5 Debt and the manager

Suppose we have a manager that is really keen on empire building - he simply cannot stop investing all cash flows available in the firm. One can think of the manager as being attracted by the perks of managing an ever larger firm.

Shareholders find it difficult to control the manager. However, we assume (and this is a key assumption) that the manager cannot raise capital without the shareholders approval, and shareholders can decide on the financing structure of the firm at the initial date 0 (you can think of date 0 as the establishment of the firm).

At time 0, shareholders meet and decide on the capital structure of the firm. The firms current assets (assets in place) will produce a cash flow R at time 1. Shareholders can decide how much debt (with a face value F) the firm should take on; the debt needs to be repaid at time 1. The bank has the ability to appropriate any cash available within the firm if the debt is not paid; if the cash is not sufficient to cover the debt obligations, the firm is liquidated.

At time 1, the manager decides how much to invest. If up to I = 1, 500, 000 is invested, then the result will be $1.1 at time 2 per dollar invested at time 1. Any dollar above I = 1, 500, 000 produces $0.9 at time 2.

At time 2, the final payoffs are realized and paid out to shareholders. The firm is liquidated.

Assume the interest rate between the stages of the model is zero (we have no discounting; everybody is also risk neutral).

1. What is the expected value of the firm if R = $2, 000, 000 for sure and we have no debt?

2. If R = $2,000,000 and shareholders choose the face value of the debt to maximize their payoff, how much will F be? What is the expected value of the firm in that case?

3. If R is uniformly distributed between $1,000,000 and $3,000,000 and share- holders choose F = $500,000, what is the expected value of the firm?

4. If R is uniformly distributed between $1,000,000 and $3,000,000 and share- holders choose F = $500,000, what is the optimal face value F of the debt shareholders should choose?