I've seen two ways to account for dilution when valuing a European option using Black Scholes. I'm not sure which is the correct way and why these methods differ. The two ways I've seen are:

1) Multiplying the value of the warrant/option by 1/(1+q) where q is the amount of dilution (e.g. q is the number of options over basic shares plus options)

2) Using an adjusted share price to calculate d1, d2 and the value of the call. This adjusted share price is calculated the number of shares outstanding multiplied by the share price plus the value of the call option (as calculated by Black-Scholes) multiplied by the number of options being issued. This is then divided by the number of options being issued plus the basic shares outstanding, which gives you an adjusted diluted share price, which you then run Black-Scholes with to get the value of the diluted call option.

Can you please advise which (if any) of these methodologies are correct?

Many thanks!


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