Valuation of equity as call option

I am not sure I agree with your first sentence 🙂
As far as the exam is concerned there are various ways you can be asked to value the equity. The Black Scholes option pricing formula is one way (and maybe the best way) but is only relevant in the exam when you are asked to do it that way (and are given the necessary information about the volatility etc.) 🙂

However, there are various ways of explaining the reasoning, but the way I find the easiest to understand is this:

Shareholders get the benefit of any value of the assets over and above the amount owed for long-term debt, but (because of limited liability) they do not suffer if the long-term debt exceeds the value of the assets (OK they lose their money, but they are not liable for the debts). That is what makes the equity similar to an option (they can only ‘gain’ but they cannot ‘lose’).

So….the value of the equity is the excess of the value of the assets over the value of the long-term debt.

If you look at the Black Scholes formula for a call option, then in respect of the value of equity it is essentially Pa (which is the value of the assets) minus Pe (which is the value of the debt). The term that multiplies Pa in the formula is there to account for the volatility, and the terms that multiply Pe in the formula are there to discount Pe to the present value.
(I explain both of these in my free lectures).

I hope that helps 🙂

You are welcome 🙂