Using BSOP to value debt and Equity

Please tell me which past question you are referring to.

The reason I asked which past question you were referring to was to check whether you were in fact asking about the standard use of BSOP for the valuation of real options, or whether you were actually asking about the application of it to valuing the equity in a company.

The valuation of real options has been asked several times and Nente is a standard valuation of a real option (and I assume that you have watched my free lectures on the valuation of share options and of real options). Pa is the present value of the future cash flows, Pe is the exercise price (which does not need discounting because, as I explain in my lectures, multiplying by the term with ‘e’ in it in the formula is effectively doing the discounting on a continuous rather than on an annual basis), ‘r’ is the risk free rate of interest, ‘s’ is the standard deviation (i.e. the volatility), and ‘t’ is the time to expiry expressed in years (so if the option is exercisable in (say) 3 months then ‘t’ is 0.25).

The only relevance in Nente to the share price is that the value of the option is, as always, the increase in the value of the firm and therefore dividing this by the number of shares is the increase in the share price that will result.

As far as the use of BSOP in the valuation of a company – you can only be asked to explain the idea (as was the case in Faoilean) and cannot be asked to perform calculations. Holding shares in a company is similar to holding a call option because if the debt in the company exceeds the asset value then the shareholders can walk away (due to limited liability) whereas if the assets exceed the debts then the shareholders will continue in the business in order to get the surplus. Although again you cannot be asked to perform calculations in the exam, Pa is the value of the assets in the firm, Pe is the amount owing to lenders, ‘t’ is the time (in years) to redemption of the debt (and ‘r’ and ‘s’ are as before).

I am not sure whether or not this does answer what you were asking, but if not (and again assuming that you have watched my lectures on share options and on real options) then obviously do ask again 🙂

Again, I am still not sure whether you are asking about real options (which is what Nente and other questions were examining) or using Black Scholes to value the equity in a company (which is being asked to explain in Faoilean.) – they are two different things even though we could use the same formula.

In neither case is anyone buying anything (unlike share options which are purchased).

With real options the situation is as follows. Normally, when appraising a project we simply calculate the NPV based on the expected future cash flows. This NPV is the amount by which the value of the company will increase if the project is accepted. However a problem always is that the future cash flows are only ever estimates and therefore the project could turn out to be better or worse than calculated.
If, however, we were offered the same project (which say is going to last 5 years) but knew we would have the chance to review it in (say) 2 years then we could maybe decide to abandon it if it was doing worse than expected (rather than be forced to carry on), or maybe decide to sell it to someone else if that turned out to be preferable than carrying on, or maybe decide to expand it if it was doing well, or simply to carry on with it because it is doing as well (or better) than expected. (I list all the different types of real options in my notes and lectures).

In all of these cases, the fact that we have the right (the option) of reviewing and doing something else if we want on a future date makes the project more attractive than if the option didn’t exist and we were forced to carry on whatever happened. We use the Black Scholes formula to be able to put a value on this option to review. It makes the investment more attractive and therefore increases the benefit of the project and therefore increases the value of the company.

Saying the same thing in a different way, which would you prefer? Accepting a project which you would have to stick with for the full (say) 5 year life whatever happened, or accepting the same project where you were able to review it after (say) 2 years and could change things (in the way explained above). Surely you would prefer the second choice (having the option to change your mind about things) and therefore it would make the project more attractive.

As far as using Black Scholes to value the equity in a company (which is a completely separate idea from real options), again it is not that anyone is buying an option. It is simply that owning the equity of a company is a bit like already owning an option because the equity always have the choice (the option) of keeping the company going and getting the future earnings or closing down if things go badly because even if there is not enough to pay off the liabilities the equity do not suffer the loss (because of limited liability) and so would just end up with nothing rather than having to pay out money. However, as I wrote before, you cannot be expected in the exam to do calculations on this but can only be expected to explain the idea.

You are very welcome 🙂