FV 3 8 0 125.97 -100 ( 29 3 1 100 97 . 125 I + =

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2-12 Solving for N: If sales grow at 20% per year, how long  before sales double?
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Chapter 02 - CHAPTER2 TimeValueofMoney Futurevalue...

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