Corporate Financing Understanding Payoffs and Risk Preference This problem is less direct than the previous ones, and you may have to work on it more slowly. It will help you think and apply the theory in more economic and graphic terms. Consider a company that has only one investment with a net return of Y (Y is a random variable, positive and smaller than infinite). The company is financed by both debt and equity; the investors of debt and equity are called lender and shareholder, respectively, and the shareholder exercises full control on the company (no debt covenants in place) and may ultimately decide on the companys risk level. The debt contract is standard; in other words, the company agrees to repay the lender a pre-determined amount D, as long as Y > D. If Y < D, then the lender gets the whole Y. Therefore, the shareholder acts as the residual claimer on Y; the firms payoff Y is first used to repay the lender, then the shareholder.

1. Describe algebraically the payoff functions of both the lender and the shareholder as a function of Y and D. Tips: A payoff is the amount received by a type of investor depending on what occurs to Y. Algebraically, it means If Y > D payoff shareholder = [], & payoff lender = [] and so on for all cases and players. There are two cases to consider: Y < D and Y > D. You may check that it does not matter whether you consider the equality Y = D at the lower or upper case.

2. If you think of financial options, what is the payoff of the shareholder akin to (suggestions: owing a call option, issuing a call option, owing a put option or issuing a put option)? On the other hand, what is the payoff of the lender akin to? Remember to consider what the sum of the payoffs of the lender and the shareholder must equal to.

3. Considering the payoffs of each investor (lender and shareholder), what will be their risk preference vis--vis the average risk undertaken by the company? Explain why.

4. Explain how the lender could use debt covenants to align the incentives of the shareholder to its own. Can you give some examples of financial covenants that the lender would like to have in place?

5. As leverage increases, how does the lenders appetite for risk change? Why?

6. As leverage decreases, how does the shareholders appetite for risk change? Why?

7.Consider an extension of the problem above by including a subordinated debt, which is supplied by a subordinated lender. Consider the lender on the first part of the problem was the senior lender, or the first one to be paid in case Y is not high enough. The subordinated debt contract is standard; in other words, the company agrees to repay the subordinated lender a pre-determined amount d as long as Y > D + d. If Y < D + d, then the proceeds first flow to the senior lender, then to the subordinated lender. The shareholder therefore still acts as the residual claimer on Y.

8. Describe algebraically the payoff functions of each investor (senior lender, subordinated lender and shareholder) as a function of Y, D and d. There are now three cases to consider: Y < D; D < Y < D + d; and Y > D + d.

9. Explain how the inclusion of the subordinated lender altered the shareholders risk preference in comparison to the previous case. How does the change in risk assumed by the company (the shareholder remains in control) affect the senior lenders expected payoff?

10. Explain why the senior lender would have liked to prevent the firm from issuing subordinated debt if it could have control over this decision (covenants).

11. Explain why the subordinated lenders risk preference has characteristics of both equity and senior debt; specifically, resembling equity at low values of Y and resembling senior debt at high values of Y. Furthermore, show that her payoff may be represented by the combination of owning (being long on) a call option (with strike price K1) and writing (being short on) another call option (with strike price K2); for that, determine both K1 and K2 in terms of D and d.

12. Based on your response on the previous question, explain how the subordinated lenders risk preference changes for different values of D and d. More specifically, explain how its risk preference changes as (i) d increases, and as (ii) D decreases.