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Chapter 2

# Chapter 2 - CHAPTER 2 Time Value of Money Future value...

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2-1 Click to edit Master subtitle style CHAPTER 2 Time Value of Money n Future value n Present value n Annuities n Rates of return n Amortization

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2-2 Time lines n Show the timing of cash flows. n 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  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%? n Finding the FV of a cash flow or series of cash  flows is called compounding. n FV can be solved by using the step-by-step,  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 n After 1 year: n FV1 = PV (1 + I) =  n After 2 years: n FV2 = PV (1 + I)2 =  n After 3 years: n FV3 = PV (1 + I)3 =  n After N years (general case):
2-7 PV = ? 100 What is the present value (PV) of \$100  due in 3 years, if I/YR = 10%? n Finding the PV of a cash flow or series of  cash flows is called discounting (the reverse  of compounding). n The PV shows the value of cash flows in  terms of today’s purchasing power. 0 1 2 3 10%

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2-8 Solving for PV: The formula method n Solve the general FV equation for PV: n PV = FVN / (1 + I)N n PV = FV3 / (1 + I)3      =
2-9 Solving for I: What interest rate would cause \$100 to  grow to \$125.97 in 3 years?

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2-10 Solving for N: If sales grow at 20% per year, how long  before sales double?
2-11 What is the difference between an  ordinary annuity and an annuity due?

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