4.2.2 The Profitability Index (PI) This method is also known as ..., Summaries of Business

Download 4.2.2 The Profitability Index (PI) This method is also known as ... and more Summaries Business in PDF only on Docsity! 4.2.2 The Profitability Index (PI) This method is also known as the “Benefit Cost Ratio” in the sense that it is used in evaluating the economic worth of a capital investment projects. The technique evaluates the return on every one Naira invested into a project. It tells how much a project has generated. The formula is the quotient of the present value of the cash inflows to the net investment/capital outlay. See the formulas below: For Projects with uneven series of cash inflow: 𝑃𝐼 = 𝐴1(1 + 𝑟)−1 + 𝐴2(1 + 𝑟)−2 + 𝐴3(1 + 𝑟)−3+, … … + 𝐴𝑡(1 + 𝑟)−𝑡 𝐶 For projects with even series (annuity) of cash inflow: 𝑃𝐼 = 𝐴𝑡[(1 + 𝑟)−1 + (1 + 𝑟)−2 + (1 + 𝑟)−3+, … … + (1 + 𝑟)−𝑡] 𝐶 Or 𝑃𝐼 = 𝐴[(1 + 𝑟)𝑡 − 1] 𝑟(1 + 𝑟)𝑡 𝐶 Decision Rule Any project with profitability index greater than or equal to 1 may be accepted, else it should be rejected. For mutually exclusive projects, the project with the highest PI is ranked highest and accepted. As you can see that the formula is similar to that of NPV just that we only divide the PV of the cash inflows by the cash outflow. This means that the same process is involved except that the ratio rather than the difference of the cash flows is taken into consideration. Using the first example as in the case of NPV A Company is to embark on a business venture for which it will require N2000000 to set up. Estimated cash inflows are N400,000 at the end of each of the first two years of operation, N280000 at the end of the third year and N800000 at the end of each of the last two years of operation and the venture is expected to wind up after five years. If the required rate of return is 20%, advise the Company on whether or not to accept the investment project using the NPV technique. Recall: 𝑊ℎ𝑒𝑟𝑒 𝐴1 𝑎𝑛𝑑 𝐴2 𝑒𝑎𝑐ℎ = 𝑁400000, 𝐴3 = 𝑁280000, 𝐴4 𝑎𝑛𝑑 𝐴5 𝑒𝑎𝑐ℎ = 𝑁800000 𝑟 = 20%, 𝑡 = 5 𝑦𝑒𝑎𝑟𝑠, 𝑃𝐼 = 𝐴1(1 + 𝑟)−1 + 𝐴2(1 + 𝑟)−2 + 𝐴3(1 + 𝑟)−3+, … … + 𝐴𝑡(1 + 𝑟)−𝑡 𝐶 𝑃𝐼 = 400000(1 + 0.2)−1 + 400000(1 + 0.2)−2 + 280000(1 + 0.2)−3 + 800000(1 + 0.2)−4 + 800000(1 + 0.2)−5 2000000 𝑃𝐼 = 400000(1.2)−1 + 400000(1.2)−2 + 280000(1.2)−3 + 800000(1.2)−4 + 800000(1.2)−5 2000000 𝑃𝐼 = [400000(0.8333) + 400000(0.6944) + 280000(0.5787) + 800000(0.4823) + 800000(0.4019)] 2000000 𝑃𝐼 = 333320 + 277760 + 162036 + 385840 + 321520 2000000 𝑃𝐼 = 1480476 2000000 𝑃𝐼 = 0.74 Decision: The project will be rejected because the PI is less than 1. *** You can try out the other worked example using the PI. Practice Question: Suppose that you are the finance manager of a company that is considering two mutually exclusive investment proposals, with the following investment characteristics; Project Y X Net Investment (N) 100000 120000 Cash inflow at the end of year 1 30000 40000 2 30000 30000 3 30000 50000 4 30000 25000 5 30000 25000 Given that the applicable cost of capital (rate of return) is 9%, determine the PI as the determining factor for your recommendation as to which of the projects should be executed. Give your recommendation to the management of the company. 4.4.3 Internal Rate of Return (IRR) The internal rate of return is an evaluation technique that indicates the actual return rate an investment project is expected to yield. This method also known as the cut off rate, the hurdle rate, the DCF yield, the target rate, the marginal efficiency cost of capital, DCF rate