Business appraisers and market participants “build” equity discount rates using several versions of the Capital Asset Pricing Model adapted to valuation. The version I use is the Adjusted Capital Asset Pricing Model, as developed in my book, Business Valuation: An Integrated Theory Second Edition (with Travis Harms). Appraisers and market participants employ these “built-up” equity discount rates when using the Gordon Model, where r in the equation below is the equity discount rate, to develop indications of equity value by capitalizing net income or net cash flow.
We then develop what is called the Weighted Average Cost of Capital, as described in a recent post, and employ this next discount rate, or WACC, in the Gordon Model to develop indications of total capital value, i.e., Enterprise Value:
I have exercised my preference to use Enterprise Value rather than Market Value of Total Capital in the equation above. There is no way that this equation can reasonably estimate the amount of cash on any company’s balance sheet. The method reasonably estimates Enterprise Value rather than Market Value of Total Capital.
In the table below, we use the equation immediately above to develop an indication of Enterprise Value. As a reminder, Enterprise Value is the sum of Market Value of Equity plus Market Value of Debt minus Cash (and other non-operating assets). Enterprise Value can be thought of as a total capital value that is both debt-free and cash-free.
The table summarizes the calculations of a fairly standard use of the Gordon Model. Appraisers use the equation to capitalize Debt-Free Net Income or Debt-Free Net Cash Flow.
In the next table, we illustrate that we can capitalize Debt-Free Pre-Tax Income and achieve the same resulting Enterprise Value.
In the right column, we converted DFNI into Pre-Tax Debt-Free Income by dividing DFNI by one minus the assumed tax rate. Then, we convert the DFNI capitalization rate into a Pre-Tax Debt-Free Income capitalization rate by dividing it by one minus the assumed tax rate. The pre-tax multiple is 6.0x, which we multiply by Pre-Tax Debt-Free Income of $1.7 million, yielding the same $10 million value for total capital we obtained using DFNI.
This “proof” may seem trivial, but it is important for what comes next.
The note under the table says: “Pre-Tax DFI = EBIT.” This is true because pre-tax income plus interest expense is Earnings Before Interest and Taxes, or EBIT.
The EBITDA Depreciation Factor and EBIT
In the last post, we introduced the “EBITDA Depreciation Factor,” which is determined by the amount (%) of EBIT that is comprised of depreciation. Depreciation is an expense that is recorded prior to reaching EBIT on the income statement. We obtain EBITDA, or Earnings Before Interest, Taxes, Depreciation and Amortization, by adding depreciation to EBIT. The EBITDA Depreciation Factor, which can be used to deflate an EBIT multiple to an EBITDA multiple is simply:
We can convert an EBIT multiple into an EBITDA multiple as follows:
In the last post, we calculated current EBITDA Depreciation factors for Exxon (1.51) and Apple (1.17). We then derived their respective EBITDA multiples by applying the equation above to their respective EBIT multiples:
EBITDA Multiple for Exxon = 11.0x / 1.51 = 7.3x
EBITDA Multiple for Apple = 11.1x / 1.17 = 9.5x
We confirmed the validity of the calculations by calculating the EBIT and EBITDA multiples for both companies based on current market pricing and financial information. Apple enjoys a higher multiple of EBITDA than does Exxon in part because its lower level of Depreciation in EBITDA creates more non-depreciation cash flow per dollar of sales. For simplicity, we assume for now that depreciation expense will be reinvested in the business to maintain its capital stock.
Building EBITDA Multiples of Enterprise Value
With this background, we can now, using the total capital version of the Gordon Model, build capitalization rates and multiples for EBIT and EBITDA. We do so in the table that follows. We will discuss the various assumptions or calculations, which are found on the numbered rows.
We begin now to develop EBIT and EBITDA multiples.
- Begin with an equity discount rate of 15% in the left column and ranging to 20% in the right column. This range of discount rates is appropriate to a broad range of private companies.
- Assume the pre-tax cost of debt is 6.0%. Some companies may be able to borrow more cheaply now, but we are assuming long-term financing, which tends to be more expensive than short-term or working capital borrowings.
- The assumed tax rate is 38%, which reflects a blended federal and state rate. This shields a portion of the cost of debt (2.3%)
- The calculated after-tax cost of debt it therefore 3.7% (6.0% – 2.3%).
- We have assumed 70% equity in the capital structure. This is in the range of equity capitalization for many private companies having debt.
- The resulting debt capitalization is 30% (1 minus 70% attributed to equity).
- The calculated WACCs range from 11.6% (left column) to 15.1% (right column). WACC is calculated by taking the sum of the weighted after tax costs of equity and debt as developed in an earlier post.
- Assume long-term growth in the range of 4% to 5% and select 4.5% (left column). Assume long-term growth in the range of 3% to 4% and select 3.5% (right column). These assumptions are in a reasonable range for many private companies over the long run.
- Subtract the long-term expected growth rate from the WACC to develop capitalization rates. The selected assumptions yield a range of DFNI capitalization rates of 7.1% to 11.6%.
- Convert the DFNI capitalization rates to Pre-Tax Debt-Free Income capitalization rates ranging from 11.5% to 18.7%. We do so by dividing the after-tax capitalization rates on Line 9 by one minus the assumed tax rate.
- Almost finally, on Line 11, we convert the Pre-Tax Debt-Free Income capitalization rate into EBIT multiples ranging from 5.3x to 8.7x. I have to say that EBIT multiples make more sense to me than do all of the preceding capitalization rates.
- Assume a range of EBITDA Depreciation Factors from 1.20 to 1.30. We will discuss this factor in more detail in a post in the near future, but this range is reasonable in light of available market evidence.
- Finally, we convert the range of EBIT multiples to a range of EBITDA multiples by dividing the assumed EBITDA Depreciation Factors into the EBIT multiples developed on Line 11. The calculated range of EBITDA multiples is 4.1x to 7.3x.
The range of EBITDA multiples developed above of roughly 4x to 7x, encompasses the so-called rule of thumb ranges of 4x to 6x or 7x EBITDA that market participants and business owners throw around, often carelessly. But we do begin to see that there is an understandable valuation rationale for the rules of thumb ranges.
What’s Coming Next
In the next post, we will focus on the valuation triumvirate of expected risk, growth and cash flow to illustrate how we can employ what we have learned thus far in a single income capitalization method where EBITDA is the income measure to be capitalized.
Then, we will examine available market evidence on the EBITDA Depreciation Factor, since this is the only additional assumption needed to move from capitalizing Debt-Free Net Income or Debt-Free Net Cash Flow income measures to capitalizing normalized EBITDA.
Unless the schedule changes, we will then examine the important topic of the normalization of earnings.
In the meantime, be well!