questionProblems with Profitability Index:
Cash Flow 1 Cash Flow 2
-Year 0: -78,000 -28,800
-Year 1: 28,300 9,600
-Year 2: 34,800 17,400
-Year 3: 43,700 15,600
1. If the required return is 11 percent and the company applies the profitability index decision rule, which project should the firm accept?
2. If the company applies the NPV decision rule, which project should it take?
3. Explain why your answers in parts (a) and (b) are different.
answer1. Steps:
Cash Flow 1
-PV of Cash Flows = npv(11,0,{28300,34800,43700}) = 85,693
-PI = PV of Cash Flows / Cost of Investment
-PI = 85,693/78,000 = 1.099
Cash Flow 2
-PV of Cash Flows = npv(11,0,{9600,17400,15600}) = 34,177.50
-PI = 34,177.50/28,800 = 1.187
-We should accept project 2 since it has a higher PI
2. Steps
Cash Flow 1
-npv(11,-78000,{28300,34800,43700})
-NPV = $7,693.02
Cash Flow 2
-npv(11,-28800,{9600,17400,15600})
-NPV = $5,377.46
-We should accept project 1 because the NPV is higher
3. Explanation:
-Profitability Index, like IRR, is a relative measure. For standard independent projects NPV, IRR and PI should give the same accept/reject decision. For mutually exclusive projects the relative rankings of IRR and PI may differ from the ranking given by NPV.
-Using the profitability index to compare mutually exclusive projects can be ambiguous when the magnitudes of the cash flows for the two projects are of different scale. In this problem, Project I is roughly 2.5 times as large as Project II and produces a larger NPV, yet the profitability index criterion implies that Project II is more acceptable.