Can a discount rate applicable to net cash flow to equity be applied to net income based solely on the assumption that over the long-run, net income and cash flow should be the same?
Someone I know wants to argue this, even though there is no discernible pattern between historical net income and historical cash flow for the subject company being appraised.
There are 52 comments to date, including three from me. The question is obviously controversial. At the outset, the question relates to net income to equity, which may be obvious, but it needs to be stated. Second, the net cash flow referred to is net cash flow to equity, as well. With some edits, I responded to the question.
Does R Change if Using Different Measures of Income to Equity?
The original question from Scott is the long-standing question regarding any so-called difference between the discount rate attributable to net income versus the discount rate attributable to net cash flow. There is one, r, or discount rate for any particular company at any particular time.
In his 1962 finance text, Myron J. Gordon showed the basic discounted cash flow model as follows:
Professor Gordon then showed the equality of the above equation with what has come to be called the Gordon Model.
This identity is discussed in Chapter 1 of my book, Business Valuation: An Integrated Theory Second Edition (with Travis Harms).
The Gordon Model initially dealt with dividends, hence it has been called the Gordon Dividend Model, or the Gordon Growth Model. For the basic discounted cash flow model and the above equation to be equivalent, the following conditions must hold:
- CF1 is the measure of expected cash flow for the next period (sometimes derived as (CF0 x (1 + g)) or otherwise derived specifically).
- Cash flows must grow at the constant rate of g into perpetuity.
- All cash flows must be: 1) distributed to owners; or, 2) reinvested in the enterprise at the discount rate, r.
- The discount rate, r, must be the appropriate discount rate for the selected measure of cash flow, CF.
The answer to the question posed at the outset is developed as follows. The following equation illustrates four equalities using the algebraic framework of the Gordon Model. Three critical insights should be drawn from these equations.
Recall that Earnings are net of depreciation and taxes, with no (net) reinvestment of earnings into the business. Earnings are derived from the core, or existing, business. V0 is constant. We show multiple expressions that indicate the same value for an enterprise. Now consider the following:
- Insight 1. Differences between Earnings and expected cash flow (CF1) are the result of differences in dividend payout policies.
- Insight 2. The expected growth rate, g, varies with the earnings measure employed (i.e., with DPO, or the dividend payout ratio, changes). This should be apparent, because earnings paid out cannot be retained to finance future growth.
- Insight 3. r, the discount rate remains unchanged with the degree of earnings retention or distribution.
We have shown that there are multiple g’s involved in single period capitalization models:
- g(e) is the growth in core earnings. It is associated with the first identity, which capitalizes Earnings.
- g(d) is the expected growth rate associated with a particular dividend, D1.
- And g(cf) is the expected growth rate associated with a particular dividend payout policy, which is to say, with a particular earnings retention or reinvestment policy.
In other words, as the portion of net earnings that is capitalized changes, g must change to retain the equality of V0.
Now focus on the fact that r did not change in any of the equations. In other words, r is the discount rate applicable to expected Earnings, to the expected dividend next period, and to the expected net cash flow of the enterprise. We have a symbolic answer to the frequently asked question: “Does r relate to net income or to net cash flow?” Clearly the answer is yes.
The correct answer to the original questions is that the discount rate does not change with changes in the earnings retention policy. The expected growth rate in Earnings, or the appropriate dividend, is impacted by the retention of earnings. If it were not so, why would anyone retain earnings?
The responses to the original question on the Valuation Group blog are many and varied. Some are confused and others are confusing. There is a formula in the PPC Guide to Valuations (Chapter 5, pp. 5-64 & 5-65) that provides for a conversion of discount rates from ones applicable to net income (based on traditional build-up methods) and ones applicable to net cash flow. This section in the PPC Guide for a number of years referenced an article I wrote for Business Valuation Review (subscription required) in December 1992, “Adjusted Capitalization Rates for the Differences Between Net Income and Net Free Cash Flow.”
In that article, I asserted that no adjustment factor should be applied, but “proved” that such a factor, if any, would be nominal under a relevant range of earnings retention rates.
My thinking has evolved since then, as should the thinking of many of the rest of the profession.
For a full discussion of Scott’s key question about whether r relates to net income or to net cash flow, see Chapter 1 of Business Valuation: An Integrated Theory Second Edition.