Using the Option Pricing Model (OPM) to value investments in companies with various share classes

In recent years, unlisted investments have gained significant prominence within the Australian financial sector, attracting heightened attention from regulatory bodies such as the Australian Prudential Regulation Authority (APRA) and the Australian Securities and Investments Commission (ASIC). This increased scrutiny stems from several factors highlighting the importance of robust governance and valuation practices in managing these assets. Unlike listed securities, which benefit from readily available market prices, unlisted investments require complex valuation methods to estimate their fair value. This complexity is due to factors such as varying share classes, differing investor rights, and the lack of observable market transactions.

Unlisted investments, including private equity (PE) and venture capital (VC), play a crucial role in diversifying portfolios and seeking higher returns than traditional listed securities. However, their illiquid nature and valuation complexities require careful oversight to mitigate risks and ensure fair treatment of investors. APRA and ASIC emphasise the need for frequent, accurate, and independent valuations to reflect these investments' true market value and maintain credibility and trust in the valuation outcomes, thereby safeguarding investor interests. This ensures fund managers provide investors with reliable information on asset performance and portfolio liquidity.

In this article, we explore how using the Option Pricing Model (OPM) can assist in understanding the value of unlisted investments. The OPM is particularly useful for valuing companies with multiple share classes and differing rights, as it allows for the allocation of equity value across these different classes based on their specific characteristics, such as liquidation preferences and conversion rights. By treating each share class as an option on the company's equity, the OPM provides a more nuanced and accurate valuation that reflects the unique risk and return profile of each class.

Unlisted investment challenges

The valuation of unlisted investments can be challenging. When there is a recent portfolio company transaction (e.g. a financing round or capital raise) deemed to be at market terms, it’s common practice for PE and VC managers to value their investment at the price indicated by the transaction.

There are instances where this practice leads to incorrect valuations, as we explore below.

Investees with various share classes

It’s common in the PE and VC space for investments in investees to include various share classes and instruments. These classes and instruments, such as ordinary shares, preference shares, convertible notes, and share options, can all have different rights and preferences.

Since fewer than half of venture capital-backed firms either go public or are acquired and the majority either liquidate or become 'living zombies' without a profitable path forward, VCs commonly safeguard themselves and incentivise entrepreneurs through specified rights in financial contracts. These rights include information, control, exit, and cash flow rights aimed at allocating cash flows to shareholders upon an 'exit'.

These varying rights result in distinct classes of shares within a venture's equity structure. Overlooking these distinctions in valuation can have significant implications, including:

Dilution of shares: Investors who are not involved in certain funding rounds must evaluate whether the reduction in their ownership percentage (dilutions) from subsequent investors justifies the assumed increase in the enterprise value reflected in post-money valuations
Mispricing: Pricing all shares proportionally to the enterprise's total value, often seen in 'post-money valuations' released after recent financing rounds, can lead to mispricing 
Ignoring cash flow rights: Crucial for unit pricing and financial reporting purposes, ignoring these differences can result in inflated net asset values reported by funds. While any fair value measurement compliant with International Financial Reporting Standards (IFRS) must account for such cash flow rights, in our experience, it’s common for investors to ignore cash flow rights and rely only on the most recent financing round valuations, i.e. post-money values, when valuing their investments.

An example of ignoring cash flow rights can be viewed within the International Private Equity and Venture Capital Valuation Guidelines from December 2022.

OPM is ideal for companies with complex capital structures (i.e. more than one class of equity securities) and the valuer is attempting to allocate value amongst share classes in the stack.

Using the OPM to value shares with different rights

The OPM is a Black-Scholes-based mathematical model that uses various inputs to calculate the option strike price - the predetermined price at which a specific security may be purchased (call option) or sold (put option) as of a future date.

In the context of a private company’s capital structure, the OPM aims to calculate the fair value of share classes based on the total equity value of a company. A series of future call options representing various share classes, rights and preferences are assigned a tranche of future value based on the current equity value, volatility, estimated time to exit and various features of the company’s equity securities, such as liquidation preferences, and anticipated dividend payouts.

An iteration of the OPM is the ‘OPM backsolve’, or reverse OPM. The OPM backsolve takes the calculation a step further and attempts to quantify the correct equity value through a number of iterations using the most recent issue of preference shares as an anchor. On its surface, it attempts to answer the following question:

What would the total equity value of the company need to be for a marginal or new outside investor to invest on a per share basis, considering the company’s current equity stack, which includes all the existing share classes with their respective seniority, rights and preferences?

The OPM relies on several inputs to assign value to each preferred share class and ordinary shares. These key inputs include:

Equity value: This is estimated either by the most recent valuation of the company (e.g. through a DCF and/or multiples approach) or the OPM backsolve method when a recent funding round has taken place
Time to exit: This is the assumed time until the underlying company has a strategic exit or an IPO
Volatility: Volatility measures how the underlying company would correlate to the overall market based on a similar set of companies in the same or similar industry and, ideally, with similar growth metrics and investment characteristics. The selected volatility needs to be reflective of the estimated volatility over the time to exit (i.e. the investment horizon or holding period)
Risk-free rate: The risk-free rate is often the Australian Government’s bond yield. Consistent with the time to exit and volatility, the risk-free rate assumption must reflect the investment horizon. Often, it’s necessary to interpolate the risk-free rate (generally calculated on a linear basis) assumption so that the interest rate matches the time to exit. Additional information on the risk-free rate can be viewed within our article 'Market valuations: The importance of selecting the ‘risk-free’ rate'.
Dividend assumptions: This is generally nil for venture capital backed companies but does come into play for private equity investments.

The end goal of the OPM is to assign equity value to each share class based on the key inputs discussed above.

So, what are the mechanics of this exercise?

Understanding a breakpoint

A breakpoint refers to the specific equity value threshold at which a particular class of shares begins to receive value in a liquidation scenario. In the context of OPM, breakpoints are used to determine the point at which different share classes, based on their liquidation preferences, rights, and seniority, become ‘in the money’. For example, a senior class of preferred shares will have a lower breakpoint compared to junior shares, meaning they start to capture value earlier as the company’s equity value increases. Each breakpoint effectively delineates the value range where the rights and preferences of a share class have financial significance, influencing the distribution of proceeds in an exit event.

The steps of the exercise explained

First, using a liquidation scenario for each share class in the company’s equity structure or ‘stack’, is assigned a ‘breakpoint’. The breakpoint demonstrates where the share classes would start to have value based on different liquidation or exit scenarios of the underlying company.

This is first performed on the most recent preferred security and continues until all share classes are ‘in the money’ (i.e. the intrinsic value is greater than zero) and ultimately until the last bucket is tipped – where preference shares convert to ordinary shares.

Following this, by employing the Black-Scholes option pricing model, an implied underlying option value (which uses key inputs) is derived for each share class to capture the time value of the securities for the passage of time over the selected time to exit (i.e. holding period).

OPM put into practice

An example of the application of the OPM based on one of our recent PE/VC portfolio valuations is set out below. The facts are as follows:

The client (Client) had an investment in ordinary shares in one of its portfolio companies (Company A)
Company A had previously issued Series A and B preference shares
Company A had recently raised approximately $60.6 million through the issuance of Series C preference shares, giving the Series C investors a shareholding of 36.7 per cent. The implied post-money valuation from the Series C transaction was approximately $165 million (fully diluted), assuming all share classes had equal rights
The Client initially valued its shareholding (ordinary shares) based on a total equity value of $165 million. However, the different share classes have different rights with each new series having more senior liquidation preferences. Hence, on a per share basis, the Series C shares are more valuable than the Series B shares (as the required investor return is lower due to the downside protection), the Series B shares are more valuable than the Series A shares, and the Series A shares are more valuable than the ordinary shares.

We use the OPM backsolve method to estimate the overall value of equity and each share class. In this case, assumptions included a 100 per cent volatility, a time to exit of five years, a risk-free rate of four per cent and a dividend yield of nil. The following outlines the key steps in this process:

Step 1: Calculate breakpoints for each share class - We calculated the ‘breakpoints’ at which each share class would start to receive value in a liquidation scenario. The Series C shares, with the highest liquidation preference, would be first to receive value, followed by Series B, Series A, and finally, the ordinary shares. Each breakpoint is determined based on the liquidation preference multiplier (in this case, all classes of preference shares have a liquidation multiplier of 1.0x, which means that the investor would receive 100 per cent of its investment back before shareholders of lower-ranked securities get anything) and the seniority of each share class
Step 2: Applying the OPM backsolve method – Having determined the valuation assumptions (e.g. volatility) and the breakpoints, we can now estimate the value of 100 per cent of the equity by using the market value information from the Series C preference shares transaction. This is done by performing a goal seek for the overall equity value (or spot price in an option model framework) that results in a value of preference C (Pref C) shares of $60.6 million (this is consistent with the recent price paid for those shares). The same goal seek is also solving the values for all other securities simultaneously.
Step 3: Overall implied equity value and value per instrument - By aggregating the adjusted values for each share class, we derive an implied total equity value of approximately $145 million. This lower valuation reflects that the Series C shares, while valued at $60.6 million (consistent with the price paid in the funding round), are more valuable on a per-share basis due to their seniority. The remaining equity value is distributed across the junior share classes, which receive less value due to their subordinate position in the capital stack.

Based on this exercise, we derived a total implied equity value of approximately $145 million based on the most recent funding round, with the Series C preference shares valued at $60.6 million (consistent with the recent price paid for those shares). Hence, saying that the Company is worth $165 million based on the price paid for the most valuable 36.7 per cent of the shares is not correct and overvalues the Company’s equity by almost 15 per cent.

The difference is even bigger when looking at individual share classes. Valuing the ordinary shares based on a total equity valuation of $165 million and assuming all share classes have the same value per share overvalues the ordinary shares by almost 30 per cent. As outlined in the table below.

$m	Pref C	Pref B	Pref A	Ordinary shares	Upper	Total
Spot price	144.9	144.9	144.9	144.9	144.9
Strike price	0	61	105	129	165
Term (years)	5	5	5	5	5
Risk-free rate (%)	4.0%	4.0%	4.0%	4.0%	4.0%
Volatility (%)	100%	100%	100%	100%	100%
Option value	144.9	124.0	116.0	112.5	108.0
Tranche option value (difference vs junior instrument)	21.0	8.0	3.4	4.5	0.0	36.9
Shareholding (when converted)	36.7%	26.8%	14.4%	22.1%	0.0%	100%
Share of remaining proceeds	39.7	29.0	15.6	23.8	0.0	108.0
Value of instrument	60.6	37.0	19.0	28.3	0.0	144.9

To ensure all investors, whether existing or new to a PE or VC fund, are treated fairly in terms of the valuation of their investments, it’s crucial to understand the instrument you are valuing and how it ranks among other securities. As is the case for investees with various share classes, complex option pricing models can be used to avoid mispricing. OPM can assist in calculating the fair value of share classes based on the total equity value of a company.

How BDO can help

BDO’s valuations team provide a range of valuation services for infrastructure investors, fund managers, private equity investors, and venture capital investors and fund managers. Contact a member of the team to discuss your needs.