In Practice Valuing Warrants

Warrants are long term call options, but standard option pricing models are based upon the assumption that exercising an option does not affect the value of the underlying asset. This may be true for listed options on stocks, but it is not true for warrants, since their exercise increases the number of shares outstanding and brings in fresh cash into the firm, both of which will affect the stock price. The expected negative impact (dilution) of exercise will make warrants less valuable than otherwise similar call options. The adjustment for dilution in the Black-Scholes to the stock price involves three steps: Step 1: The stock price is adjusted for the expected dilution from warrant exercise. Dilution-adjusted S = (S ns+W nw) / (ns + nw)


S = Current value of the stock nw = Number of warrants outstanding

W = Market value of warrants outstanding ns = Number of shares outstanding When the warrants are exercised, the number of shares outstanding will increase, reducing the stock price. The numerator reflects the market value of equity, including both stocks and warrants outstanding. Making this adjustment will lower the stock price used in the model and hence the value of the warrant.

Step 2: The variance used in the option pricing formula is the variance in the value of the equity in the company (i.e., the value of stocks plus warrants, not just the stocks).

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