We started the last post by introducing the basic valuation equation. Then, we proceeded to talk about something else entirely known as the Gordon Model. Both equations are shown below for perspective. We will see that the basic valuation equation is derived from the Gordon Model.

(Net) Cash Flow

Look at the numerator of the Gordon Model. We said the CF₁ was the expected cash flow of a business for the coming year. That net cash flow can be defined as follows:

Most business owners don’t think of the earnings of their businesses like this. But this is the (net) cash flow called for by the Gordon Model. Consider the following:

• Many pass-through entities like partnerships, S corporations and limited liability companies (LLCs), don’t even show “corporate” taxes on their income statements. Those taxes are distributed to owners who pay their pro rata share of taxes.
• All business owners are familiar with depreciation, a non-cash charge to earnings that can shelter taxes. They often accelerate depreciation for tax purposes, understating reported earnings in a given year.
• Depreciation, however, is not a “free” expense. Depreciation in the current period relates to historical capital expenditures, or to the recouping of the investments in fixed assets made in prior periods.
• Depreciation is not free, because depleting capital stock must be replaced with current capital expenditures. If a company is growing, it may be necessary to invest in new buildings, machinery and equipment, software, or other fixed assets, and these capital expenditures can lower the net cash flow of a business. Business appraisers and market participants analyze the relationship between depreciation and working capital and their analyses impact their value conclusions.
• If a company is growing, it will also be necessary to invest in working capital items like inventory and accounts receivable, which are called working capital items. Working capital needs can also have an impact on value.

Determining the distributable earnings of a business is a bit more complicated than many business owners think. However, that’s what creates value – i.e., the expected future benefits to be derived from a business. Those future benefits, when earned, can then be distributed or reinvested in the business to facilitate future growth and returns.

Growth and Risk Impact Multiples

At this point, at least conceptually, we know what the earnings are for purposes of Professor Gordon’s model.

We also know something about what the multiple is. Look at the denominator of the equation below:

The multiple for the Gordon Model can be shown by dividing the denominator, which is the result of subtracting the expected growth rate, g, from the discount rate, r, into 1.0. That’s a little bit of algebra, and that’s all we’ll do. The rest is basic arithmetic.

Assume that the discount rate is 15% and the expected growth rate for the long term is 5%. Doing a little math, we can determine that under these assumptions, the multiple, M, is 10x (i.e., 1 / (15% – 5%))

This multiple is like the price/earnings multiple that we read about for public companies and that we see for all public companies on Google, Yahoo, and other financial data sources. That price/earnings multiple, or P/E, is typically applied to trailing 12 month’s earnings for public companies as well as to their expected earnings for the next year (or next 12 months).

Let’s focus on the equation for the multiple for a minute, because it will illustrate some important points:

• Risk impacts the multiple and value. The discount rate, r, has a positive sign in the denominator. That means that if risk goes up, other things being equal, then value goes down. So if the discount rate increased in our example from 15% to 16% and growth stayed the same at 5%, then the multiple would decline from 10.0x to 9.1x, or 9%. It works the other way as well. If risk goes down, other things being equal, then value will rise. If the discount rate declines to 14% from 15%, and growth stays the same, then the multiple rises to 11.1x, or 11.1%. That’s why business appraisers and market participants who buy companies focus on the risks of private companies. And that’s why business owners should focus on reducing controllable risks while they can. That is all part of getting a business READY for sale.
• Expected growth impacts the multiple and value. The growth rate, g, has a negative sign in the denominator. If the growth rate increases, the denominator gets smaller and the multiple rises. That’s why business appraisers and market participants focus on the outlook for growth when they are valuing companies.

The theory lessons are over for now. We have shown that the Gordon Model is the underlying, theoretical foundation for the basic valuation equation, which, once again, is:

So far, we have been talking about an equation that develops indications of the equity value of a business. As we will see shortly, there is another concept of value related to the total capital of a business, i.e., the sum of its equity value and its debt. The owners of a business provide the equity necessary to run a business. Debt providers like banks and other lenders then provide debt capital to help finance businesses with the use of leverage.

We will work our way into these concepts shortly, but next, we will talk about what business owners often think about the value of their businesses – and why it doesn’t matter.

Until next time,

Chris