Company X has zero-coupon debt outstanding with a face value of F > 0 due in exactly one year. This debt does not contain any covenants. The value of the company’s assets when the debt comes due will either be 0, 90, or 180 with probabilities 0.2, 0.6, and 0.2, respectively. The current market (and also fair) value of the company’s equity is 16. There are no taxes or direct costs of financial distress, all investors are risk neutral, and the risk-free interest rate is zero. The managers of the firm always act in the interests of existing shareholders.

When answering each question, state any additional assumptions you may need to make. Show all working/calculations.

(a) Determine F, the face value (i.e. promised payment) of the company’s debt.

Suppose X’s managers can choose to costlessly restructure the company’s assets so that they will be worth 0 or 180 next year with probabilities 0.7 and 0.3, respectively.

(b) Assuming the firm retains its existing assets, graph the expected payoff to X’s shareholders as a function of F, i.e. for all feasible face values of debt, 0 ≤ F≤ 180. On the same diagram, repeat this exercise assuming the firm restructures its assets. Make sure to clearly label all relevant features, including axis-intercepts, gradients, and any intersection(s) between payoff functions.

(c) Given the actual face value of debt calculated in (a), what does your answer to (b) imply about how the managers of Company X will behave? Who wins/loses from this behaviour and by how much? Briefly describe the agency problem of debt that this behaviour represents.

Assume X’s managers decide to restructure the company’s assets. After restructuring, they consider a plan to repurchase enough of the company’s debt to halve its face value. The company’s debt is callable at par (i.e. at face value). Alternatively, the repurchase can be done in the secondary market. Any repurchase would be financed via an equity issuance. The company’s debtholders are all small, rational, and dispersed. The managers of the company can freely switch between the new and old asset structure after the repurchase.

(d) Explain why the call provision attached to Company X’s debt is worthless.

(e) What equity stake does the firm need to offer new shareholders to raise the required financing? Given these terms, demonstrate and explain why the firm will/won’t proceed with the issuance.

(f) Determine if the decision in (e) would be different if the company had not restructured its assets prior to the equity issuance and debt repurchase. Using your calculation here and in (c), comment on the sources of the total gain/loss to existing shareholders in (e)