Consider a highly levered firm with sole proprietorship – a single owner runs th

Question

Consider a highly levered firm with sole proprietorship – a single owner runs the firm. Suppose that all the debt will mature in one year. The owner will pay off the debt if the firm value (V) is greater than the face value of the debt (D). Otherwise, the owner will declare bankruptcy – the debtholders will receive the firm value, which is less than the face value of the debt, and take the control of the firm. A. Describe the payoff from the owner’s position. Can you express the owner’s position with an option on the firm value? B. Describe the payoff from the debtholders’ position. Show that the debtholders’ position is a combination of a risk-free loan and a written put option on the firm value. You may find it useful that “min(A, B) = – max(A, B).” Using the results above, evaluate the following statement: “Shareholders have an incentive to expropriate debtholders by taking high-risk projects that increase the volatility of the firm.”

Explanation / Answer

Payoff to the owner=max(V-D,0)

It is analogous to call option where payoff is max(S-X,0)..SO, here the owner has bought a call option on the firm with underlying as the firm's value V and exercise price as D and as the firm value increases, he benefits but if it is less than strike price, he lets the option expire

Payoff to the bondholders=min(V,D)=D+min(0,V-D)

It is analogous to risk free loan of D and put option with exercise price D and underlying as the firm's value V..Because Payoff from a written put=min(0,S-X)

As price of call option increases with the volatility of the firm, the owner would want to increase the value of his call option. He can do so by increasing volatility of the firm which is possibile through high risk proejcts.

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