Tuesday, January 5, 2010


Ordinary Share as an Option

One distinguishing feature of ordinary share is that it has limited liability. The limited liability feature provides an opportunity to the shareholders to default on a debt. If a firm has incurred a debt, each time a payment is due, the shareholders can decide to make payment or to default.

If the firm’s value is more than the payment that is due, the shareholders will make payment since they shall be left with a positive value of their equity and keep the firm. If the payment that is due is more than the value of the firm, the shareholders will default and let the debt holders keep the firm. Since the shareholders have a hidden right to default on debt without any liability, the debt contract gives them a call option on the firm.

The debt holders are the sellers of call option to the share holders. The amount of debt to be repaid is the exercise price and the maturity of debt is the time to expiration.

The value of the shareholders equity is the difference between total value of the firm and the value of the debt. The value of equity cannot be negative. If the value of the firm is less than the value of the debt, the shareholders will not exercise the option of owning the firm. Thus, at the time of exercising the option, the value of equity will be either the excess of the total firm’s value over the value of the debt or zero.

There is an alternate way of looking at ordinary share as an option. The shareholders’ option can be interpreted as a put option. The share holders can sell (handover) the firm to the debt holders at zero exercise prices if they do not want to make the payment that is due.

We can use the black-scholes model to value the ordinary share as an option.

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