# Option Pricing Model(OPM) for Valuing Early Stage and Venture Backed companies

With regards to valuation, I would like to think that I have been roughly exposed to a few types of valuation methods. This can range from self-learning a 3 statement model along with DCF analysis to determine a stock’s value and determine its potential upside/downside, Company Comparable Analysis(CCA) for relative valuation, to a Black Scholes Model that deals with valuing stock options when i took Financial Economics I/II modules in school. Prior to my internship, through chatting with individuals that are in the valuation space/reading up books in my free time, I have always assumed that a DCF would be the right way(more or less) in valuing start-ups(that are revenue generating) as after all, its has always been the holy grail to identify the fair value of your stock price.

However, upon attending several meetings during my internship and listening to the team bouncing off ideas from their valuation methods, it was a huge shock to me that an option pricing model is actually one of a commonly used valuation methods in the venture capital/private equity space! It didn’t come off intuitively for me as I have always associated Black Scholes/Binomial Pricing models with options, a financial derivative. I was trying to wrap my thoughts around how option pricing valuation can be used for venture capital/private equity — which go against what I have fundamentally learnt in school and what theoretical books have been teaching us. Have Bodie, Kane and Marcus been lying to us all along??

I sought some help from the experienced team that I’m working with into some insights of why such valuation is possible, along with reading some books/articles/research papers during my free time to understand the concept behind it, fundamentally and technically. After all, if I were to understand such a thought process better, I will be in a better footing to listen actively during fair value discussions during meeting and enhance my learning process. With that, after having spent some time dwelling and pondering about the theory and technicals behind it, I believe that I have grasped a good intuition on OPM valuation — Hooray!

# Option Pricing Model — Combing Art with Science

The Option Pricing Model(OPM) combines art with science, providing new insights towards venture valuation. OPM models common and preferred stock as call options on the company’s enterprise value, with claims on future distributable asset depending on the rights and preferences of the company’s preferred stock as opposed to its common stock. In line with the definition of an option — the investor in this context, **is given the right but not an obligation to buy the residual underlying enterprise value at a certain exercise price.** It may not come off as intuitive initially since by going off with a definition of an option, the investor doesn’t have the **‘right’** to purchase the stock or not, since he/she has already **owned** it in the first place. However, what comes off as amazing here is also that if the start up isn’t successful, the ‘option’ will expire without any worth and you forfeit your investment, like how you will follow up with your regular call/put option and not exercise it. Hence, by imagining and placing the art in the science of valuation, the OPM is actually a rather brilliant way to bring valuation into start-ups.

OPM valuation generally falls in 2 categories:

- Black Scholes model
- Binomial price model

While there isn’t a right or wrong way to choose either of the model to conduct a valuation, either method provides a different insight into how an investor wants to conduct his/her own due diligence, which i will cover later in the article. But first, let us clear out the parameters needed since the model requires multiple inputs.

Given the classification of the stocks with respect to prioritisation of rights and preferences, we can dive into the ‘breakpoints’ and calculate the different scenarios respectively.

**Breakpoint 1: Company going bust**

Every breakpoint in a start-up starts off with $0, which is when the company goes bust and there is no residual value in Beany. Both investors of Series A Preferred and Common stock get nothing out of it.**Breakpoint 2: Series A Liquidation Preference, $1 million**

Prior to Common stock shareholders receiving any residual claim on the company, Series A shareholders have a liquidity preference of 1x as stated in the term sheet. For the company to be valued up to $1 million, Series A Preferred stock will have the whole sum of money to be distributed to them, based on priority.**Breakpoint 3: Series A Participation Preferred, $3 million**

The next breakpoint happens as Series A Preferred shares have a 2x participation cap, where the residual claims are divided on*pari-passu*basis till the valuation hits the 2x cap. For the 2x cap to be met, Series A shareholders have to receive their liquidation preference of $1 million along with an addition $1 million to be divided equally, which has to have a further amount of $2 million( split half-half between Series A and Common Stock). With that, the total enterprise value amounts to $3 million.**Breakpoint 4: Common Stock residual claim, $4 million**

The last breakpoint occurs when Series A Preferred shares hit their 2x cap, including their liquidation rights and them also being participation preferred, on till a value when Series A stocks will rather convert into common stock to benefit from a normal*pari-passu*basis. Intuitively, it suggests that that at $4 million onwards, Series A shareholders will conduct the conversion, with residual claims distributed based on the diluted percentages.

Table 2 now shows the different breakpoints involved in the above analysis, breaking down the valuation with respect to the respective breakpoints and what are the residual values for the respective shareholders.

# Option Pricing Valuation Method

With the key parameters being laid out as above, let us move forward into the OPM valuation with an example. Assume that Brown has founded a new autonomous technology(vehicle-related) company Grizz and has recently closed a Series C funding round. One of their Series C investors, 2Ventures, is currently doing their portfolio management due diligence and is updating the current fair value of Grizz. Let us conduct an OPM valuation to check the fair value of different securities involved.

**Step 1: Find out the Enterprise Value**

For FY2020, Brown has provided a form of rough revenue guidance with what the company is presumed to achieve. Moving down the bottom line, Grizz has a rough EBITDA projection of $4 million. Further, by conducting a comparable companies analysis in the autonomous/ride-hailing space with other companies such as Uber, Lyft, etc, the median EV/EBITDA multiple is around 29.3x, giving Grizz an Enterprise Value of $117.2 million, assuming that Grizz has not raised any debt so far.

**Step 2: Analyse the Equity Rights for each class of stock to establish key breakpoints** ***Disclaimer: The values below are ballpark figures that I have formulated at the back of my head and it does not represent what an investor/VC will intend to structure a term sheet associated with such values.**

Table 3 shows how the different classes of stocks are identified in the capital structure for Grizz. Series C Preferred shares take precedence with Liquidation of 1x and a Participation cap of 2x. Series A&B shares then have priority at *pari-passu* basis, with Liquidation of 2x. After all the priorities are cleared out, the remaining distributable rights will proceed to Browns. Additionally, the last nuance here will be that for the Preferred shares, they have the rights to convert their Preferred shares into common stock — which will prove to be useful if valuation proceeds towards the high end as described in the example above.

Table 4 then shows the key identification of different breakpoints at different valuation levels.

- Breakpoint 0: 0 Enterprise Value

Situation occurs if Grizz goes bust and nothing is to be distributed amongst shareholders since there is no residual value. - Breakpoint 1: Series C Liquidation

Series C Preferred shares as per equity rights, will have $12 million to be distributed to them as highest priority. - Breakpoint 2: Series C Participation cap

Series C Preferred shares then joins Series A&B Preferred shares in*pari-passu*basis, till they hit their participation cap of 2x. At the participation cap, Series C Preferred shareholders receive their remaining $12 million, with Series A&B Preferred shareholders receiving a*pari-passu*value of $24 million each. - Breakpoint 3: Series A&B Liquidation

Series A&B Preferred shareholders will receive the remaining bulk of money needed to compensate their liquidation preference, up to $32 million. Also at this point, Series A&B Preferred shareholders have the right to convert their stock in common stock since they will be indifferent between the returns that they will receive at this valuation point moving forward - Breakpoint 4: Series C Conversion

Similar to breakpoint 3, Series C preferred shareholders will rather convert their shares into common stock since they will have their participation cap at 2x, that will prevent them from attaining more returns from a $240 million valuation onward.

**Step 3: Decide between using Black-Scholes model/Binomial option pricing model**

Both models are roughly similar, with Binomial option pricing allowing investors conducting financial modelling to see the different valuations at different time periods, providing more transparency and flexibility. However, it will come across as more complex and time consuming. With the benefits and drawbacks between either model, most analysts are inclined to use the **Black Scholes model.** I will not be going through how the Black Scholes/Binomial model works here as I will assume that one has a rough intuitive idea on the equation and how to use it. However, if you’re interested behind the derivation of Black Scholes/ Numerical pricing — stemming from Ito’s lemma, do contact me and I can walk you through the mathematical theory behind it. Alternatively, you can dig into** Options, Futures and Derivatives, written by John C Hull**. It explains how Ito’s lemma was created through stochastic math — resulting in the formulation of Black Scholes that is now used to price financial derivatives.

**Step 4 : Select key valuation inputs**

As discussed with the parameters above, let us provide certain inputs.

- Enterprise value —
**$117.2 million** - Exercise prices — As identified with given breakpoints
- Term — Investors are looking towards an exit in
**5 years** - Volatility — Using Damodaran’s volatility rates for Software(Systems and Applications) :
**46.03%** - Risk free rate — 5Y Treasury rate of
**0.34%** - Dividend yield — Grizz will
**not**be providing any dividends

**Step 5: Allocate value to the different classes of stock**

Table 5 uses the Black-Scholes formula as derived by Ito’s lemma to deduce the different values of common stock as a call option at each different breakpoint. The incremental value of option as we back track from the final to first breakpoint — will help to allocate value to each equity right accordingly. This will be seen in Tables 6 & 7 below.

With all the allocation settled for different equity rights, we can move on to the last step.

**Step 6: Calculate fair market value of underlying security**

Table 8 shows the final fair value per share which is modelled out by the team in 2Ventures. They have realised that the fair value per share has increased by a healthy 60% margin — at** $10.33/share**. This can keep them assured that Grizz is on the right track and the investment from all shareholders are profitable.

It is to note also that the current fair value per share can be subjected to further discount premiums — for a variety of reasons. One example can be the current COVID pandemic resulted in the autonomous vehicle space to be hit really badly, and this can perhaps lead to investors setting a 20% discount premium on the fair value. This is due to the fact that financial modelling although requires the hard science, is still a form of art after all. The science lays out the fundamentals, with the art bringing about precision on the actual fair value.

# Closing Thoughts

In summary, the OPM has been a backbone in deriving fair value of securities in the PE/VC space, and also often accepted by auditors as it can be audited and tested more efficiently than other allocation models. Further, what is impressive is that the OPM can associate a form of value to the common stock, when it does not have a rough value to begin with other than by going to the last closed financing round.

However, some pitfalls in the model through intuition, is that the future value may not necessarily follow a lognormal distribution, which is what the Black Scholes model mainly weighs its assumption on. As such, the OPM does not capture the very high possibility of failure which tends to be an outlier of a normally distributed function. Furthermore, certain inputs in the Black Scholes model involve them to be constant throughout the lifespan of the option, which may not necessarily hold true (Volatility and interest rates are changing almost everyday — leading to change in the actual valuation).

It was definitely tricky to learn the option price model from scratch by my own but I’m really thankful for my prior knowledge in financial economics, which helped to expedite the learning process. There is huge room for improvement though, such as providing an even more complex setup of equity rights along with guiding the final step of OPM, which is to backsolve the implied equity/enterprise value. I will look into this in the near future and hopefully roll out more content! Also, there has been talk about using PWERM — Probability weighted expected modelling approach, which is also something to consider.

Nevertheless, I hope that you will have learnt something out of this, and I will compile the different materials that I have used to learn this below. The arduous journey to sit down and read these books along with placing the theory into practice has been nothing short of fulfilling!

[1] Options, Futures and Derivatives — John C Hull

[2] A Layperson’s Guide to the Option Pricing Model — Travis W. Harms

[3] Valuing Early Stage and Venture Backed Companies — Neil J Beaton

[4] Global Venture Valuations — IHS Markit

[5] Valuation of Early-Stage Ventures: Option Valuation Models vs. Traditional Approaches — Robert H Keeley

*Originally published at **http://nathanielventureinsights.wordpress.com** on June 19, 2020.*