Size Premium #2: How to incorporate the impact of size into a valuation.

[15 minute read]

[July 2023]

Our first article addressed the merits of adjusting the discount rate to account for a size premium.  We caution against this approach. The justification for a size premium is essentially based on evidence that smaller firms have earned higher returns.  In reality, this empirical evidence is mixed, with measured size premia weakening over time, and many researchers arguing the historical size premium is zero. In any event, the empirical research has a number of issues which affect its relevance for business valuation. These issues are compounded when valuers use a “one size fits all” premium, by applying a common number across all types of valuations. Smaller firms are adversely affected by a number of factors, most notably higher risk, higher transactions costs, lower liquidity and access to finance, and less transparent disclosure. Even if there is a size premium it is still not clear exactly which of these factors it is accounting for…sounds like a black box, with little clarity as to what is exactly being accounted for.

1. Introduction

Expecting discount rate adjustments to handle any perceived gaps in a valuation is unrealistic – it is better to reframe the analysis around a holistic approach to valuation. In this article we outline a framework which assists you to individualise the impact of size on the specific entity being valued. DCF provides the best framework for doing this, with a focus on cash flows, growth, risk and discount rate. The best way to incorporate risk into a valuation is to explicitly account for risk in the cash flows, by using expected cash flows, monte carlo simulation or scenario analysis. This is especially important if there is not complete clarity about what any discount rate adjustment is meant to achieve; for example, if historical size premia are really reflective of transaction costs (which is the prevailing view) then that suggests the additional risk of a smaller firm still needs to be accounted for.

2. Benefits of the valuation process

Rather than simply producing a “number”, a valuation process should give us deeper insights into the business being valued. The process should provide insights into risks and other strategic and commercial elements that will be critical in making an investment decision, or structuring a transaction. Adjusting the discount rate to account for additional risks really just buries any issues. Any discount rate adjustment makes an implicit assumption about a risk profile: so, is it better to bury your assumptions about risk, or make them explicit? This approach involves more work however we need to recognise the broader potential benefits of the valuation process.

Whether this more detailed approach is worth the effort will depend on the circumstances. For a small valuation exercise, it may be sufficient (and commercially justifiable) to use a simple model and industry specific rules of thumb. In addition, if there are trade sales with good quality industry comparables then multiples might be a reliable guide. However, if the valuation is being used as an input into important decisions, such as capital investment, M&A or fundraising, then this process can add considerable value. As the valuer, you will have systematically worked through the value drivers of the business, assessed key risks and the ability of the business to withstand those risks. And you will have a value range that is more transparent and robust. How does that compare to just whacking a number onto the discount rate and thinking “problem solved”?

3. Recommended Approach

Most valuation exercises involve a two pronged approach, using both DCF (which requires a discount rate) and multiples (which requires comparable transactions or trading in comparable listed companies). Our recommended approach builds on this traditional approach. We suggest the following four step framework for those grappling with how to address the impact of size on valuation.

3.1 Complete the base case DCF analysis

Specifically identify the individual elements of business performance that are impacted in the negative, and positive, by smallness and include in forecast cash flows, growth rate and cost of capital.

Most valuation exercises involve a two pronged approach, using both DCF (which requires a discount rate) and multiples (which requires comparable transactions or trading in comparable listed companies). Our recommended approach builds on this traditional approach. We suggest the following four step framework for those grappling with how to address the impact of size on valuation.

Forecast Cash Flows: if you are valuing a Micro or Small company using a discounted cashflow or earnings multiple approach, a valuer should consider what costs and risk factors, which are specific to being a smaller firm, are not present in the forecasts or earnings of the company:

  • If the company’s costs are expected to be higher than for a larger company, due to economies of scale or poor systems or controls, then ensure the higher costs are reflected in earnings.  Most likely, the higher costs are already reflected in the historical earnings of the company.  This point highlights the clear double count possible when valuing small companies – if you have added a small company premium because the company’s costs are expected to be higher, it is clearly double counting that disadvantage if the base for your projections of expected cashflows assumes those higher costs are present.  If you are determined to apply a small company premium in your discount rate to account for the higher costs, you would need to eliminate the impact of size on costs in your projections (somehow);
  • If the company is too small or unreliable to be given credit by suppliers, then model COD terms from suppliers in your DCF;
  • Particularly for tightly held smaller firms, ensure items such as a management salaries and other “related party” transactions are included at market rates;
  • It is not all bad news for small firms. Advantages of small firms which can help profitability include agility, closeness to customer, lower overheads and greater alignment of owners and management. The problem usually relates to scaling these advantages;
  • If the earnings of the company are volatile, then do not select the most recent result as a basis for future maintainable earnings or as a launchpad for a “hockey stick” projection of cashflows.  It may be preferable to study the returns of the company over a longer time period or undertake a Monte Carlo analysis. As we continue to emerge from the covid affected economic environment it is particularly important to consider the appropriate earnings base, as the covid environment may have helped some companies generate an unsustainably high level of earnings, and the reverse for others;

Growth: realistically assess growth prospects for the small firm, and do not assume the usual “hockey stick” projections. Smaller firms will likely be limited by access to finance, resources (often limited by the key person), capacity to absorb risk, and ability to carry longer lead time projects;

Cost of Capital: the WACC of a small company may be expected to be higher than for larger companies, because small companies will generally have a greater proportion of equity, have higher betas than larger companies, and a higher cost of debt. If the company being valued is unable to obtain debt at a reasonable price, then model the unreasonable price in your valuation, or assume there is no debt.

For example, the recent Productivity Commission report[1] on small business found:

  • In 2019, only 15% of SME’s actually applied for debt finance, either because they do not meet bank lending criteria, or they do not need credit;
  • SME’s that do borrow have significantly higher cost of debt than larger enterprises, in the +200 bps vicinity. The graph below shows how borrowing costs vary for small and larger businesses.

Figure 1: Borrowing costs for small and large businesses: 2000 – 2021

Pre-July 2019: Small loans: < $2m; Large loans: > $2m. Post July 2019: Small business: turnover < $50m & Loan < $1m; Medium business: turnover < $50 & Loan > $1m; Large business: turnover > $50m.

Source: Australian Productivity Commission, Small Business Access to Finance: The Evolving lending Market, September 2021.

3.2 Apply risk and resilience lens to your forecasts

Having developed base case projections which incorporate the anticipated impact of smallness, the next step is to address risks to these forecasts, and the ability of the firm to respond to those risks, which we can label with the favourite post covid term of “resilience”. The objective of this analysis is to develop a downside scenario[2] and assess the potential for failure or early termination of the business being valued.

Why should I do this?

If there is a chance that the company will fail, then take account of that probability in your expected cashflows.  If there was a 5% probability of a B rated company (or equivalent non-rated company) defaulting on its debt and presumably failing, there would be a 5% chance that the forecast cashflows of the company are Nil (or negative), with a consequent impact on the long term value of the business.  How often do you specifically recognise the risk of failure or early termination when valuing a smaller business?

Do smaller firms really have a higher chance of failing or early termination?

In a upcoming post we review data on business survival rates, but some key conclusions are:

[a] The Australian Bureau of Statistics August 2022 publication[3] shows:

Unfortunately, the largest revenue bucket in the study is $10m+ , but we can conclude very small businesses have much lower survival rates. Not surprisingly, newer businesses also have higher exit rates, indicating age should be one factor in determining any discount applied to a small business. Variation across industries also implies the need for individual adjustments rather than a common discount factor being applied.

Exiting is not necessarily the same as bankruptcy. Owners may terminate a business by choice (even if not bankrupt the business may not generate sufficient cash flows for the owner), or be acquired or merged.  The paper by Gilbey et al mentioned in our earlier post found that 63% of IPO’s delisted over the period, but only 17.6% delisted due to failure. Particularly for tightly held smaller firms, this type of exit still needs to be considered – rather than bankruptcy being the trigger for early termination, it can simply be a case of insufficient returns, whether compared to the opportunity costs of a wage/salary or alternative investments, or inability to find successor owner/operators.

[b] Looking directly at bankruptcy risk, the Productivity Commission report, cited earlier, reported that small firms consistently have a higher probability of bankruptcy. The probability of default of small firms varies around the 2.0 – 2.5% range, while for large companies it averages around 1%. It also shows this probability can vary over time. This estimate is probably at the lower end, as it measures the risk of firms that can actually borrow from a bank.

Figure 2: Estimates of bankruptcy risks for small and large borrowers

While it is not specified, we would assume that given the general nature of small firm loans this bankruptcy probability can be interpreted as an annual rate.

Source: Australian Productivity Commission, Small Business Access to Finance: the Evolving lending Market, September 2021 https://www.pc.gov.au/research/completed/business-finance

[c] Credit rating default rates. The most recent report by Fitch credit ratings for the period 1990 – 2022[5] shows:

  • BBB non financial firms, the lowest investment grade, had a 10-year cumulative default rate of 2.03% (an annual default rate of close to zero);
  • BB firms, the highest non-investment grade borrowers had a 10 year default rate of 7.62%, an annual rate of 0.8%. All non-investment grade borrowers had a 10 year cumulative default rate of 14.28%, an annual default rate of 1.5%.

On average, smaller firms are more likely to have a lower credit rating. How many of the SME’s that you value would earn an investment grade rating?

This data suggests that early termination is not uncommon, particularly for smaller firms, and that early termination risk varies across industry, with the age of the business and no doubt across individual firms.…not the environment suitable for a “one size fits all” adjustment!  Early termination risk suggests the period for which we would discount forecast cash flows of a smaller business is likely to be shorter than for a larger business.

Developing a risk profile will help you assess the risk of early termination

Having hopefully convinced you that smaller firms have an incrementally higher risk of early termination the next step is to consider how to realistically assess that incremental risk. Developing a risk profile that provides a realistic downside scenario is the goal. That will involve three steps:

[a] Identify and quantify key individual risks for the business.

You should also consider including the costs of mitigating individual risks in the cash flow forecasts. For example, if supply chain issues are a risk, then include the additional cost of having diversified the supplier base, or the cost of holding higher inventories to provide better resilience against disruption. If there is key man risk, include the cost of hiring in professional management. The decision whether to carry the risk or include the mitigation cost involves trade-offs as to costs and benefits, but will affect the level of cash flows and their risk profile – important decisions worthy of consideration.

[b] Develop a scenario that realistically combines key downside risks.

While it is important to account for the individual costs (and benefits) of a smaller enterprise, the fundamental concern about smaller stocks is the higher risk of failure, potentially resulting in forecast cashflows of Nil (or negative). So, having accounted for individual risks, the second step is to take a holistic view of the risk profile of the business (Business Risk Profile) being valued and assess the overall probability of extreme downside risk and the resilience of the business to withstand those risks.

A Business Risk Profile could help you understand the strategic and operational robustness of a business and help you assess the organisation’s ability to respond to sudden shocks. This will be influenced by factors such as profitability, market position, strategy, business model resilience, governance processes, diversification within the business, strength of systems and organisation processes, reliance on key individuals or groups (customers, management or suppliers), etc. The degree of effort is obviously a function of the valuation assignment and could range from pro-forma check lists to financial models.

[c] Financial Resilience

The Financial Risk Profile should assess the financial strength of the business and its ability to withstand sudden shocks. This involves more than just looking at debt levels. It also includes looking at cash balances and access to finance (from banks, business owners and suppliers), etc. The pandemic has provided strong evidence that firms with stronger financial resilience were better able to survive. This risk and resilience profile should be tailored for the business being valued.

The combination of Business Risk Profile and Financial Risk Profile should help you position the business being valued on a risk spectrum and assist in the development of a reasonable downside scenario and a likelihood of early termination. Assigning a notional credit rating may help in quantifying a likelihood of failure. There are a number of methodologies available for this.

Of course, looking past the valuation exercise, it will also help the you identify key points of vulnerability which could be addressed by owners.

3.3 Incorporate risk profile into valuation

You should now have a set of forecasts and WACC that reflect the individual circumstances of your valuation target, and the impact of size. You should also have an idea about the risk to longevity of the business. Incorporating this into a valuation can be completed using an amended DCF style model, Monte Carlo simulation or real options approaches. We examine the first two here.

DCF models usually use single-point forecast data, forecasts that are usually optimistic. Ruback[6] presents an amended DCF model that demonstrates how temporary and permanent downsides can be incorporated into the DCF approach. One version of his model assumes there is a probability of permanent failure each year equal to λ. Should the firm fail then the business is assumed to simply stop generating cash flows. This probability can be estimated for specific firms based on industry and the risk and resilience assessments described earlier. Under this assumption the amended DCF model for a level perpetuity is as follows:

EV is the estimated Enterprise Value and FCF is the forecast Year 1 Free Cash Flow. The version for a perpetuity growing at g% p.a. (not included in Ruback’s article) would be:

Let’s imagine two broadly similar firms except one is “large” and one is “small”. Based on our analysis described above we can specify assumptions for each firm as summarised in the table below:

Table 1: Example application of Ruback valuation model

These relatively reasonable assumptions generate a small firm valuation that is less than 50% of the large firm. Is there a need, therefore, to add a further size premium? We would argue that all the traditional elements of a valuation have been accounted for. Other factors affecting value, such as liquidity and transaction costs may justify an additional discount but this process has hopefully facilitated some transparency about the purpose of any size premium.

Limitations of this model

The Ruback model is simply a formula for valuing a debt cash flow with default risk, so it is reasonably simple and straightforward to apply.  There are, however, some limitations:

  • The perpetuity valuation makes the formula very simple. For non-perpetuity businesses, a more likely scenario for smaller businesses, the value needs to be calculated using slightly less friendly looking models;
  • Secondly, it assumes that the probability of failure is constant over time, which tends to overstate the impact of bankruptcy risk.  In reality, the probability of failure may change over time – the longer a business survives the less likely it is to fail. Declining risk over time would result in smaller impacts. This can be incorporated, but is more complex;
  • It assumes that once a negative cash flow occurs the business stops. More realistic scenarios might have the business continuing on with negative cash flows if owner support is available, or the business might stop before cash flows ever become negative due to lack of investment by the owner;
  • Assumptions about cash flow behaviours are simplistic. Cash flows are either at their forecast level, or zero. While that is improvement over single-point DCF forecasts, they still may not represent realistic cash flow behaviour.

More complex versions of the Ruback model can be developed to include more realistic assumptions but the simple perpetuity version should provide a simple back of the envelope method for cross checking valuations.

A Monte Carlo simulation model offers several advantages – if these benefits to valuation analysis are worth the effort. It allows for greater flexibility for deciding when to stop the business, and can incorporate different assumptions about the behaviour of cash flows. The output of a simulation presents a distribution of potential returns, providing greater insights into the value of the business.

Both approaches allow you to include specific assumptions that address the impact size has on the business being valued rather than relying on ad hoc rules of thumb.

3.4 Triangulate with multiples

Probably the best valuation guide is the valuation multiple of an exactly matching company. Assuming these are not easily available, the next best is to use a comparable group of peers, similar to the process of finding peer betas.  Our discussion has highlighted the impact of industry, stage in life cycle , profitability, growth and risk on value and these should be factored into selection of comparables. That said, it is often difficult to identify genuinely comparable companies for which there is sufficient, appropriate data.

A complementary approach is to attempt to triangulate the valuations from the DCF approach above with market multiples that are available. Attempting to “explain” the multiple by effectively back solving for the implied cash flows should give greater confidence in valuations from both approaches.

4. Practical Application

We have provided the skeleton of a framework for valuing a small business. Upcoming posts will expand on the discussion and include: [i] detailed review of data on business survival and default rates, [ii] a case study demonstrating the application of the default adjusted DCF model and monte carlo simulation, and [iii] further default-adjusted DCF models that incorporate more realistic assumptions, and allow straightforward back of envelope calculations.

While this approach will require additional effort over simply adjusting the discount rate, if you work in specific industries it will be possible to build up benchmark data and inputs.

5. Conclusion

In practice, a size premium is really a “catch all” for a number of factors, such as liquidity, non-diversified shareholder base, key person risks, and other factors. It also is meant to pick up the additional risk inherent in a small business. It is important to distinguish between systematic risk, which is incorporated in CAPM and beta and idiosyncratic risk, which is not picked up by CAPM, and for which there is no real theory about how to incorporate into a discount rate. The absence of a compelling theory on how to adjust the discount rate for idiosyncratic risk is the reason why we need to adjust cash flows for idiosyncratic risk.

When valuing smaller companies it is important to address the impact of size on both discount rate and multiples. Of these two methods, multiples for listed companies or from contemporaneous transactions in genuinely comparable companies will often be the best evidence of value, capturing all the idiosyncratic risks of the business, its growth prospects, size and other relevant factors.  The potential evidentiary impact of such transactions is very high.

If using a DCF approach, it is strongly preferable to use expected cashflows – hopefully we have provided some inspiration on how to think about that.  Moving from the application of a standard rule of thumb to using company specific adjustments will require more effort by the valuer. The analyst needs to focus on identifying: (i) the specific impact of smallness on the individual business, (ii) the probability of adverse outcomes, (iiI) the size of any such outcomes, and (iv) the ability of the business to withstand adversity.We have demonstrated a simple application of these ideas using a perpetuity model.

If all else fails (or project budgetary constraints do not enable sufficient analysis) you may need to adopt an alpha in your discount rate. Even so, the alpha will need to be function of the industry, age, profitability, implied credit rating and size of the business being valued.

We are interested in your feedback – use the comment box below. For example:

What do you think of this approach?

How do you tackle the challenge of smallness in your valuations?

Footnotes

[1] Australian Productivity Commission, Small Business Access to Finance: The Evolving lending Market, September 2021 https://www.pc.gov.au/research/completed/business-finance

[2] At a minimum, or a range of scenarios depending on the nature of the business and importance of the valuation.

[3] ABS Counts of Australian Businesses, including Entry and Exits, July 2022 Reference period. Datacube 1: 8165.0: Counts of Australian Businesses, including entries and exits: June 2018 – June 2022. Tables 19 & 20

[4] For data on individual industries contact the authors by commenting on blog site or DM on LinkedIn.

[5] https://www.fitchratings.com/research/fund-asset-managers/2022-transition-default-studies-29-03-2023

[6] Ruback, Richard S., “Downsides and DCF: Valuing Biased Cash Flow Forecasts”, Journal of Applied Corporate Finance, Volume 23 Number 2.  The paper looks at the ways in which the DCF approach can be adapted to value upwardly biased cash flows, focussing on temporary and permanent omitted downsides.

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