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You are the manager and sole owner of a highly leveraged company. All the debt will mature in one year. If at that time the value of the company is greater than the face value of the debt, you will pay off the debt. If the value of the company is less than the face value of the debt, you will declare bankruptcy and the debt holders will own the company. (a) Express your position as an option on the value of the company. (2 marks) (b) Express the position of the debtholders in terms of options on the value of the company. (2 marks) (c) What can you do to increase the value of your position? (2 marks)

Question

You are the manager and sole owner of a highly leveraged company. All the debt will mature in one year. If at that time the value of the company is greater than the face value of the debt, you will pay off the debt. If the value of the company is less than the face value of the debt, you will declare bankruptcy and the debt holders will own the company. (a) Express your position as an option on the value of the company. (2 marks) (b) Express the position of the debtholders in terms of options on the value of the company. (2 marks) (c) What can you do to increase the value of your position? (2 marks)

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Solution

(a) Your position as the manager and sole owner of a highly leveraged company can be expressed as a call option on the value of the company. This is because a call option gives the holder the right (but not the obligation) to buy an asset at a certain price within a specific period of time. In this case, if the value of the company is greater than the face value of the debt at the time of maturity, you will exercise the option to pay off the debt and keep the company. If the value of the company is less than the face value of the debt, you will not exercise the option and will instead declare bankruptcy.

(b) The position of the debtholders can be expressed as a put option on the value of the company. A put option gives the holder the right (but not the obligation) to sell an asset at a certain price within a specific period of time. If the value of the company is less than the face value of the debt at the time of maturity, the debtholders will exercise their option to sell the company (i.e., take ownership of it). If the value of the company is greater than the face value of the debt, the debtholders will not exercise their option and will instead receive the repayment of the debt.

(c) To increase the value of your position, you can take steps to increase the value of the company. This could include strategies such as improving operational efficiency, investing in growth opportunities, or reducing costs. Additionally, you could also try to renegotiate the terms of the debt to reduce the face value or extend the maturity date.

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