$8.$ If it is managed efficiently, Remel Inc. will have assets with a market value of $$50$ million,

$$100$ million, or $$150$ million next year, with each outcome being equally likely. However,

managers may engage in wasteful empire building, which will reduce the firm$$s market value

by $$5$ million in all cases. Managers may also increase the risk of the firm, changing the probability of each outcome to $50\%,10\%,$ and $40\%,$ respectively.

a$.$ What is the expected value of Remel$$s assets if it is run efficiently?

Suppose managers will engage in empire building unless that behavior increases the likelihood

of bankruptcy. They will choose the risk of the firm to maximize the expected payoff to equity

holders.

b$.$ Suppose Remel has debt due in one year as shown below. For each case, indicate whether

managers will engage in empire building, and whether they will increase risk. What is the

expected value of Remel$$s assets in each case?

i$.$ $$44$ million

ii$.$ $$49$ million

iii. $$90$ million

iv$.$ $$99$ million