# Equity Allocation Using Option Pricing Method for Privately Held Companies

## With Simple Capital Structure (Part 1)

Today's post is by Upasak Shah, the Co-Founder and Director of Knowcraft Analytics Private Ltd. Mr. Shah has an extensive background with 15+ years’ experience in providing business valuation, and transaction and advisory services for companies spanning technology, life sciences, and various other industries. Mr. Shah has performed valuations for hundreds of privately held businesses and a handful of publicly traded companies for a variety of purposes, including mergers and acquisitions, gift & estate taxes, 409(A) compliance, purchase price allocations, mark to market for large portfolios, embedded derivatives, intellectual property, complex securities, and goodwill impairment.

Mr. Shah has spoken at several webinars for Indian valuation professionals on topics related to business valuation and opportunities for valuation professionals in India, among others. Prior to co-founding Knowcraft, he worked at EXL, where he pioneered transaction advisory and complex security valuation services. He has proven expertise in valuing derivatives and embedded securities using complex models, such as Lattice or Monte Carlo simulations.

In 2019, Mr. Shah was nominated for 40 Under 40 by NACVA. Mr. Shah holds a Master of Commerce degree from Gujarat University, India and a Master of Science degree in Finance from the ICFAI University, India. He is the Director of Academy of Certified Valuators and AnalystsTM (ACVA) — NACVA’s India Chapter focused on nurturing business valuation talent in India.

Mr. Shah can be reached at ushah@knowcraftanalytics.com.

## Complex Capital Structure in a Privately Held Company

High-growth and early-stage companies have access to well-established means of funding from venture capital industry. These investors typically acquire a class of preferred shares with additional or priority rights compared to founders, as their investments are larger and at higher valuations. These rights include features such as liquidation preference, right of first refusal, anti-dilution/down round protection, and information rights, resulting in a complex capital structure. Further, a private company may raise several rounds of funding creating multiple series of preferred shares at different issue prices with rights and preferences that may vary because of the differences in company valuation and circumstances prevailing at the time of funding.(1)

As prescribed in the Practice Aid by AICPA (2), the option pricing method is widely used for equity allocation in privately held companies with multiple classes of stock.

## Option Pricing Model

The option pricing model (“OPM”) relies on financial option theory to allocate value among different classes of members’ equity based upon a “claim” on value on the expected date of exit. Under the OPM, the values of the various classes of shares are estimated as the net value of a series of call options, representing the present value of the expected future returns to the shareholders at a series of exercise prices that coincide with the liquidation and conversion preferences of the holders of preferred and ordinary shareholders.

The popularity of the OPM stems from its ability to avoid complex, subjective assumptions and that it is not limited by a discrete set of scenarios. The need for a limited number of assumptions/inputs and the potential full distribution of possible outcomes covered in an OPM make it suitable for valuing option-like payoffs such as common stock, warrants, and preferred share interests. OPM considers the various rights and preferences mentioned in the stockholder agreements that would affect the distributions to each class of equity upon a liquidity event, including the level of seniority among the classes of equity, dividend policy, conversion ratios, and cash allocations.

Additionally, the method takes into account the impact of the liquidation preference at the future liquidation date rather than at the valuation date, implying a more appropriate method when the liquidity event is not imminent.

OPM calibration may also be used to infer the equity value implied by a recent financing transaction by incorporating assumptions for the expected time to liquidity, volatility, and risk-free rate and then solving for the value of equity such that the value of the most recent financing equals the amount paid. This method, known as the Backsolve method, is most appropriate when financing is an arm’s-length transaction.

## Key Assumptions and Steps in the Application of Option Pricing Model

The OPM involves estimating the value of the call options using either the Black-Scholes option pricing model (“Black-Scholes”) (3) or a or Cox, Ross, Rubinstein binomial option lattice model (“Lattice”) (4), or a risk- neutral Monte Carlo simulation.

Black Scholes is the most commonly used methodology and requires the following inputs:

• Stock Price: This represents the company’s equity value estimated using traditional valuation approaches or the implied equity value computed based on a recent financing round.

• Strike Price: This represents the exercise price based on value inflection points considering the rights and preferences of security classes in a complex capital structure. See below for a detailed explanation.

• Term: This represents the OPM term, which is usually a weighted average term to exit based on successful and unsuccessful, or dissolution scenarios.

• Risk-free Rate: This represents a government bond yield with maturity consistent with the OPM term.

• Volatility: This represents the equity volatility assumption based on publicly listed comparable companies’ data.

• Dividend Rate: This represents the dividend yield of the classes of equity. Typically, no yield is applicable in early-stage companies.

The Black-Scholes formula (excluding dividends) is:

Where:

C0 is the call option value

S0 is the current stock price

X is the exercise or strike price

r is the annualised risk-free interest rate

T is the term to expire

SD is the standard deviation of continuously compounded annual returns of the stock, or volatility

N Is the normal distribution and can be calculated using NORMDIST function in Excel

d1 = ln(S0/X) + (r + SD2/2)T) / (SD * SQRT(T))

d2=d1–(SD*SQRT(T))

N(d1) is the expected percentage increase in stock price if call option has been exercised

N(d2) is the probability of call option being exercised

This model makes certain assumptions:

• No dividends are paid out during the life of the option.

• Markets are random (i.e. market movements cannot be predicted).

• There are no transaction costs in buying the option or taxes, i.e. perfect capital markets.

• The risk-free rate and volatility are constant through the option term and predictable.

• The returns of the underlying asset are normally distributed.

• The option is European and can only be exercised at expiration.

The model assumes that stock prices follow a lognormal distribution because asset prices cannot be negative and are bounded by zero. Impact of the inputs to the option values are summarised in the table below:

A more volatile stock has greater upside potential and greater downside risk relative to a less volatile stock. As such, holding all other assumptions constant, an option on a stock with high volatility has greater value than an option on a stock with low volatility. Since the call option is not exercised until the end of the term, higher the interest rate, higher the interest the call option holder gets on the cash invested in lieu of the asset.

## Key Steps to Perform an OPM Analysis

Consider an early-stage technology company, founded in 2015, with a common share capital of £5 million in the angel round at £1 per share. In 2017, the company received Series A preferred investment of £15 million at a post-money valuation of £50 million, implying a pre-money valuation £35 million and a consequent price per share of £7.00. In 2019, the company received Series B preferred investment of £30 million at a post-money valuation of £100 million, implying a pre-money valuation £70 million and a consequent price per share of £9.80. The two investments have been summarised below, followed by the capitalisation table of the company.

All investors have liquidation preference (“LP”) equivalent to their investment amount. Series B is senior to all other equity holders, and Series A is senior to common. The preferred investment does not accrue any dividend and in the event of a liquidation, dissolution or winding up of the company, can participate in the remaining proceeds after receiving its liquidation preference. Assume that the equity value of this early-stage technology company is £125 million.

• **Step 1: Calculation of Breakpoints: **The call-option value calculations are established at different breakpoints, which are value inflection points representing changes in the allocation of proceeds to the investors in the company’s capital structure (also widely termed as the ‘waterfall distribution’). These breakpoints essentially represent the strike prices as they pertain to Black- Scholes OPM. Each consecutive breakpoint represents an incremental claim on the equity value by a certain class of shareholders triggered by their respective liquidation, participation and/or conversion rights.

**Step 2: Tranche Value:** The value differential between sequential options (also known as tranche) is computed using the call option value for the underlying tranche and the call option for the next tranche.

**Step 3: Allocation of Value: **The proportion in which the incremental equity value between two consecutive breakpoints will be distributed is determined based on the underlying security’s interests in the allocation between the sequential breakpoints. Common shares have value if proceeds from the liquidity event exceed the value of the preferred shares’ liquidation preferences.

**Step 4: Distribution of Tranche Value: **Tranche value is distributed among different classes of shareholders based on their respective distribution proportion as calculated in Step 3.

**Step 5: Determination of Per Share Value: **It is calculated as the aggregate value allocated to each security class in Step 4 divided by the number of shares of the underlying security class.

## Comparison to Current Value Method (“CVM”)

In contrast to an OPM, note below the difference in the per share values concluded using a CVM. CVM is a simple waterfall analysis based on the equity value and outstanding capital structure of the company as of a “current date”. As such, it fails to account for any possible increase or decrease in the value of the company and does not capture the potential exit scenarios and payoffs. CVM is likely to undervalue the Common Stock as it fails to account for the potential upside between the valuation date and exit of the company at a future date.

In a CVM, from the equity value of £125 million, £30 million (Series B LP) is first distributed to Series B based on its seniority, followed by £15 million (Series A LP) to Series A. The remaining £80 million is then distributed among all the three share classes pro rata resulting in the below value per share:

**Part II – Topics to be Covered: **

Types of Preference Shares and Differences to Common Stock.

Equity Allocation using OPM for Privately Held Companies with Preferred Shares that are non- participating and have conversion rights.

Equity Allocation using Probability-Weighted Expected Return Method (“PWERM”).

**Sources:**

1. “A Guide to Venture Capital Term Sheets”, British Private Equity and Venture Capital Association 2. AICPA refers to the American Institute of Certified Public Accountants, a professional organisation for Certified Public Accountants (CPAs) in the United States.

3. Originally created in 1973, the Black‐Scholes option pricing model attempts to calculate the price of an option by considering several key factors, such as the underlying security price, exercise price, expiration date, risk‐free rate, and the standard deviation of a stock’s return. Numerous assumptions underlie Black‐Scholes, including but not limited to, the log‐normal distribution of returns, and static risk‐free rates and volatility. 4. The binomial model was first proposed by Cox, Ross, and Rubinstein in 1979, and essentially uses a “discrete‐time” (lattice based) model of the varying price over time of the underlying financial instrument. In general, such models do not have closed‐form solutions.