Lecture 03 - IRR 2010

Lecture 03 - IRR 2010 - Lecture 3 DADSS Engineering...

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1 Lecture 3 Engineering Economics Internal Rate of Return and Other Metrics DADSS
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2 Administrative Details Homework #2 due Thursday Questions from last class?
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3 A note from a former student on inflation …  As you may know, Zimbabwe has been experiencing hyperinflation for the  last few years.  In fact, by last November, inflation was estimated at 89.7 sextillion percent  per year (89.7 x 10^21). I had been dying to buy some Zimbabwe dollars (Z$) for a while and  finally found them on Ebay.  When they were first released, the Z$50 billion note was enough to buy 3  eggs. It's now worthless, and the largest note currently printed is Z$100  trillion (which is worth about 30 U.S. cents. ..ooops! Not any more. ..). At any rate, I bought 20 Z$50 billion notes, which makes me a trillionaire  in Zimbabwe (or worth less than 1 U.S. penny currently).
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4 Agenda IRR – Internal Rate of Return Comparing Projects EUAC – Effective Uniform Annual Cash  Flows
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5 Internal Rate of Return IRR is the “break-even” discount rate How is IRR calculated? First, look at calculating NPV For some series of cash flows (CF) and some  discount rate ( r ), we arrive at the net present  value of the cash flow stream: NPV is  some   number ( 29 ( 29 ( 29 T T r CF r CF r CF CF NPV + + + + + + + = 1 1 1 2 2 1 1 0
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6 Inverting NPV For IRR, we want to solve for the  r  that  will make the NPV = 0 Consider a shorter cash flow stream: Year 0: -$10 Year 1: $12 What is the NPV if the discount rate is  10%? ( 29 91 . 0 1 . 1 12 10 1 12 10 1 = + - = + + - = r NPV
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7 Calculating IRR Now, what would the IRR be? We want NPV =  0… The IRR is 20% That is, this project will break even (have a  positive or zero NPV) until the discount rate  exceeds 20% ( 29 ( 29 ( 29 % 20 1 2 . 1 10 12 1 12 1 10 1 12 10 1 12 10 0 1 1 = - = = + = + + = + + - = r r r r r
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8 But wait… There’s a complication What happens with larger cash flow streams? The IRR is the root of the discounted cash flow  equation, which is a large polynomial 2 periods (highest power = 1) Easy 3 periods (highest power = 2) Quadratic formula 4 periods (highest power = 3) Cubic roots… ¦ ¦ 6 periods (highest power = 5) Fields medal 7+ periods Need computer
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9 Numerical Methods Excel uses an algorithm (Newton-Raphson) to quickly find the  correct IRR – given a guess Another complication: Descartes’ Rule of Signs The number of possible roots (or zeroes) of a polynomial is equal to  the number of sign changes Cash Flow Stream #1: 1 change in the cash flow    Year       0    1    2    3    4    5 Cash Flow -10  +2  +2  +5  +5  +10 Cash Flow Stream #2: 3 changes, 3 possible IRRs
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Lecture 03 - IRR 2010 - Lecture 3 DADSS Engineering...

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