How to value growth shares

The Black-Scholes method of valuation was initially used as a pricing model for call options on a stock exchange; in essence, valuing the upside potential of a security beyond a hurdle. Today, it is also used to determine the value of growth shares due to the similarities between both mechanisms; if share price does not hit the ‘strike price’ level, there will be no payoff on the options, however, if the share price exceeds the strike price, then the payoff increases linearly.

In simplified terms, the model works by considering future scenarios for business performance, applying a probability weighting to each of those scenarios and then discounting the outcomes to today’s present value. To utilise the model, a valuer requires the following inputs: current share price, the exercise price (the valuation hurdle), the risk-free rate, the expected term (i.e. time before exercise), the volatility, and the dividend yield (if applicable).

People generally get nervous about using the Black-Scholes model for valuing growth shares for a few reasons, including:

• A general fear of the model as it appears confusing and the inputs, outputs, and workings are not intuitive;
• Confusing the calculations for a model which includes versus excludes dividends;
• Not intuitively understanding how a company’s plans for growth relate to the inputs;
• Misunderstanding acceptable levels for inputs; and
• Not knowing the extent to which the valuation ‘answer’ or output is acceptable.

The critical step in valuing growth shares with the Black-Scholes model is to make sure the planned choices around growth connect to commercially justifiable inputs (which may include adapting the formula or structure of the inputs into the model itself) in order to form an answer.

For example, we commonly see the volatility input being poorly appraised. Why? Because, for privately held companies (with non-quoted shares), it can be difficult and subjective to ascertain market value, never mind the volatility of that market value. Errors in the volatility input amplify the error in the Black-Scholes model leading to erroneous or commercially suspect valuation outputs. What this means is that the actual understanding of the different scenarios that may or may not lead to growth in value, and how those different scenarios relate to one another (i.e. it is possible that more than one scenario, or aspects of different scenarios, could occur), is often quite limited, which could subsequently expose the shareholders and company to unexpected risks.

To use the Black-Scholes method effectively, a valuer needs to be able to understand:

• The growth plan and the key drivers of growth;
• The reasoning behind the resultant performance increases in your model and the evidence sitting behind those assumptions;
• The identified challenges to this plan and where other, similar businesses have gone wrong previously;
• Alternative growth scenarios in the event that these challenges are realised; and,
• Finally, taking this all together, they will need to be able to step back and assess what all of this means for the true risk factor to growth.

Only after these questions have been considered and the valuer is comfortable with the inputs, should you be computing the output.

In one sense, a Black-Scholes model can be thought of as a complex DCF. If you don’t have the relevant information for a Black-Scholes calculation, a DCF can be considered with scenario planning covered by an accompanying method – the most robust accompaniment might be a real options analysis.

The real options approach is, simply put, the cost of doing versus not doing something based on assumptions about how a market will operate. The analysis involves both the company and the valuer thinking strategically about the decisions available to the company, and the competition, and then using the outcomes to generate ideas on future performance and, ultimately, overall value. This methodology is particularly relevant for a business where the possible growth scenarios are either completely perverse to one another and/or completely binary (because of events not necessarily under management’s control), or when the business exists in a dynamic market with competition that could create polar opposite outcomes.

A great example of these sorts of market conditions exists for rights-based businesses, such as film, sports, 5G networks, and music rights businesses. Once the outcomes are detailed, a simple DCF remains.

Now, a DCF on the most likely outcome could be considered overly simplistic, therefore, we have the PWERM model. The Probability-Weighted Expected Returns Method is a scenario-based valuation approach primarily used when valuing equity interests in companies with complex capital structures, uncertain future outcomes, or that are early-stage businesses.

To perform a PWERM valuation, a valuer identifies all potential scenarios for the growth shares to reach exercise, and then assigns a probability to each which will be used to calculate the expected return, by multiplying the probability of each scenario with its estimated value. Finally, the expected return must be discounted to present value using an appropriate discount rate (as we do with individual outcomes under the DCF approach).

This method is particularly useful when future maturity events for the growth shares (such as a sale) are expected to create spikes in value, as an option pricing method such as Black-Scholes is inappropriate due to the non-lognormal distributions or variable capital structures.

Making the distinction between lognormal and non-lognormal scenarios is beyond the scope of this article, however, to extend slightly for those who are academically minded: The distinction is important because in some scenarios, value is triggered by an event and is not assumed to grow in value gradually over time. Lognormal scenarios assume that volatility is symmetric, which it rarely is in real terms. Symmetric volatility assumes that the probability of price going up is the same as the probability of price going down. In the case of a startup, it may have a 70% chance of failure and a 30% chance of a big exit, a highly asymmetric scenario. A PWERM model can take into account such likelihoods, whereas the complex mathematics behind a Black-Scholes model may be tripped up by the various exercise outcomes. PWERM models are also ideal for valuing complex shareholder structures, where different shares or options act differently depending on outcomes, as these can be built into the basis of individual scenarios.

The issue for PWERM-based models is where the company or management have no clear exit strategy, and therefore, no meaningful probability-weighted scenarios. Ultimately, PWERM is better for complex, scenario-based situations with a multitude of possible outcomes; otherwise, a DCF or Black-Scholes model may be more appropriate.

For robustness, it can be comforting to undertake multiple approaches (or potentially the same approach with varying input assumptions) and consider if the answers broadly align, or, if they do not, then what the commercial and economic reasons for the difference might be.

Given that at the time of writing, it is not possible to seek statutory clearance for growth shares valuations and that HMRC are quite rightly pursuing cases where growth shares have been undervalued, an additional level of comfort may be desirable.