BVR. Free Download. Does Black Scholes Overvalue Early Stage Company Allocations? What It s Worth

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2 Business Valuation Update From the developers of Pratt s Stats Timely news, analysis, and resources for defensible valuations Vol. 16, No. 1, January 2010 Does Black Scholes Overvalue Early Stage Company Allocations? By James Walling and Cindy Moore Valuation practitioners have adopted the Black Scholes Merton option pricing model ( BSOPM ) as a method for allocating the value of a firm amongst the various securities within a firm s capital structure. This adoption has been promoted both by its acceptance even as a preferred method by the auditing community, and by its inclusion in the AICPA practice guide as an example of an acceptable method for allocating value. However, a growing group of practitioners and auditors are acknowledging the model s weaknesses and indentifying a number of cases when its use is not appropriate. A key underlying assumption of the BSOPM is that the distribution of future equity values is log-normally distributed. Understanding this assumption, and the limitations it creates for applying the model, is critical in deciding if the model is appropriate for the facts and circumstances of an allocation calculation. Our recent research into the distribution of exit values in the software, medical device/equipment, and biopharmaceuticals industries suggests that the exit prices are highly skewed toward failure. This data raises questions regarding the frequency of the industry s use of this model. Why the BSOPM works better for public vs. private companies. The BSOPM has several underlying assumptions that are typical of academic finance, including risk free positive drift, no taxes, and, perhaps most importantly, a lognormal distribution for evolving future prices. The model was developed for pricing options on publicly traded firms. At the time the model was developed, the vast majority of options on publicly traded firms had terms of nine months or less. Given that a firm is sufficiently large such that they are public, that they have sufficient trading volume to have options trading, and have a focus on a term of nine months or less, the likelihood of failure is low. Thus, a lognormal expectation of price outcomes, with its probability of failure approaching zero, is a reasonable representation. Contrast this to an early stage, venture-backed software company where failure is the most likely outcome. Further, finance professionals have long known that the BSOPM overvalues options with extended terms and that the model tends to break down for options that are deep in or out of the money. This is a function of both a constant volatility assumption and risk free positive drift. Valuation professionals allocating the equity of early stage companies often use terms of three years or more and, depending on the preferred investor liquidation preferences, these options are often deep out-of-the-money or in-the-money. Early stage company prices. Much early stage pricing (defined for our purposes as the exit value divided by the capital invested, i.e., Gross Value Multiples ( GVM )) has focused in the aggregate to try to contrast the distribution of these prices to that implied by the lognormal distribution assumption underlying the BSOPM. These aggregate studies have shown that a lognormal distribution understates the likelihood of failure as well as the likelihood of a massive success. Some practitioners have resolved this with the justification: well, they should offset each other, so it s still a reasonable representation. BVResources.com

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No one has done the work to figure out just what this impact is, but anecdotal evidence implies that the impact is to overstate common stock values. Further, differing industries may have differing exit value distributions. Consider the medical device industry. A successful exit in this space provides a 4-5x return to investors and a 10x return is considered a homerun. Compare that to the software industry, where a 10x return is a success, but homeruns are measured against the likes of Google or Microsoft. Research and results. To try to measure the degree to which a lognormal distribution is not a representative distribution, we have performed an empirical examination of the returns to equity holders in venture-financed technology and life sciences firms, limiting our analysis to subsectors for software, medical devices/equipment, and biopharmaceuticals. As with most research in this area, getting sufficiently complete data is the greatest challenge. We selected the Dow Jones/VentureSource data set. Our research focused on all exits from January 2001 through January 2008 and defined an exit as an Initial Public Offering (IPO), a merger/acquisition (M&A), or an out-of-business exit. It is important to note that for a significant portion of M&A exits each year, the deal value is not reported. We have excluded these exits from our analysis. Specifically, for software, approximately 35% of the exits were excluded; for biopharmaceuticals, approximately 16% of the exits were excluded; and for medical equipment and device, approximately 18% of the exits were excluded. While we have excluded these due to lack of an exit value, common sense would infer that these are mostly fire sales of assets or companies that most investors are not particularly excited to disclose. Our view is that these would likely materially increase the 0-1x return segment of the exit data. It is also likely that a small percentage of companies in the dataset have missing (unreported) equity financings, or that the amount of the equity Reprinted with permissions from Business Valuation Resources, LLC 2 Business Valuation Update January 2010

4 Figure 1 Exit Volume (# of co.'s) Exit Multiples: Software for Exit Years Exit Years Exit Years Exit Years < < Exit Multiple Figure 2 Figure 3 January 2010 Business Valuation Update 3

5 Figure 4 Figure 5 Figure 6 4 Business Valuation Update January 2010

6 financing is misreported. We have not accounted for this, as we surmise the portion is small enough that it will not materially affect our findings. Figures 1-3 show the distribution of exits based on the actual number of companies. We define an exit as an Initial Public Offering (IPO), a merger/acquisition (M&A), or an out-of-business exit. Exit values are defined as follows: IPO: the Company-Value-at-Exit is the premoney value at IPO. M&A: the Company-Value-at-Exit is the amount the company was acquired for. Out-of-business exit: the Company-Value-at- Exit is zero. Consistent with aggregate industry research, our analysis suggests that the underlying distribution of equity values is highly skewed toward failure for early stage technology and life sciences companies, and, as can be seen, it varies significantly by industry. Figures 4-6 show the distribution of exits as a percent of the sample set, which is more appropriate for comparison against the typical lognormal probability density function. The difference in these distributions, as compared to that implied by a lognormal distribution, is sufficiently pronounced to bring into question the efficacy of using the BSOPM for equity allocation for early stage companies. Equity allocation using the BSOPM for these types of companies may materially over-estimate the optionality in the common shares, and, hence, overstate their value. However, a careful look at the impact at various points on the GVM exits provides some additional insights. Distributions and the Preferred-to-Common Ratio. Standard operating procedure in Silicon Valley startups until the late 1990s maintained a preferred to common ratio of 1:10, (i.e., the common shares were worth ten percent of the preferred share value). What few people know is that this ratio was not established by valuation professionals or even by investors; it was established in the late 1970s by a group of high-powered Silicon Valley lawyers as way of limiting their risk in advising clients it had no economic basis. More recently, anecdotal evidence puts the relationship in the 1:4 to 1:7 range, with instances outside this range not unheard of. But what drives this range and relationship? The distribution of exits is enlightening. Consider the research results. A large volume of exits result in zero return to investors. In such cases the returns to the preferred and common shares are the same, so within this segment the common equals the preferred. Next, consider the segment where returns vary from.1x to 1x, a small segment at seven to fifteen percent of exits. In this segment, the preferred has value but the common does not, as a result of the liquidation preferences. Recall that we have a large number of M&A deals without pricing (35 percent in software!). We would expect most of those deals to reside in this space, where preferred investors are getting some level of return and common receive little, if any. Recent trends in liquidation preferences are expanding this segment to as high as 3x, which increases this segment materially, ranging from 18 to 42 percent. Further, with the majority of preferred shares now including participation rights, once the liquidation preferences are satisfied the preferred shares participate in value accretion with the common stealing value and further disadvantaging the common relative to the preferred. In the 3x and above segment, ranging from eight to twenty seven percent, there is usually sufficient value that the common and preferred will be equal, as the preferred will convert to common and receive more value than by simply taking their liquidation preference. However, the type of exit becomes relevant and participating preferred often double dip in an M&A exit, receiving both their liquidation preference and their participation, while in an IPO, it s an either/or situation. Now consider a lognormal distribution. There are virtually no zero exits. Exit values depend heavily on the current value of the company and the volatility. The high volatilities of these companies, applied over an extended term, push the exit values to the 3x and above range, easily making the common appear of similar value to January 2010 Business Valuation Update 5

7 the preferred, unless the common is materially out-of-the-money at the current valuation. Thus a lognormal distribution minimizes the zero value, common equals preferred segment, but may maximize the 3x+ common equals preferred segment. The relevance of the segment where preferred is superior to common depends on the starting point of the valuation relative to the preference stack. Conclusion Our research shows that the actual distribution of exit prices for early stage companies is materially different than the lognormal distribution underlying the BSOPM model that the industry relies upon. It further shows that exit distributions can vary materially based on industry. Careful consideration of these distributions provides insight into expected preferred to common ratios, and the factors impacting this relationship. These differences may skew the results when BSOPM models are inappropriately applied. Understanding how the future distribution equity values assumption performs when applied to companies at different growth stages and in different industries will help the valuation practitioner to make better informed decisions on allocation model selection and implementation. Cindy Moore joined SVB Analytics as a research director in She brings more than 10 years experience in mathematical modeling and statistical analysis. Moore has worked for Andersen Consulting (Accenture) and the Federal Reserve Bank, as well as for software start-ups in the affinity recommendation, price optimization, and supply chain collaboration sectors. This material, including without limitation to the statistical information herein, is provided for informational purposes only. The material is based in part on information from third-party sources that we believe to be reliable, but which have not been independently verified by us and for this reason we do not represent that the information is accurate or complete. The information should not be viewed as tax, investment, legal, or other advice nor is it to be relied on in making an investment or other decision. You should obtain relevant and specific professional advice before making any investment decision. About the Authors James Walling is the chief operating officer for SVB Analytics, which provides solutions to analytical problems that are specific to emerging growth technology, life science, and venture capital companies. In that regard, SVB Analytics is rendering valuation opinions for clients to help them comply with tax and financial reporting requirements. Walling oversees SVB Analytics valuations services team, which counts more than 1,100 clients to date. 6 Business Valuation Update January 2010