### The Gordon Model and Equity-Based Multiples

In the last post, we talked about the basic valuation equation.  This equation is derived from something called the Gordon Model (and a couple of other names).  We said before that valuation is a combination of art and science.  It is time for a bit of the science.

We’ll introduce a few equations in support of the basic valuation equation, so don’t let this bother you.  After we see the “science” underlying this equation and understand a few more things about valuation, we can talk about more interesting questions, like:

How do buyers really value private businesses? and, Where do EBITDA multiples come from? and, Why do some companies command higher EBITDA multiples than others? and, How can I work on my business so that it will command a higher multiple when I am ready to sell it?

The basic valuation equation was stated as:

We briefly discussed this equation and the concept of fair market value in the last post.  Fair market value is important to the valuation of private businesses because most transactions other than outright sales occur at what is called fair market value (for gift and estate tax purposes, many buy-sell agreements, divorce in many jurisdictions, and other).

## The Gordon Model and the Basic Valuation Equation

The basic valuation equation is derived from what is called the Gordon Model, which is also called the Gordon Dividend Discount Model and the Gordon Growth Model.  Professor Myron Gordon published about this model in the 1960s, although the underlying ideas have been around longer.  The Gordon Model for business valuation purposes to determine the market value of equity for a business can be stated as:

The net income (net cash flow) above is expected cash flow for the next period under the Gordon Model.  The net income is also net income after all interest and taxes have been paid.

This net income is capitalized, or divided by, the equity discount rate (r) minus the expected growth rate (into perpetuity), or (g). The equation is often summarized as follows:

In the above equation, the subscript “0” on the V refers to value, today.  The subscript “1” on the CF refers to next period cash flow, or one year after today.  Now that we have shown the subscripts, we will ignore them going forward for simplicity, but we will not forget their meaning.  We can break down the Gordon Model into its components as follows:

Note that the subscript has been omitted for simplicity, but we are still talking about expected cash flow.  The second component of the equation above can be converted into the multiple of the basic earnings equation above.

To make this clear, assume that the equity discount rate (r) is 15% and that the expected long term growth rate (g) is 5%.  We can talk about the reasonableness of these assumptions later.  The equation then can be solved:

This multiple, as noted above, is applicable to the net income (or net cash flow) of businesses, and is the equivalent of the Price/Earnings Multiples (p/e multiples) observed for publicly traded companies.

The denominator of the multiple above is (r – g), which is 10.0%.  We divided that amount into 1 to get the multiple.  The (r – g) figure has a name and it is a capitalization rate for after-tax income.  So 10.0% is the after-tax capitalization rate applicable to ABC.

Now we see the underlying logic of the basic valuation equation.  The market value of equity (MVE) can be stated in general terms as:

The bottom line is that value of the equity of private (and public) businesses is a function, as shown by the Gordon Model above, of three factors:

• Expected cash flow (CF)
• Risk, as reflected in a discount rate that is appropriate for the riskiness of the expected future cash flows (r)
• Expected growth of the cash flows (g)

This triumvirate of expected cash flow, risk and expected growth provides the underpinnings of private and public company valuation.

Assume that the expected net income (or cash flow) of ABC Private Company is \$1.0 million after state and federal taxes (for C corporations) or after state taxes and the pass-through distribution for taxes (for tax pass-through entities like S corporations and limited liability companies).

Using the formula above, the Value of ABC Private Company is \$10.0 million, as seen below:

All this may seem rudimentary, but these basic concepts are important to developing an understanding of private company valuation.

We can carry this example one step further by looking at expected earnings before taxes.  If we eliminate state and federal taxes from net income, we obtain what is called pre-tax income.  Assume for simplicity that the appropriate blended federal and state rate for C corporations and for pass-through entity shareholders is 40%.  Pre-tax earnings can be developed:

So how do we “value” the pre-tax earnings of ABC?  Recall that the discount rate (r or 15%) is applicable to after-tax earnings.  We just grossed up net income to obtain pre-tax income.  We can similarly gross up the after-tax capitalization rate (10.0%, as noted above) to obtain the pre-tax capitalization rate.

If the pre-tax cap rate is 16.67%, the pre-tax multiple is 6.0x (1 / 16.67%).  If the pre-tax multiple is 6.0x and pre-tax income is \$1.67 million, then the value of the equity (MVE) of ABC Private Company is \$10.0 million (\$1.67 million x 6.0).

The value of ABC Private Company is \$10.0 million whether we capitalize net income or pre-tax income.  That makes a lot of sense, because it is the same company either way.  We just had to develop an appropriate valuation multiple to apply to pre-tax income, rather than net income as in the Gordon Model directly.

We have focused on market value of equity (MVE) thus far.  Both net income and pre-tax income reflect the payment of interest expense on corporate borrowings.  Both of these measures reflect earnings to the equity holders of a business.

This discussion is important because it is foundational to developing an understanding of of what are called total capital valuation methods.  Total capital methods look at the earnings streams of businesses from the viewpoint of all stakeholders, including both equity holders and lenders, or holders of debt owed by private (or public companies).

We will soon see that the same basic valuation equation that works for returns to equity holders will also work as we look at the holders of all capital, including debt and equity.

## Where is the Discussion Headed?

In the next posts, we will examine two total capital measures of income, Earnings Before Interest and Taxes (EBIT) and Earnings Before Interest Taxes, Depreciation and Amortization (EBITDA).  We will begin with a summary income statement for ABC Private Company to see these total income measures are derived.

We will also discuss why some analysts and market participants prefer to use total capital measures in their valuations.  For example, business owners and market participants often express private company values in terms of multiples of EBITDA.  So we will want to understand where these multiples come from.

After we have an understanding of the income measures that reflect returns to equity and returns to total capital, we will then look at the equity discount rate (r) to see where it comes from.

We will then look at the discount rate that measures returns to total capital, including equity and debt.  This discount rate is called the Weighted Average Cost of Capital (WACC).

Once we have a better understanding of the equity discount rate (r) and the WACC, we will circle back to the total capital measures of income and see that we can value ABC Private Company (or any private company) based on estimates of total capital earnings measures like EBIT or EBITDA.

## Closing Thoughts

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.  If you like it, as most readers have, please take a few minutes and review the book on Amazon!

In the meantime, be well!

Chris

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