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Alex Bäcker's Wiki / On the valuation of private company securities
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On the valuation of private company securities

Page history last edited by Alex Backer, Ph.D. 12 years, 11 months ago

If you start a company, sooner or later you will be faced with the question of how to value stock options in order to determine their strike price. One of the trickiest aspects of this is allocating the enterprise value between common and preferred stock. Wilson Sonsini provides a great primer on three common methods to do this. Yet beware an error sometimes made by professionals in applying the options pricing model: just as explained in WSGR's primer on the probability-weighted expected return model, the enterprise value (and the price of the option) needs to be computed at the future time when the liquidity event is expected to occur, and only afterwards should this be discounted to present value at the risk-adjusted discount rate.


This is because the options pricing model simulates the probability-weighted expected return model, estimating returns at the time of a future liquidity event, and not a liquidation in the present. The reason for this, in turn, is aptly put in WSGR's primer: "the principal limitation of the [current value] method is that the immediate liquidation of the company is not, in most cases, a realistic assumption. As a result, the Practice Aid limits the application of this method to situations in which a liquidation or acquisition transaction is imminent or the company is an early-stage enterprise where no material progress has been made on its business plan and there is no reasonable basis for estimating the timing and amount of any common equity return that might be realized in the futurewhich makes the application of the other methods described below difficult, if not impossible."


Why use an options pricing model to begin with? In truth, the Probability-Weighted Expected Return Method is theoretically sounder, as pointed out by the WSGR bulletin. The use of an options pricing model implicitly weighs the probability that the enterprise value will have each of several future values that influence the distribution between common stock and preferred stock by modeling it as a call option, whose price is itself determined by the market's estimate of the probability that the price will exceed the call value or exercise price. The problem is that theoretical models to estimate the value of a call option, such as Black Scholes, assume continuous trading and a measure of volatility, both of which are absent for stock options in a private company. Appraisers get around this by using volatilities from so-called comparables, publicly traded companies in the industry, but this is not how Black & Scholes intended volatility to be measured. Whether the volatility in stock price fluctuations of large publicly traded companies is a good predictor of the variance in future price of a small privately held company seems doubtful at best.


But the problems with the options pricing method do not stop there. The approach is based on the following:

1. The assumption that stock options are like a call option, to be exercised if the value of the company exceeds the exercise price. This assumption seems harmless enough --it's a pretty good description of a stock option.

2. If you had an estimate of the volatility, the value of stock options can thus be determined using Black Scholes.

3. Subtract the value of stock options from the enterprise value, and you know how much is left for holders of stock.

4. The method, as I have seen it applied, then stipulates that you consider common stock as a call option. I have seen this done where the option has exercise price equal to the liquidation preference, and I have seen it with exercise price equal to the remaining value immediately after the preferred stock is liquidated. You compute the value of such an option, and subtract that from the enterprise value to derive the value of preferred stock. Here is where it gets tricky. If that option was a freely traded security and you had an accurate estimate of the volatility, that value would correctly capture a weighted average made by the sum of the probabilities that the enterprise value will be above the liquidation preference at the time of a liquidity event times that enterprise value. But that's only equal to the value of the common stock for enterprise values below the value at which preferred stockholders choose to convert their stock, because above that the value is divided among common and preferred stock. This is ignored in every implementation of this method that I have seen.


One way to see why the application of Black-Scholes to computing the distribution of equity value between commmon and preferred stockholders requires modifications from the standard Black-Scholes model is that the value of a call option, the case for which Black and Scholes developed their model, is clearly greater the greater the volatility, as the option holder has the option not to exercise it in the case of a fluctuation that makes the value of the stock lower than the exercise price, whilst the option seller does not have the option not to sell if the value of the stock fluctuates above the exercise price. In contrast, the same does not universally apply to the value of common stock relative to preferred stock. The dependence on volatility of the value of the ratio of the value between common and preferred stockholders is more complex; it depends on the enterprise value. For enterprise value below the liquidation price, common stock is worthless in the limit of zero volatility. For enterprise value above the liquidation price, common stock has its maximum value (equal to that of preferred stock) in the limit of zero volatility, as higher volatility scenarios introduce a probability that the common stock will be worthless.


In their original 1973 paper, Black and Scholes discussed the application of their model to the valuation of common stock in a very different context, that of the value of common stock in the absence of preferred stock and in the presence of bond debt by the company.


So, while the realization that there are interesting analogies between the valuation of call options and common stock in private companies is certainly clever and interesting, the use of an options pricing model seems to derive mostly from the fact that "there is no generic or textbook version of this model (such as the Black-Scholes approach to the option pricing method)". Perhaps the time for such a textbook version has arrived.


P.S. On a different but related topic, read an interesting article appearing this month arguing that the assumptions behind Black-Scholes break down in times of catastrophe, which the author argues is rather frequently.



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