Q: A firm has the following risky assets on its balance sheet which will yield the following random payoff in one period: (listed below in the picture). Assume further that the firm has a cash balance of 20 and debt with a face value of D to be paid out in its entirety in one period. The firm can invest in an asset which will produce the following risky payout in one period: (also listed below in the picture)

The project requires an investment of 20 today. Note that the random states of the project payout match those of the risky asset payout. In other words, with probability Px the state of nature will be high and both the firm and the project will yield the high state payout. Note that the firm has cash and therefore does not have to issue debt or equity to finance this investment. If the firm chooses to invest, it will use the cash balance of 20 for the investment.

Assume that the risk free rate equals zero and all investors are risk neutral:

A) Assume D=200, p=.5 and X=30. Should the firm undertake the risky project? Will the firm undertake the risky project? Assume the investment decisions are being made on behalf of shareholders.

B) What is the size of the agency cost generated by the investment decision made in part A?

state of Nature High state (w/ probabiliter) LOW 180 state Risky asset pay off 80 state of Nature High Stare (w/probabilen) Low stath Investment pay off 0 state of Nature High state (w/ probabiliter) LOW 180 state Risky asset pay off 80 state of Nature High Stare (w/probabilen) Low stath Investment pay off 0