Using option pricing theory to value equity

 The Black-Scholes option pricing model can also be used to value the equity of a company.

The basic idea is that, because of limited liability, shareholders can walk away from a company when the debt exceeds the asset value. However, when the assets exceed the debts, those shareholders will keep running the business, in order to collect the surplus.

Therefore, the value of shares can be seen as a call option owned by shareholders and we can use Black-Scholes to value such an option.

Five factors to input into the Black-Scholes model

It is critical that we can correctly identify the five variables to input into the Black-Scholes model. 

For company valuation, these are as follows:

P_a = fair value of the firm's assets
s = standard deviation of the assets' value
P_e = amount owed to bank (see below for more details)
t = time until debt is redeemed
r = risk free interest rate

Note that the value of P_e will not just be the redemption value of the debt. The amount owed to the bank incorporates all the interest payments as well as the ultimate capital repayment.

The value of P_e to input into the Black-Scholes model should be calculated as the theoretical redemption value of an equivalent zero coupon debt.

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Tags:	Valuing equity;Black Scholes