Valuing Venture Companies Using the Black-Scholes Pricing Model
With regard to valuation, much attention is placed on post or pre-money. However, post and pre-money valuations only consider investment size and equity ownership. Venture investments almost always have terms that imply a different value for the company. As the saying goes, “you tell me the price, and I’ll tell you the terms.” An alternative method for valuing early stage companies is an options based approach. This method calculates an implied valuation for the company based on the size and payout structure of a venture capitalist’s investment.
Valuing the payout structure under this method relies heavily on the Black-Scholes option pricing model, which requires specific assumptions with regard to interest rates, investment time horizons, and the volatility of the company’s worth. While these assumptions do create caveats option based valuations, the overall approach is still useful for pricing deal terms. By comparing how implied valuations change with changes to deal terms, we can effectively measure the worth to the investor (or cost to the founder) of featuring those terms in a given deal.
Creating the Model
For the purposes of comparing deal terms, the model is capable of valuing the three most common types of venture investments: preferred, capped participating preferred, and uncapped participating preferred. Each of these payouts are made up of a combination of the following four components:
1. Preferred Debt
2. Participation
3. Participation Cap
4. Equity Conversion
All three payouts have at least the preferred debt and equity conversion components while the uncapped participating preferred payout adds a participating component, and the capped participating preferred payout adds both a participating component and a cap component.
For describing the model creation, consider the following capped participating preferred investment:
· Investment Size: $5mm
· Equity Ownership: 50%
· Liquidity Preference: 3.0x
· Participation Cap (of total investment): 5.0x
Note that these extreme terms would never exist in a real deal!
The payout diagram for this investment is as follows:
The first component to value is the preferred debt portion created by the 3.0x liquidity preference. This is a line with slope = 1 from 0 to $15mm (the value of the $5mm investment * the 3.0x preference) and flat thereafter. The value of this component is the value of the company, less the value of the company after $15mm, which can be replicated with a short call option:
The strike for the call option is the value of the company, and the exercise price (the company value after which it begins to payout) is the liquidity preference, or $15mm. The company value is simply the value, and the call option’s value is derived from the Black-Scholes formula.
The second and third components of this payout are the participation and the participation cap. This payout is a line with a slope = equity ownership % (for each additional increase in company valuation along the x-axis, the investor is paid their ownership % of that increase along the y-axis) up until the total payout to the investor reaches the participation cap. The value of this component is a long call option beginning where the preferred debt component left off, less a short call option beginning where the participation stops:
Both option values (as calculated by the Black-Scholes equation) are multiplied by the slope of the line, which is the equity ownership percentage. For the short call option’s exercise price, or the company value at which the cap is enforced, must be backed out from the cap’s value using the equation in the chart above.
The final component is the equity conversion. This payout is a line with slope = equity ownership % beginning at the value where owning equity is equal to the value of the cap (after which owning equity pays out more than retaining the capped participating preferred shares).
This component’s value is again an option with a strike price equal the company value and an exercise price equal to the company value where the capped participation equals the equity value. This value is multiplied by the equity ownership amount to match the slope of the line.
Putting these components together yields the following equation:
The option implied valuation of the company is the company value, V, that makes the investor’s portfolio of options (the right side of the equation) equal to their investment in the company (the left side of the equation). The critical assumption here is that the investor pays exactly what the options are worth.
Using the model linked above, the option implied post-money value for this company is $7.92mm, which is lower than the $10.00mm post-money valuation derived the traditional way.
Using the Model
As stated above, the value of the company can be solved for by using goal seek to change the value of V, but the equation can also be solved in different ways. For instance, if the company’s value is known, any other deal feature can be solved for.
If an investor believes a company to worth $30mm, and is willing to make a $15mm non-participating preferred investment with a 2.0x liquidity preference, what equity ownership % will they require? Goal seek can be used to solve for a $15mm option portfolio value by changing equity ownership %. As it were, the investor would require roughly a 40% ownership to make this investment. But, what if the investor instead was offering the same $15mm investment, but with participation up to 4.0x of their initial investment? Using goal seek again, the investor would only require a 35% ownership to make the investment. In essence, the model has determined that to gain capped participation, the investor should be willing to give up 5% in equity, or conversely, if the founder would like to negotiate away from capped participation, they should be willing to give the investor 5% more in equity.
Pricing Deal Features with the Model
By making incremental changes to different deal features within the model (i.e. a sensitivity analysis), the different deal features can actually be priced by dollar or equity amount. The following table assumes a similar deal as above: $30mm company valuation and a $15mm investment with a 2.0x liquidation preference and participation up to 4.0x where applicable. The numbers within the table represent the value of the portfolio of options as it changes with equity ownership. Based on the equation derived earlier, the value of the portfolio of options is the amount of money an investor would be willing to invest to own that specific percentage of the company.
This table can be read bi-directionally. As before, the investor should be willing to give up 5% equity for capped participation, and 8% for un-capped participation. If instead, the founder will only part with 32% equity, the investor would offer roughly $1.8mm less (~$15.05mm — $13.23mm) for a preferred investment than they would for an un-capped participating preferred investment.
However, the equity and dollar values of different deal types are not consistent. Conceptually, if the investor is receiving very little equity, the value of participation is diminished because it represents such a small increase over the preferred debt portion of the investment. Similarly, at high equity ownership %’s, the value of participation is diminished because a preferred investment will convert to equity almost immediately after crossing its liquidity preference, which is essentially a participating deal. Put another way, participation with 0% equity is a preferred investment, and a preferred investment with 100% equity is a participation investment. The value of investment types for the table above is outlined below over different levels of equity ownership:
For this specific deal, capped participation is most valuable at roughly a 25% equity stake, and an uncapped participation is most valuable at roughly a 33% equity stake.
Sensitivity analysis can also be used to price other types of deal features such as liquidity preference. Again holding the valuation of the deal at $30mm, the following table shows the value of the portfolio of options across liquidity preference multiples:
Unsurprisingly, the changes in value of deal type at a liquidity preference of 2.0x are the same as the differences in the previous table at 40% equity. As with the first table, this table can also be used bi- directionally to calculate the values of liquidity preferences in terms of dollars, or investment types in terms of liquidity preference. Together, the two tables can be used to calculate the value of liquidity preference in terms of equity ownership. For instance, the drop in value of a preferred deal from a 1.0x step down in liquidity preference is roughly equal to 5% drop in equity ownership %.
Conclusion
Much like the traditional post/pre-money valuation methods, the option based approach for valuing early stage companies has its own caveats. However, unlike traditional methods, the option approach allows for the comparison of different deal types and as a result, allows us to price key deal features. Though negotiating ability can push the terms of a deal in the favor of either investors or founders and non-monetary factors like reputation or fit can influence a deal’s value, the attractiveness of one deal as compared to another from strictly an economic perspective is cut and dry. Hopefully investors and founders alike have access to and understanding of these types of models and can negotiate deal terms on equal footing.
Originally published at www.robbygreer.com
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