# 07 Profitability Index and WACC.pdf - Matemu00e1ticas...

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Investment Projects & Firms’ Valuation Fernando Martínez, MBA, CRM MMXX-II
VII. Profitability Index Fernando Jesús Martínez Eissa, MBA MMXX-II School of Economic and Business Sciences
Another method used to evaluate projects is called the profitability index. Is defined as the ratio of the present value of the future expected cash flows after initial investment divided by the amount of the initial investment. i.e. ࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵? ࠵?࠵?࠵?࠵?࠵? ࠵?࠵? = ࠵?࠵? ࠵?࠵? ࠵?࠵?࠵?ℎ ࠵?࠵?࠵?࠵?࠵? ࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵? ࠵?࠵? ࠵?࠵?࠵?࠵?࠵?࠵?࠵? ࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵? ࠵?࠵?࠵?࠵?࠵?࠵?࠵? ࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵? Profitability Index
Profitability Index 1 2 Investment (\$20) (\$10) 1 \$70 \$15 2 \$10 \$40 NPV @ 12% \$50 \$35.3 PV CF \$70 \$45 PI 3.52 4.53 Option
Application of Profitability Index We consider three situations: 1. Independent projects: Assume that this two projects are independent. According to the NPV rule, both projects should be accepted because NPV is positive in each case. The profitability index (PI) is greater than 1 whenever the NPV is positive. Thus, the PI decision rule is: Accept an independent project if PI > 1. Reject it if PI<1. 2. Mutually exclusive projects: Let us now assume that we can only accept one of this two projects. NPV analysis says accept Project 1 because this project has the bigger NPV. Because Project 2 has the higher PI, the profitability index leads to the wrong selection. For mutually exclusive projects, the profitability index suffers from the scale problem that IRR also suffers from. Project 2 is smaller than Project 1. Because the PI is a ratio, it ignores Project 1’s larger investment. Thus, like IRR, PI ignores differences of scale for mutually exclusive projects.
Application of Profitability Index However, like IRR, the flaw with the PI approach can be corrected using incremental analysis. We write the incremental cash flows after subtracting Project 2 from project 1 as follows: Because the profitability index on the incremental cash flows is greater than 1.0, we should choose the bigger project that is, Project 1. This is the same decision we get with the NPV approach. Incremental 1 2 Cash Flow Investment (\$20) (\$10) (\$10) 1 \$70 \$15 \$55 2 \$10 \$40 (\$30) NPV @ 12% \$50 \$35.3 \$15.00 PV CF \$70 \$45 \$25 PI 3.52 4.53 2.52 Option
Application of Profitability Index 3. Capital rationing: The previous cases implicitly assumed that the company could always attract enough capital to make any profitable investments. Now consider the case when the firm does not have enough capital to fund all positive NPV projects. This is the case of capital rationing . Consider a project with the following cash flows: In addition consider that there are available only 20 million for investing. Therefore If you choose P1 you cannot choose any of P2 or P3. Conversely P2 and P3 can be chosen at the same time given that the initial investment is 10 million for each. Notice that even P2 and P3 have lower NPV, jointly they bring higher NPV than P1 Option 3 Investment (\$10) 1 (\$5) 2 \$60 NPV @ 12% \$33 PV CF \$43
Application of Profitability Index In the case of limited funds, we cannot rank projects according to their NPVs.