Size premium #3: some examples

[5 minute read]

[October 2023]

Introduction

Our previous post outlined a four-step process for incorporating the impact of size into a valuation. The four steps were:

[1] Generate base case DCF model which explicitly incorporates the impact of being small on cash flows, growth rate and Weighted Average Cost of Capital;

[2] Assess downside scenario with an emphasis on assessing risk of failure or early termination;

[3] Complete valuation which incorporates risk of early termination. Possible approaches include a cessation risk-adjusted DCF model developed by Ruback, and Monte Carlo simulation;

[4] Triangulate the DCF approach with comparable multiples, with peers selected on size, industry, stage in life cycle and profitability.

In this post we provide a case study to demonstrate.

Case Study

Let’s assume there is a large global widget producer, Big Widget, with a valuation of $1,000 million, calculated using the Gordon Growth model¹, as follows

Table 1: Valuation of Big Widget

Assume a valuer has been asked to value Sydney Widget.  The valuer identifies Big Widget as a comparable company and develops a discount rate based on its beta and adds a size premium to the cost of equity of 5%.  Here is the valuation, again adopting the Gordon Growth model:

Table 2: Valuation of Sydney Widget using 5% size premium

The valuer has valued Sydney Widget at $10 million, which implies a discount of 54.8%² to the valuation using the Big Widget parameters. There are a few challenges with this valuation:

• An appropriate beta for Sydney Widget is likely to be higher than for Big Widget.  It is therefore not appropriate to add a size premium to a cost of capital derived from significantly larger companies, unless that size premium was derived in the same way;
• Whilst it will depend on the facts of the situation, it may not be reasonable to expect Sydney Widget’s cashflows will increase at the same rate as for Big Widget;
• It is difficult to assess whether the size premium adequately compensates for the perceived additional risks of Sydney Widget.

On further digging, the valuer uncovered two more comparable companies, which are also comparable sizes; Auckland Widget and Melbourne Widget, with betas of 1.3 and 1.1 respectively.  The valuer has now decided to adopt a beta of 1.2 for the valuation of Sydney Widget and a free cash flow growth rate of 1.5%. 

Valuation using adjusted DCF formula

Given the small size of Sydney Widget, the valuer may also perceive that there is a risk, in any given year, of a temporary downside, that the cashflows could be zero perhaps.  For example, the valuer determines that there is a once in ten-year risk that adverse FX rates on imported supplies cannot be recovered from customers.  After reviewing the historical results of Sydney Widget, the valuer determines the risk of a one-off zero outcome in any year, µ_t, to be 10%.  One could now model this risk as a 10% reduction in free cashflows, as the “expected” cashflows³.

Table 3: Valuation of Sydney Widget using comparables and temporary downside

In another scenario, the valuer may consider that Sydney Widget has significantly worse operating leverage than Auckland Widget and Melbourne Widget and, as a result of this, there is an ongoing risk of permanent failure, λ_t, for Sydney Widget, in excess of the risk for the comparable companies.   This risk impacts both the denominator and the numerator of the Gordon Growth model, as set out in the paper by Richard Ruback discussed in our previous post.  This model assumes the business ceases to operate whenever the cash flow in any year is negative, and so can be labelled as a cessation risk-adjusted DCF model⁴. The numerator will be the same as for the example above for temporary downsides, reducing free cashflows by the risk of permanent failure.  The denominator will also be affected, increasing the discount rate by the risk of permanent failure⁵. The outcome of this version of the valuation is:

Table 4: Valuation of Sydney Widget using comparables and permanent downside

The impact of a risk of permanent failure of 5%, in isolation, is broadly equivalent to adding a “size premium” to the overall WACC of 5%, implying a discount of 63% relative to the Big Widget parameters, although it is difficult to know how you could determine 5% was appropriate in advance for the circumstances of this valuation. A 5% risk of permanent failure in any year implies a four-year survival rate of 81.5% and a ten year survival rate of 60%⁶.

In the tables above we have shown the FCF/EBITDA multiples (used for convenience, you may prefer to calculate EBIT or EBITDA multiples), that will reflect the relative risk, growth and operating leverage of the business being valued.  Multiples implied by trading in comparable listed companies or implied by transactions involving comparable businesses will provide the valuer with an excellent cross check, to the extent to which the comparable businesses share the risk, growth and operating leverage of the Sydney Widget.  Multiples from Melbourne Widget and Auckland Widget may provide great benchmarks (and Big Widget may not).

Valuation using Monte Carlo simulation

Another alternative, where profits and free cashflows are volatile, could be to consider a Monte Carlo approach, as opposed to adopting ‘hockey stick’ projections and trying to tame them with a high discount rate.  In this analysis, we have assumed free cashflows follow a random walk with a standard deviation of $0.40 around the base case free cashflow of $0.72 (perhaps determined by an analysis of historical results of Sydney Widget and the truly comparable companies) and a WACC of 8.33%.  The business is assumed to fail if and when cashflows are negative in any year (solvency test).  In this case the terminal value has been based on the average of the projections for years 6 to 10 of the explicit valuation period (assuming the business is not assumed to have failed).  The outcome of one iteration only the Monte Carlo are is follows:

Table 5: Example of one iteration of Monte Carlo simulation

Here is a histogram of the NPV distribution and summary statistics from the Monte Carlo simulation.

Figure 1: Distribution of NPV outcomes of Monte Carlo simulation

Table 6: Summary Statistics for Monte Carlo Simulation

Conclusion

The adoption of specific assumptions can result in values that are very different to those calculated by adding a simple size premium to a discount rate. And there will be differences between a simple cessation risk adjusted DCF model and a Monte Carlo model that allows for a richer (and more complex) set of assumptions and outputs.

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

What approaches do you use?

Which of the above approaches resonate for you?

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Footnotes

1. EV = FCF/(K_e – Growth Rate) ↩︎
2. ($0.72/(6.16% – 3.0%))/(1 + 6.16%)^0.5= $22.12. Then ($22.12 – $10.00)/$22.12 = 54.8% ↩︎
3. EV = FCF(1 – µ_t)/(K_e – Growth Rate) ↩︎
4. The original post had the term ‘default adjusted‘ however cessation risk adjusted is more appropriate. As noted in our earlier posts, smaller businesses may cease to operate simply because the returns may not be sufficient to provide the owner(s) with sufficient income to continue operating the business. This is not default, but it is cessation risk, and the hurdle for the owner is probably before default may happen. ↩︎
5. EV = FCF(1 – λ_t)/(K_e– Growth Rate + λ_t + Growth Rate x λ_t) ↩︎
6. Calculated as (1 – 0.05)⁴ = 0.8145 and (1 – 0.05)¹⁰ = 0.5987 ↩︎