# Dividends and Earnings Retention, Expected Growth and Business Value

### The Earnings Retention Rate Determines Reinvestment Which Determines Growth

Some appraisers seem to think that there is only one long-term expected growth rate, or G, in a single period income/cash flow capitalization for any company.  Nothing could be further from the truth.

Most readers are familiar with what I call the basic valuation equation, or the Gordon Model, which is used to capitalize net income or net cash flow to yield an indication of value of equity.  Here is the model:

Value is expected cash flow, which for now we’ll call CF, capitalized by a discount rate, R, minus an expected growth rate, G.  I’m using capital letters in the text to match up with a table that we’ll see shortly.

What is CF?  Cash flow, or net cash flow, is the portion of the expected net income of a business (after all expenses and all taxes, including corporate taxes) that remains for distribution after all necessary reinvestment is made to support the G in the denominator above.

## Reinvestment Impacts Expected Growth

It seems logical that if a larger portion of net income is reinvested, assuming in productive assets that will yield the discount rate, R, the greater will be the G.  We will show that this is true.  There is an equation for CF that illustrates what we’ve just said symbolically:

CF1 = Net Income x (1 – Earnings Retention Rate)

If expected net income is \$1.00 and the Earnings Retention Rate is 0%, then CF is equal to \$1.00.  In other words, CF equals net income under this assumption, since net income is the beginning point for deriving CF.

What about G?  Some would argue that without reinvestment there can be no growth.  However, this is not true in an inflationary world.  Net income can grow as the result of inflation, which is included in the G‘s employed by appraisers.

## Inflation Influences Growth

For discussion purposes and without proof, assume that the long-term expected inflation rate is 3.0%.  If this is the case, there is a floor long-term G of 3.0%.  But this is the G under the assumption of no reinvestment.  In other words, the Earnings Retention Rate, which is the net reinvestment in a business for a period, is 0%.  We know that owners do reinvest in their businesses.  And we value them accordingly.

## Hypothetical No Reinvestment “Valuation”

Let’s assume that the discount rate for a hypothetical company is 15.0% (R).  Further assume that the inflationary discount rate is 3.0% (3.0%), which is the growth that can be expected based on inflation, productivity and the like.  The capitalization rate (R – G) is therefore 12.0%.

Expected net income (CF) for the business is \$100.  So what is the value of the business?  We determine the value as follows.

The capitalized value of \$100 of net income in our hypothetical business is \$833.3.  That was determined by dividing expected net income (cash flow) of \$100 by the capitalization rate of 12%.

## One Discount Rate But Many Gs

Some appraisers argue that net income should never be capitalized and argue for capitalizing only net cash flow.  We have already seen, however, that net income is net cash flow when the earnings retention rate is equal to zero, so when we capitalize net income, we are, in fact, capitalizing net cash flow.

We started with the statement that some appraisers seem to think there is only one G for a company.  Intuitively, we already know that this is not the case.  If the business we defined above reinvests in productive assets (at the discount rate, R), it should grow faster than inflation.

With limits of productive reinvestment opportunities and owners’ desires for growth, there are potentially many Gs for our hypothetical company – and for any company.  We illustrate this in the following table, which begins in the highlighted first row with a recap of the “valuation” just above.  The value of capitalized net income is \$833.3.

In the first “valuation,” the earnings retention rate was 0% and net income equals net cash flow.   In a hypothetical world with no taxes, investors are indifferent between current income and future growth in income.  Even in a real world with taxes, many owners would prefer to take advantage of growth opportunities and grow their businesses.

## Earnings Retention (Reinvestment) and Value

Look at the second row in the table.  The earnings retention rate is 5.0%.  This means that a net \$5 is reinvested in the business (see the third column).  As opposed to the first row with a \$100 dividend, the owners’ dividend (net cash flow) is only \$95 in the second row.

Why would an owner accept lower dividends?  Because the reinvestment of \$5 is expected to produce more rapid growth than inflation.  In the column labeled “Growth from Earnings Retention” we see that there is additional growth of 0.6%, and in the column labeled G.  We see expected growth of 3.6% as opposed to only 3.0% in the first case.

In the first “valuation” the owners’ expected return was 15.0%, or the discount rate.  It was composed of 3.0% inflationary growth and a 12.0% dividend return (the \$100 dividend divided by the value of \$833.3).

In the next “valuation” with 5% earnings retention, the expected return is a 3.6% return from internal growth and an 11.4% dividend, for the expected return of 15.0%.

So what is the value of the hypothetical business with 5% earnings retention?  It is \$833.3, of course.  How is this determined?

Value = Cash Flow / (R – G)

= \$95.0 / (15.0% – 3.6%)

= \$833.3

The value of the business with 5% earnings retention is precisely the same as the value with 0% earnings retention.  The owners of the business substituted some current return (\$5 reinvested) for expected future growth.  The value of the business is the same, regardless of which strategy is chosen.

## Looking at the Range of Assumptions

Note that as the earnings retention rate is increased in column one, the expected return from reinvestment in the column labeled with G rises from 3.0% (0% earnings retention) to 9.0% (50% earnings retention).  And value remains at \$833.3 for all strategies.  The earnings retention rate determines the rate of reinvestment and the portion of the total expected return of 15.0% (the discount rate, R) that will be received from growth and the portion that will be received in current returns.

So there are lots of potential Gs for the same company, and not just one.  This above analysis is a fairly straightforward illustration of the truth of this statement.  Note that the discount rate remained constant at 15.0%, and that value is \$833.3 for all strategies.

## Concluding Thoughts

This post has focused on the earnings retention rate and its impact on growth.  In many previous posts, we have discussed the concept of dividends and dividend policy.  Dividends represent the portion of earnings that is available for distribution after the payment of all taxes and accounting for all net reinvestment in the business.

The idea for business owners is to get both sides of this balancing act right.  It is good to reinvest for future growth.  It is not good to reinvest in unproductive assets.  This lowers expected returns and postpones current returns in the form of dividends.

If a business has productive reinvestment opportunities, it is good to try to grow through reinvestment.  Reinvestment, as we see, lowers the potential for current returns in favor of future returns gained through growth.

Take your pick.  Current returns or future returns or both.  Your results will be determined by your earnings retention policy and the mirror dividend policy.

Be well,

Chris

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