# SEC05 - UNIVERSITY OF PENNSYLVANIA THE WHARTON SCHOOL...

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UNIVERSITY OF PENNSYLVANIA THE WHARTON SCHOOL LECTURE NOTES FNCE 601 FINANCIAL ANALYSIS Franklin Allen Fall 2003 WEEK 3 (part 2) Th: 9/18/03 Copyright 2003 by Franklin Allen

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FNCE 601 - Section 5 - Page 1 Section 5: A Comparison of Investment Criteria Read Chapter 5 BM Motivation Consider a project with the following cash flows: C 0 C 1 C 2 C 3 -925 +1000 +1400 -1500 Initial Clean-up Investment Costs Internal Rate of Return = 4.62% Opportunity Cost of Capital = 10% Should we accept this project? Introduction In Section 2 we looked at the NPV rule and showed that it was a good rule for the managers of corporations to follow. NPV is a measure of wealth created for shareholders so maximizing NPV is like maximizing the wealth of shareholders. We had a simple model, but you can show that in much more complex environments the same rule still holds, i.e., NPV is like pushing out the budget constraint, and makes shareholders as well off as possible. The NPV rule always works. In addition to the NPV rule, we also had the rate of return rule. In that case they were equivalent, but in general which should we use? Why go to the bother of calculating NPV when
FNCE 601 - Section 5 - Page 2 we could find out whether to invest or not by comparing rate of return with opportunity cost? As the motivation example illustrates it’s not always easy to get the correct answer with the rate of return rule. In this section we are going to argue for the superiority of the NPV rule over the rate of return rule or, in its more general form, the internal rate of return (IRR) rule and also over various other traditional methods of project appraisal. We will start with why it is better than the IRR. We shall argue that they are equivalent provided the IRR rule is properly applied, but it is more difficult to apply the IRR rule, and hence we should use the NPV rule. In the one period case we considered before, the one period rate of return R was given by 1 + R = Payoff => 1 + R = C 1 => C 0 + C 1 = 0 __________ ___ ______ Investment -C 0 1 + R In the more general case with more than one period it is not entirely clear what is meant by the rate of return, so instead we use the more general concept of IRR. What is the IRR? The IRR extends the last form given above for the rate of return. It is the rate you discount at such that the discounted cash flow (DCF) is zero. The DCF is a function of the rate, i, and the cash flows: T T 2 2 1 0 ) i 1 ( C ... ) i 1 ( C i 1 C C ) i ( DCF + + + + + + + = The IRR is the value of i such that DCF = 0, i.e.: 0 ) IRR 1 ( C ... ) IRR 1 ( C IRR 1 C C ) IRR ( DCF T T 2 2 1 0 = + + + + + + + =

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FNCE 601 - Section 5 - Page 3 Finding the IRR The easiest way to find IRR is a calculator. One question that may occur to you is how is the calculator finding it? To see this, it is helpful to consider what is going on graphically. We can calculate the DCF at a number of values of the discount rate, join them up and then read off the value of the discount rate at which DCF = 0. This is the IRR. For example, suppose we have the following cash flows: Example 1 C 0 C 1 -1 +1.1 In this case we have the following values of DCF for various values of i: i DCF(i) 0 -1 + 1.1 = 0.1 0.05 -1 + (1.1/1.05) = 0.0476 0.1 -1 + (1.1/1.1) = 0 0.15 -1 + (1.1/1.15) = -0.0435
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## This note was uploaded on 03/16/2010 for the course FNCE FINANCIAL taught by Professor Franklinallen during the Spring '03 term at UPenn.

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SEC05 - UNIVERSITY OF PENNSYLVANIA THE WHARTON SCHOOL...

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