A Single Period Income Capitalization Model to Capitalize EBITDA

In 1989, I wrote an article for Business Valuation Review addressing what I called at the time the Adjusted Capital Asset Pricing Model. I talked about how to build up an equity discount rate and to develop capitalization rates applicable to net income (or net cash flow).

It was the first time, to my knowledge, that a build-up method for developing equity discount rates was published. In that article, I created a range of equity multiples based on ranges of expected risk and growth assumptions and divided the range into four quadrants, just as you will see for EBITDA multiples in this post.

The 1989 ACAPM article received a great deal of attention, and within a couple of months, I was speaking about the topic at valuation conferences around the country. Since then, obviously, many articles and books have been written on developing discount rates.

I have thought about extending the concept of discount rates to pre-tax, total capital measures of income on a number of occasions in the past. In particular, I was interested in developing a single period income capitalization model to capitalize EBITDA, because of the ubiquitous nature of its use by business appraisers, business owners, and market participants.

Recently, I thought of the relationship between depreciation expense, EBIT and EBITDA, and developed what I call the EBITDA Depreciation Factor, or (1 + Depreciation / EBIT).

We discussed this factor in the last post. Now, in this post, we develop what I believe is a credible valuation technique under the single period income capitalization method and under the income approach to valuation. This technique capitalizes EBITDA to achieve indications of Enterprise Value (cash-free and debt-free).

Brief Review

In the last post, we demonstrated how the Capital Asset Pricing Model can be used to build up EBIT and EBITDA multiples. We began by capitalizing Debt-Free Net Income with an after-tax capitalization rate, showing that an equivalent Enterprise Value is obtained by capitalizing EBIT, or Pre-Tax Debt Free Income, with a corresponding pre-tax capitalization rate.

We introduced the EBITDA Depreciation Factor, which is equal to one plus Depreciation divided by EBIT, as the factor which will convert an EBIT multiple into an EBITDA multiple. Next, we developed a range of EBITDA multiples that are in the common rule of thumb range of 4x to 6x or 7x EBITDA. The table summarizing this analysis is reproduced in Figure 1 below.

Figure 1

Now, we examine the development of EBITDA multiples over a broader range of assumptions, specifically focusing on how the valuation triumvirate of expected risk, growth and cash flow impact EBITDA multiples as calculated using the model developed above.

Key Assumptions of the Analysis

Begin with a series of assumptions, which are summarized in Figure 2 below. The numbered lines will focus our attention on each assumption at the outset. The purpose is to develop a range of assumptions that might encompass the expected risk and growth profiles of a large number of closely held and private companies.

Figure 2

The assumptions are generally the same as in Figure 1, but we look at ranges in a different manner.

The cost of pre-tax debt is assumed to be 6.0%, which seems reasonable in today’s lending climate.
The tax rate is a blended federal and state tax rate of 38%.
Again, assume 70% equity in the market value capital structure. This leaves the residual assumption of 30% attributable to debt.
Rather than a range of depreciation factors as above, we have assumed an EBITDA Depreciation Factor of 1.25. We won’t vary this assumption in the analysis. Since you have no perspective on this assumption, let me state that the median EBITDA Depreciation Factor for almost 600 NAICS Code sub-industries (i.e., those with available data) in the Risk Management Association (RMA) 2014-15 database is 1.28. Further, the median EBITDA Depreciation Factor for the non-financial companies of the S&P 500 Index is also 1.28. We will discuss this EBITDA Depreciation Factor in more depth in a later post.
Assumption 5 helps to develop the range of equity discount rates (and corresponding WACCs) used in the analysis.
Similarly, Assumption 6 helps to develop the range of expected growth rates for the analysis.
We assume the highest equity discount rate of 20%, which, with Assumption 5, sets the range used in the analysis.
We also assume the highest expected growth rate of 6.0% for the analysis, which, with Assumption 6, sets the range used.
Assumption 9 is the estimate of normalized EBITDA or $2 million the analyst considers appropriate for use in an income capitalization method.
Total debt is assumed to be $2 million.
Finally, the subject enterprise has $3 million of cash on its balance sheet.

Developing a Range of Implied EBITDA Multiples

With the above assumptions we can, using the technique outlined in the Figure 1 above, calculate a range of implied EBITDA multiples. We can then, with the additional assumptions about cash and debt, calculate estimates of Enterprise Value and the Total Value of Equity for the various sets of assumptions.

The objective is to create the range so that it can reflect the potential valuations of a number of companies with different expected risk and growth characteristics, which we do in Figure 3.

Figure 3

Before beginning a discussion of Figure 3, let me say that it is meant to be representative and is created for discussion only. Neither the table nor any calculations in it are meant to represent the valuation of any entity.

My assumptions or yours might differ, even considerably, in an actual appraisal situation. As with any valuation, there are several key assumptions, and appraisers (or market participants, if they don’t want to overpay) must develop their assumptions carefully in light of facts and circumstances in each situation.

Having set the ranges, we can begin to look at various combinations. The valuation triumvirate is expected cash flow, risk and growth.

In Figure 2 above, expected cash flow is represented by EBITDA of $2.0 million. Assume that this is an indication of normalized EBITDA that reflects the types of adjustments we will discuss in future posts. Once we have determined an EBITDA multiple, we can capitalize it and develop an indication of Enterprise Value.
The equity discount rates and calculated Weighted Average Costs of Capital (WACCs) represent varying degrees of expected risk. Equity discount rates range from 13% to 20%. The corresponding WACCs range from about 10% to 15%. Obviously, a company with an equity discount rate of 13% is a different animal than one with a corresponding discount rate of 20%.
The range of expected growth rates represents varying levels of expectations for the future. The indicated range is from 6.0% down to 2.5%. There is a significant difference in expected growth over this range.
Finally, each EBITDA multiple calculated in the table is based on the assumptions in Figure 2 and calculations as represented in Figure 1.

Focus on one combination to verify how the table works. Look at the intersection of a 17% equity discount rate and a 4.0% expected growth rate. With all the assumptions in Figure 2, this combination implies an Enterprise Value to EBITDA multiple of 5.5x. All of the implied EBITDA multiples in Figure 3 are calculated similarly.

Look at the column in Figure 3 with an equity discount rate of 16%. The calculated multiples range from 5.1x to 7.9x as expected growth rises from 2.5% to 6.0%. Value, as represented by the EBITDA multiples, is positively correlated with expected growth. More rapid expected growth yields higher multiples and higher values, other things being equal.

Look now at the row in Figure 3 with expected growth of 4.0%. The implied EBITDA multiples range from 4.5x where the equity discount rate is 20%, up to 8.0x where the equity discount rate is 13%. Value, as represented by the EBITDA multiple, is inversely correlated with risk. As risk decreases, the EBITDA multiples increase and value increases, other things being equal.

Tradeoffs Between Expected Growth and Risk and the Impact on Value

We have, somewhat arbitrarily, divided Figure 3 into four quadrants. They are called, Quadrants I, II, III, and IV. Clever. There are a lot of numbers in Figure 3. In Figure 4, we show only the ranges of implied multiples and the average multiples for each quadrant.

Figure 4

With fewer numbers in Figure 4, we can, hopefully gain some insight into how EBITDA multiples relate to varying expectations regarding expected risk and growth.

Quadrant I Higher Risk/Lower Growth. Companies in Quadrant I (and having all the assumptions in Figure 3) have equity discount rates ranging from 17% to 20% and expected growth from 2.5% to 4.0%. The EBITDA multiples in the Quadrant I range from 3.9x to 5.5x. The range makes intuitive sense for the risk profiles defined by the quadrant, at least to me. The average of all the multiples in Quadrant I is 4.6x. We calculate the averages only for perspective between quadrants.
Quadrant II Higher Risk/Higher Growth. Companies in Quadrant II have equity discount rates ranging, like Quadrant I, from 17% to 20%, but they are growing more rapidly (from 4.5% to 6.0%). The EBITDA multiples range from 4.7x to 7.1x. While still risky, companies in Quadrant II, because of their more rapid expected growth, are more valuable. Again, this makes intuitive sense. The average EBITDA multiple in Quadrant II is 5.7x, or 24% higher than the average for Quadrant I. For a given level of expected risk, it pays to create expectations for more rapid growth.
Quadrant III Lower Risk/Lower Growth. Companies in Quadrant III exhibit relatively lower risk, but they are expected to grow relatively slowly. The range of discount rates is from 13% to 16%, and expected growth is 2.5% to 4.0%. Implied EBITDA multiples range from 5.1x to 8.0x, with an average of 6.3x. For a given level of expected growth, it pays in terms of higher EBITDA multiples to decrease expectations regarding the risk of a business. The average EBITDA multiple for Quadrant III is 37% higher than the 4.6x average multiple for Quadrant I and more than 10% higher than the 5.7x average multiple for Quadrant II. These calculations suggest that even relatively slow-growing companies can increase value significantly by decreasing risk.
Quadrant IV Higher Growth/Lower Risk. Companies in Quadrant IV are generally attractive in that they have relatively good expectations for growth and lower perceptions of expected risk. Here, the equity discount rates range from 13% to 16% and expected growth ranges from 4.5% to 6.0%. Calculated EBITDA multiples range from 6.3x to 11.8x. The average EBITDA multiple in Quadrant IV is 8.5x. Quadrant IV is the place to be if you can get there, but not too many companies make it.

Many business owners think that the primary way to create value is by increasing earnings. If earnings or cash flow increase, value certainly tends to increase, even at the same valuation multiple.

Figures 3 and 4 suggest two other ways to work on increasing value at any given level of earnings. EBITDA multiples and value can also be increased by working on the other two elements of the valuation triumvirate, expected risk and growth.

Look above at Figure 3 at the intersections of 16% and 17% equity discount rate columns and the expected growth row of 2.5%. The EBITDA multiple at a 17% discount rate is 4.7x while the multiple at a 16% discount rate is 5.1x, or about 9% greater. Business owners can increase value by working to reduce common risks related to concentrations of customers, suppliers, products or other risks. This won’t happen at once, but over time it is always good to be working to reduce risk – increasing value in the process.

Look in Figure 3 at the intersection of a 16% equity discount rate column and the rows for expected growth of 4.0% and 4.5%. The EBITDA multiple where growth is 4.5% is 6.3x, or 5% greater than the multiple of 6.0x where growth is 4%. Other things being equal, increasing expected growth tends to increase multiples and value.

Look again at the multiples we have discussed. The multiple for a 17% equity discount rate and 4% growth is 5.5x, while the multiple for a 16% discount rate and 4.5% growth is 6.3x. Consider a business owner who, over a period of time, increased expected growth a little, from 4% to 4.5% and lowered risk by reducing the discount rate from 17% to 16%. The EBITDA multiple would increase by 14.5%, or from 5.5x to 6.3x. Now that would be a worthwhile increase, and worth a bit of effort.

The real world of market valuation is not necessarily as precise as our examples here. The lesson is nevertheless clear. Business owners should always be working, over time, to move to the right on Figure 3 (by reducing risk) and up, as well (by increasing growth).

Another Look at the Assumptions

Assume with me for a moment that the range of assumptions in Figure 1 is reasonably representative of the risk and expected growth profiles of a large number of private companies. Your assumptions may vary, of course, but let’s consider:

An equity discount rate range of 13% to 20% captures most of the discount rates for companies I have valued for some time. There are exceptions, of course, but most of my client companies have discount rates in this range.
The assumed pre-tax cost of debt is 6.0%. The analysis is not overly sensitive to this assumption, but it appears to be reasonable. An assumed tax rate of 38% is fairly typical. So the resulting range of WACCs that are calculated should be reasonable as well.
Expected growth in the range of 2.5% to 6.0% for long-term growth is a range from expected inflation to some reasonable real growth. Growth rates outside this range capture adverse conditions on the downside and likely expected rapid near-term growth on the upside.
The assumption of 70% equity capitalization and 30% debt capitalization can be tested. For Quadrant I, on average, the implied debt represents 1.4 turns of EBITDA. The comparable EBITDA turn calculations for the remaining quadrants are: II (1.7 turns); III (1.9 turns); and IV (2.5 turns). These calculations vary because we have assumed that EBITDA is a fixed $2 million and with higher multiples, there is greater implied debt in the capital structure for the sets of assumptions that yield higher EBITDA multiples and higher indications of Enterprise Value.
All of these assumptions are necessary to develop value indications by capitalizing Debt-Free Net Income using a WACC and expected growth. The only additional assumption needed to develop EBITDA multiples is the EBITDA Depreciation Factor. I already mentioned that the assumed 1.25 factor is very close to the median multiple for nearly 600 NAICS codes in the Risk Management Association data base and also close to the median EBITDA Depreciation Factor for the non-financial companies in the S&P 500 Index. This suggests that the assumption of an EBITDA Depreciation Factor of 1.25 is reasonable for purposes of our analysis.

The assumptions are reasonable, in my opinion, for discussion purposes and for the limited inferences we have drawn thus far.

Developing Enterprise Value and Total Value of Equity

We can now illustrate how the model outlined in the figures above can be used to develop indications of Enterprise Value and Total Value of Equity under a specific assumption set. We will use the same basic assumptions as above, but make the further assumption we are valuing a specific company. The assumptions are shown in Figure 5.

Figure 5

Assume that the relevant discount rate for our sample is on the order of 16.5%. The highest equity discount rate is set at 17.0%, and the decrement is set at 0.50%, setting a range of equity discount rates between 16% and 17% (and corresponding WACCs between 12.3% and 13.0%). The highest long-term growth rate is set at 5.0%, because our sample enterprise has growth expectations on the order of 4% to 5%. The decrement in growth rate is set, like above at 0.50%.

In Figure 6 below, we will calculate the implied EBITDA multiples for a much smaller range of assumptions based on the hypothetical analysis for the sample enterprise.

Figure 6

Walking through Figure 6, we can develop value conclusions for Enterprise Value. Taking into account debt and excess assets (cash), we can then derive Total Equity Value.

The assumptions center on an equity discount rate of 16.5% and expected growth of 4.5%. The implied EBITDA multiple is 6.1x. This is found in the upper left portion of Figure 6. Normalized EBITDA for a single period income capitalization is assumed to be $2 million.
In the upper right portion of the figure, we see that the result of applying the 6.1x EBITDA multiple to $2 million of EBITDA yields an Enterprise Value of $12.15 million (rounded).
The resulting Total Equity Value is $13.15 million after subtracting the assumed $2 million of debt and adding the $3 million of cash.

What we have just accomplished is to develop credible indications of Enterprise Value and Total Value of Equity for a sample enterprise by employing the generally accepted single period income capitalization method and a technique that capitalizes EBITDA.

Wrap-Up

I hope you enjoy reading about this new (?) valuation technique. If it is out there, I haven’t seen it. If anyone can refer me to where the idea has been published before, I would appreciate it.

Feel free to comment on the post or to me directly at mercerc@mercercapital.com.

For the rest of this week, we will tackle normalizing adjustments in two posts. Then, we will address the EBITDA Depreciation Factor and provide the perspective of market evidence regarding this new factor. As you will see, it varies between companies, like with Exxon Mobil and Apple, and across industries.

In the meantime, be well!

Chris