A corporation must decide between two mutually exclusive projects. Both projects

Question

A corporation must decide between two mutually exclusive projects. Both projects require an initial outlay of 100 million euro, and they generate cash flows that are independent of the growth of the economy. Project A has an equal probability of four gross payoffs: 80 million euro, 100 million euro, 120 million euro or 140 million euro. Project B has a 50:50 chance of paying either 90 million euro or 130 million euro. Assuming that shareholders are all risk averse, show that they unanimously prefer Project B to Project A.

Explanation / Answer

Expected Payoff, project A (Million Euros) = 0.25 x 80 + 0.25 x 100 + 0.25 x 120 + 0.25 x 140

= 20 + 25 + 30 + 35

= 110

Profitability Index = Expected Payoff / Initial investment

= 110 / 100 = 1.10

Expected payoff, project B (Million euros) = 0.5 x 90 + 0.5 x 130

= 45 + 65

= 120

Profitability Index = Expected Payoff / Initial investment

= 120 / 100 = 1.20

Since profitability index of project B > profitability index of project A,

Shareholders will unanimously prefer B to A.

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