What’s in the Forecast? The Black-Scholes Formula and Forecasting Factors

In our last article, we described the three present factors that go into the Black-Scholes option pricing model. Now we’ll turn our attention to the forecasting factors.

Expected life

A lot hinges on the expected life, also called expected term. Expected life is the number of years after the grant date that you estimate your employee will exercise the option. Public companies that have roughly five to seven years of activity calculate this term by looking at the number of years employees have historically taken to exercise their options. However, private companies, or newly-public companies with little history, will take their cue from SAB 107/110. This rule sets out a simplified method for calculating expected term, which involves taking the number of years in which your awards will vest (three years, in our example) and the number of years to expiration (seven years), and averaging them (3 + 7 = 10 ÷ 2 = 5).

Dividend yield

Public companies arrive at this input by estimating the amount of dividends that will be paid over the expected life of the award based on historic dividend payments. Of course, because private companies rarely declare dividends, there’s normally no calculation at all. The dividend yield factor is simply set at zero.

Volatility

Volatility is the anticipated fluctuation of your stock price over the expected term, expressed as a percentage. In our example, calculating volatility means determining by what percentage your stock price will go up or down over the expected five year term. Mature public companies have relatively easy access to this input – they can use a standard volatility formula that analyzes how their exchange-traded stock prices changed over the past five years (or whatever the expected term is) to the date of the grant, and use that as an input.

Private and recently public companies, however, must once again turn to SAB 107/110, which allows them to use a peer group’s volatility as a proxy for their own. Typically, you’ll select between four and ten peer companies that are similar to yours – usually selecting public companies in the same or similar industry, that are a similar size, and have a similar business model or financial standing – usually using the same companies that were used to prepare your company’s 409A-compliant stock value. From there, you’ll calculate the volatility of the closing prices for each peer company for a period equal to the expected term, take the standard deviation of these stock prices over the number of days in each trading year, and average the rate (or do a more advanced weighted average) to determine volatility. If you’d like assistance calculating your volatility, drop us a line.

See it in action

Black-Scholes inputs can seem a bit abstract and it can be useful to see how they work in practice. Check out Solium’s online Black-Scholes calculator to see your inputs in action. But that’s just half the battle. The hardest part, as you’ve no doubt gathered, is coming up with the assumptions. That’s where Shareworks can help.

 

 

 

 

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