Use the following information to answer the question(s)below.
If managed effectively,Rearden Metal will have assets with a market value of $200 million,$300 million,or $400 million next year,with each outcome being equally likely.Managers,however,may decide to engage in wasteful empire building,which will reduce Rearden's market value by $20 million in all cases.Managers may also increase the risk of the firm,changing the probability of each outcome to 50%,5%,and 45% respectively.
-Suppose that the managers at Rearden Metal will engage in empire building unless that behavior increases the likelihood of bankruptcy.If Rearden has $190 million in debt due in one year,then the expected value of Rearden's assets is closest to:

Question

Quizplus · Accepted Answer

Since the managers at Rearden Metal will engage in empire building only if it does not increase the likelihood of bankruptcy, we need to consider the possibility of bankruptcy. If Rearden's assets are worth less than $190 million, they will not be able to pay off their debt and will go bankrupt. Therefore, we need to calculate the expected value of Rearden's assets, taking into account the probability of bankruptcy.
The probability of bankruptcy is the probability that Rearden's assets are worth less than $190 million, i.e., the probability that they are worth $200 million, which is the lowest possible outcome. Since the probability of each outcome changes to 50%, 5%, and 45%, the probability of Rearden's assets being worth $200 million is 50%. The probability of Rearden's assets being worth $300 million or $400 million is now 5% and 45%, respectively.
Therefore, the expected value of Rearden's assets is:
(0.5 x $200 million) + (0.05 x $300 million) + (0.45 x $400 million) = $300 million
However, if the managers engage in empire building, the value of Rearden's assets will be reduced by $20 million in all cases. Therefore, the expected value of Rearden's assets, taking into account the possibility of empire building, is:
(0.5 x ($200 million - $20 million)) + (0.05 x ($300 million - $20 million)) + (0.45 x ($400 million - $20 million)) = $280 million
Therefore, the best choice is D, with an expected value of $300 million if the managers do not engage in empire building, and $280 million if they do.

Use the Following Information to Answer the Question(s)below