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Present Value Methodology EZ

Present Value Methodology EZ - Present Value Methodology...

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1 Present Value Methodology Econ 422 E. Zivot 2006 R.W. Parks/L.F. Davis 2004 Investment, Capital & Finance University of Washington Eric Zivot Last updated: April 11, 2010 Present Value Concept Wealth in Fisher Model: W = Y 0 + Y 1 /(1+r) The consumer/producer’s wealth is their current endowment plus the future endowment discounted back to the present by the rate of interest (rate at which present and future consumption can be exchanged). Why do this? Purpose of comparison—apples to apples (temporal) comparison with lti l t l t l i f i t t/ ti E. Zivot 2006 R.W. Parks/L.F. Davis 2004 multiple agents or apples to apples comparison of investment/consumption opportunities Uniform method for valuing present and future streams of consumption in order for appropriate decision making by consumer/producer Useful concept for valuing multiple period investments and pricing financial instruments Calculating Present Value Present value calculations are the reverse of compound growth calculations : Suppose V 0 = a value today (time 0) r = fixed interest rate (annual) E. Zivot 2006 R.W. Parks/L.F. Davis 2004 T = amount of time (years) to future period The value in T years we calculate as: V T = V 0 (1+r) T (Future Value)
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2 Example A $30,000 Certificate of Deposit with 5% annual interest in 10 years will be worth: • V T = V 0 (1 + r) T = 30 000 *(1 + 0 05) 10 = E. Zivot 2006 R.W. Parks/L.F. Davis 2004 V V 30,000 (1 + 0.05) = $48,866.84 Note: Computation is easy to do in Excel = 30,000 *(1 + 0.05)^10 Present Value In reverse: V 0 = V T /(1+r) T (Present Value) The present value amount is the future value discounted E. Zivot 2006 R.W. Parks/L.F. Davis 2004 The present value amount is the future value discounted (divided) by the compounded rate of interest Example : A $48,866.84 Certificate of Deposit received 10 years from now is worth today: V 0 = $48,866.84/(1+0.05) 10 = $30,000 Exam Review Be able to calculate present and future values For any three of four variables: (V 0 , r, T, E. Zivot 2006 R.W. Parks/L.F. Davis 2004 V T ) you should be able to determine the value of the fourth variable. How do changes to r and T impact V 0 and V T ?
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3 Example: Rule of 70 Q: How many years, T, will it take for an initial investment of V 0 to double if the annual interest rate is r? E. Zivot 2006 R.W. Parks/L.F. Davis 2004 A: Solve V 0 (1 + r) T = 2V 0 => (1 + r) T = 2 => Tln(1 + r) = ln(2) => T = ln(2)/ln(1+r) = 0.69/ln(1 + r) 0.70/r for r not too big Present Value of Future Cash Flows A cash flow is a sequence of dated cash amounts received (+) or paid (-): C 0 , C 1 , …, C T C h t i d iti h h E. Zivot 2006 R.W. Parks/L.F. Davis 2004 Cash amounts received are positive; whereas, cash amounts paid are negative The present value of a cash flow is the sum of the present values for each element of the cash flow Discount factors: Intertemporal Price of $1 with constant interest rate r 1/(1+r) = price of $1 to be received 1 year from today • 1/(1+r) 2 = price of $1 to be received 2 years E. Zivot 2006 R.W. Parks/L.F. Davis 2004 1/(1+r) price of $1 to be received 2 years from today • 1/(1+r) T = price of $1 to be received T years from today
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