Direct Derivation of the EBITDA Multiple Did you ever wonder where EBITDA multiples for private companies come from?  Everyone talks about transaction pricing in terms of multiples of EBITDA.  Transactions in many industries for attractive private businesses often occur in the range of 4.0x to 6.0x EBITDA, plus or minus a bit.  Why?  Every business owner should have an idea.

However, in spite of the almost universal references to multiples of EBITDA by market participants and business owners, you cannot find a single textbook that defines these multiples in terms of the valuation triumvirate of expected earnings (cash flow), risk and expected growth (of those earnings).

The closest you will find is an article I wrote recently for the Business Valuation Review of the American Society of Appraisers.

In the last post, we talked about EBITDA and enterprise value, and we used a backdoor method to calculate EBIT and EBITDA multiples (of enterprise value) for the hypothetical ABC Private Company.  The EBIT multiple was 6.66x and the EBITDA multiple was 5.19x.

We calculated those multiples by adding market value of equity (\$10.0 million) and debt (\$1.8 million) to get enterprise value of \$11.8 million.  The EBIT and EBITDA multiples are the result of dividing enterprise value (\$11.8 million) by EBIT (\$1.8 million) and EBITDA (\$2.3 million).

I mentioned that this was a backdoor way to calculate multiples.  In most instances, for example, take your private business (or one of your clients if an adviser),  we don’t know enterprise value to calculate EBTIDA multiples.  Therefore, we want to develop reasonable multiples to determine enterprise value directly.  We do so for ABC Private Company in these steps:

• Develop the equity discount rate for ABC (we assumed 15.0% previously) showing the assumptions necessary to obtain this discount rate.
• Make assumptions about the cost of debt (we assumed 5.67% previously for pre-tax debt cost) and the allocation of the capital structure between equity and debt.  We can calculate 85% equity (\$10.0 million market value of equity divided by \$11.8 million enterprise value), and the debt portion as 15% (100% – 85%) to calculate the WACC, or weighted average cost of capital.
• Develop a debt-free net income (cash flow) capitalization rate by subtracting the expected growth rate of enterprise value from the WACC.
• Convert the debt-free net income cap rate into a pre-tax debt-free cap rate (i.e., EBIT) and calculate an EBIT multiple.  Then, convert the EBIT multiple into an EBITDA multiple using a factor we will discuss.

ABC’s Equity Discount Rate

We develop the equity discount rate for ABC Private Company using what is called the Adjusted Capital Asset Pricing Model (ACAPM).  The following figure shows the development of the ABC equity discount rate, with a brief numbered explanation below it. The Adjusted Capital Asset Pricing Model “builds” a discount rate by adding components of risk to estimate the level of risk that investors would require for investments in private companies.  This example provides a quick overview that is short on detailed explanations but hopefully adequate to illustrate how discount rates are developed in general terms.

1. Long-term Treasury rate.  We begin the “build-up” with a long-term, so-called risk free investment, or the long-term (about 20 years) Treasury rate.  A current rate as we write is about 2.70%.
2. Equity risk premium.  Investors desire a premium in return to riskless (as to principal) Treasuries to invest in private company equity.  The premium begins with the equity risk premium, which is an expectation for a premium return similar to that expected for large capitalization stocks.  This equity risk premium is estimated to be 5.50% at present.
3. Beta.  Beta is a statistic that looks at the volatility of returns.  If a company has a beta of 1.0, it is assumed to have volatility comparable to large capitalization stocks (see #2).  In the case of ABC, the beta is 0.87, so it is expected to be a bit less risky than the market (because of the stable nature of its business relative to the overall economy).
4. Beta-adjusted equity risk premium.  Line #4 is the product of lines #2 and #3.  Since ABC is considered less risky than “the market,” its beta-adjusted equity risk premium is 4.80%, or less than the expected equity risk premium of 5.50% (Line #2)
5. Size premium.  Smaller public companies tend to have higher returns – and higher required returns for investors – than large capitalization stocks.  This size premium is estimated by business appraisers using available information on market returns.  Assume that the appropriate size premium is 6.0%.
6. Specific company risk.  The theory then says that, given that ABC (and lots of private companies) are smaller than even the smaller public companies that helped develop the size premium, appraisers and market participants must estimate the degree of additional risk over smaller public companies necessary for investing in smaller private companies.  We estimate a premium on the order of 1% to 2% and use 1.50% in the example.
7. Equity discount rate.  The sum of Lines #1, #4, #5 and #6 provides the equity discount rate of 15.0%.  This is the dominant return requirement in the valuation of private businesses.

So ABC’s equity discount rate is 15.0%, just like we assumed earlier.  The above illustrates how such discount rates, or required returns, are developed.  For a more detailed discussion of the Adjusted Capital Asset Pricing Model, see my book (with Travis Harms) Business Valuation: An Integrated Theory Second Edition.

ABC’s Weighted Average Cost of Capital (WACC)

We learned earlier that enterprise value is comprised of the market value of equity plus debt.  The WACC is a return concept that looks at the required return for total capital, or for enterprise value.  We show the WACC (and the equity discount rate) in the next figure.  Simplistically, the WACC is the weighted average of returns to equity and to debt based on the capital structure assumption the appraiser makes. Lines #1 to #7 repeat the development of the equity discount rate of 15%.

1. Equity discount rate.  The sum of Lines #1, #4, #5 and #6 provides the equity discount rate of 15.0%.  This is the dominant return since the equity discount rate is higher than the debt rate and the majority of the capital structure in most private companies is comprised of equity.  We assumed 85% equity, so the product of 85% and the 15.0% discount rate is 12.75%.
2. Pre-tax cost of debt.  This cost is assumed to be 5.67% as we discussed earlier.  We make this assumption based on ABC’s actual cost of debt in this case.
3. Tax rate.  The tax rate on corporate earnings is assumed to be 40%.  The tax rate benefit (to get to an after-tax cost of debt) is 2.27%.
4. After-tax cost of debt and the debt/enterprise value assumptions.  The after-tax cost of debt is 3.40% after subtracting the tax benefit from the pre-tax cost of debt.  Given that equity is 85% of the capital structure, the remainder is 15.0% for debt (i.e., 1 – 85%).  The after-tax cost of debt is multiplied by 15% to yield the portion of WACC comprised of the cost of debt (0.51%).
5. Weighted average cost of capital (WACC).  The WACC is the sum of the portion of return required for equity (12.75%) and the portion required for debt (0.51%), or 13.26%.

The WACC is applicable to debt-free earnings (net income or net cash flow) of a business, and can be used to develop enterprise values based on capitalizing debt-free net income/cash flow.

EBITDA (and EBIT) Multiples for ABC

Now that we have developed the WACC for ABC of 13.26%, we can go a couple of steps further and develop multiples of EBITDA using the same Adjusted Capital Asset Pricing Model.  First, recognize that so far, we have used standard valuation theory and practice.  To develop EBITDA multiples for ABC directly, we have to make one additional assumption, which we see below. We again follow the discussion line-by line.

1. WACC. Repeat the WACC of 13.26% from Line #11 above.
2. Long-term growth rate (total capital).  We assumed that the long-term growth rate for equity in the discussion earlier was 5.0%.  If equity, with some assumed leverage, grows at 5.0%, then total capital, which is assumed to have no debt or leverage, must grow somewhat slower.  For our purposes, we have assumed total capital growth of 4.25% (less than the 5.0% we assumed in developing the market value of equity earlier).
3. Debt-free net income (cash flow) capitalization rate.  We subtract the long-term growth rate of 4.25% from the WACC of 13.26% to obtain the debt-free capitalization fate of 9.01%.  We could turn this into a multiple of 11.1x (1 / 9.01%) to capitalize debt-free net income.  However, this concept, while clear theoretically, has less practical relevance because there is virtually no available market evidence of debt-free net income multiples.
4. Tax rate.  The tax rate is again assumed to be 40%.
5. Pre-tax debt-free cap rate.  The pre-tax debt-free cap rate is obtained by dividing the debt-free net income cap rate of 9.01% (Line #14) by (1 minus the tax rate from Line #15).  The result is 15.02%.  Note that the pre-tax debt-free cap rate is precisely the EBIT cap rate.
6. EBIT multiple.  We convert a cap rate into a multiple by dividing it into 1.0.  The EBIT multiple is therefore 6.66x (or 1 / 15.02%).  So how can we convert an EBIT multiple into an EBITDA multiple?
7. EBITDA depreciation factor (EDF).  There is a relationship between EBITDA and EBIT.  In the acronyms, we see that the difference between the two terms is “DA.”  If the sum of (D)epreciation and (A)mortization is greater than zero (and it almost always is), then EBITDA exceeds EBIT by the sum of depreciation and amortization.  We can convert this difference into a factor, which I call the EBITDA depreciation factor, by looking at the ratio of EBITDA to EBIT.  The EBITDA depreciation factor ranges from just over 1.0 for non-capital-intensive companies, to greater than 2.0 for companies in telecom and a few other highly capital intensive industries.  The average EDF for a broad cross section of private companies in many industries was 1.28 in a recent year.  So assume the EBITDA depreciation factor for ABC is 1.28 for purposes of our example.  In a real situation, we would analyze this relationship over a period of years in making this assumption.
8. Implied EBITDA multiple.  The EBITDA multiple is obtained by dividing the EBIT multiple (Line #17) by the EBITDA depreciation factor (Line #18), and is 5.19x for ABC Private Company.

We have now calculated EBIT and EBITDA multiples for ABC Private Company directly.  Note that these multiples are identical to the “back door” calculations in the last post.

Note also that we have calculated these multiples, not indirectly based on known values from a private or public company, but directly, based on the expected cash flows (e.g., EBITDA), risk (WACC) and expected growth.

We can estimate EBITDA multiples in the valuation of private businesses directly based on the same Adjusted Capital Asset Pricing Model appraisers and market participants use routinely.  We just need to make one more assumption about the EBITDA depreciation factor, which is observable for every private company and subject to analysis.

Concluding Thoughts

We have been through a good deal of math and calculations to get to the point of developing the EBITDA multiple for the hypothetical ABC Private Company.  We can do the same thing for any private company.

We can also use this methodology to better understand multiples observed in transactions and why transactional multiples for many private companies tend toward a range of 4.0x to 6.0x in many industries (a bit higher for some industries and a bit lower for other industries).

The answer lies in what I keep calling the valuation triumvirate of expected earnings (cash flow), risk, and expected growth.

We will continue to use this triumvirate to better understand business valuation.  This is not an academic exercise.  Business owners typically have only one business and sell it only one time.  Many buyers of businesses, on the other hand, tend to be serial buyers and have a good deal of experience with real world valuation and transactions.

The purpose of this series, now called the “Handbook on Business Valuation for Business Owners,” is to help level the playing field between inexperienced business owner sellers and experienced corporate and private equity buyers.

Be well,

Chris

Reminder Valuation is important for business owners for many reasons.  One of these reasons is for the operation of buy-sell agreements.  If you are thinking about your buy-sell agreement (and you should be), then take a look at Buy-Sell Agreements for Baby Boomer Business Owners, my Kindle book on the topic.

I’ve priced it at \$2.99 so you won’t have to think about the expense.  So click on the image of the book.  You will be taken to Amazon.  Then buy the book.  Don’t be mislead by the price.  It is a full length book.  If you like it, as most readers have, please take a few minutes and review the book on Amazon!

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