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# 361-CH2a - 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 Which would you rather have? Today     In One Year      Int. Rate \$100 \$100 0% \$100 \$1m      999,900% \$100 \$1,000 900% \$100 \$500 400% \$100 \$200 100% \$100 \$150 50% \$100? \$110? 10% \$100? \$105? 5%
2-3 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%

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2-4 General Assumption: Cash Flows (CFs) occur at the END of the  period, unless stated otherwise.  Payments (PMTs) occur at the END of the  period (ordinary annuity), unless stated  otherwise (annuity due). Calculator: Orange Key, BEG/END
2-5 CFs can either be:  a) Lump Sum (\$1000 to received in 1  year or 5 years, or \$1000 invested  today), or  b) recurring CFs (non-constant CFs),  e.g. \$100 in YR1, \$200 in YR 2, \$300 in  YR) 3) or PMTs (constant CFs, e.g.  \$100 per year for 3 years).  Calculator: CF j  key vs. PMT key

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2-6 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
2-7 Drawing time lines 100  50  75 0 1 2 3 I% -50 Uneven cash flow stream

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2-8 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,  financial calculator, and spreadsheet methods. FV = ? 0 1 2 3 10% 100
2-9 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

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2-10 See graph on p. 31.   Note that FV grows geometrically, or  exponentially, because of the  compounding process.  Why isn’t it a  straight line?
2-11 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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2-12 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
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