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 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 (1 + r T = 30 000 *(1 + 0 05 10 = E. Zivot 2006 R.W. Parks/L.F. Davis 2004 V V 0 (1 + r) 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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4 Present Value of a Cash Flow •{C 0 , C 1 , C 2 , …C T } represents a sequence of cash flows where payment •C i is received at time i. Let r = the interest or
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This note was uploaded on 12/21/2011 for the course ECON 422 taught by Professor Staff during the Fall '08 term at University of Washington.

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Present Value Methodology EZ - Present Value Methodology...

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