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A Corporation must decide between two mutually exclusive projects. Both projects requirean initial spending of $100 million, and they generate cash ows that are independent of thegrowth of the economy.Project A has equal probability of four gross payos: $80 million, $100 million, $120 million,or $140 million.Project B has a 50/50 chance of paying either $90 million or $130 million.Assuming that the shareholders are all risk-averse, prove that they unanimously prefer projectB to project A.1

Question

A Corporation must decide between two mutually exclusive projects. Both projects requirean initial spending of 100 million, and they generate cash ows that are independent of thegrowth of the economy.Project A has equal probability of four gross payos: 80 million, 100million,100 million, 120 million,or 140million.ProjectBhasa50/50chanceofpayingeither140 million.Project B has a 50/50 chance of paying either 90 million or $130 million.Assuming that the shareholders are all risk-averse, prove that they unanimously prefer projectB to project A.1

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Solution

To prove that shareholders unanimously prefer project B to project A, we need to consider the expected payoff and the risk associated with each project.

  1. Calculate the Expected Payoff:

For Project A, the expected payoff is the average of all possible outcomes, which is (80million+80 million + 100 million + 120million+120 million + 140 million) / 4 = $110 million.

For Project B, the expected payoff is also the average of all possible outcomes, which is (90million+90 million + 130 million) / 2 = $110 million.

So, the expected payoff for both projects is the same.

  1. Evaluate the Risk:

For risk-averse shareholders, they prefer the project with less risk. The risk of a project can be measured by the variance or standard deviation of the possible outcomes.

For Project A, the possible outcomes are more spread out, ranging from 80millionto80 million to 140 million.

For Project B, the possible outcomes are less spread out, only ranging from 90millionto90 million to 130 million.

Therefore, Project B is less risky than Project A.

  1. Conclusion:

Since the expected payoff is the same for both projects, and Project B is less risky than Project A, risk-averse shareholders would unanimously prefer Project B to Project A.

This problem has been solved

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