In How to Value Stocks: A Defense of P/E Ratios and What Drives Earnings Growth, I assumed that the growth in earnings once a company reaches a steady state is the return on incremental equity multiplied by the reinvestment rate (the percentage of earnings not paid out as dividends).
growth = return on incremental equity * reinvestment rate
g = ROIE * b
This post explores that assumption a little more. I conclude that for most or almost all companies it is a reasonable assumption (hence why I used it in those prior two posts) but it is possible in theory for a steady state company to grow earnings without reinvestment by perpetually increasing its return on existing equity.
Background
The dollar growth in earnings (net income, NI) is the difference between this year's earnings and last year's earnings.
$g = NI.t - NI.t-1
The percentage growth in earnings (the growth rate) is the dollar growth divided by last year's earnings.
g = (NI.t - NI.t-1)/NI.t-1
g = NI.t/NI.t-1 - 1
Return on equity is earnings divided by book equity.
ROE = NI/equity
Therefore, earnings equals the ROE * book equity
NI = ROE*equity
In estimating the earnings growth, earnings from the prior year is the total return on on the prior year's equity multiplied by the prior year's equity
NI.t-1 = ROE.t-1*equity.t-1
Likewise, earnings in the new period is the total return on equity on the new amount of equity multiplied by the new amount of equity
NI.t = ROE.t*equity.t
The new equity is the prior year's equity plus any retained earnings from the prior year's earnings.
equity.t = equity.t-1 + RE.t-1
Retained earnings are the amount of last year's earnings that are reinvested
RE.t-1 = NI.t-1 * b
So the new equity can be expressed as
equity.t = equity.t-1 + NI.t-1 * b
So, the net income in the growth period is the total return on equity on the sum of the pre-existing equity plus the additional equity from retained earnings:
NI.t = ROE.t*(equity.t-1 + NI.t-1*b)
The total ROE is weighted average of the return on pre-existing equity, the ROEE, and the return on the incremental equity from retained earnings, the ROIE. So earnings in the growth period can also be expressed as
NI.t = ROEE.t*equity.t-1 + ROIE.t*NI.t-1*b
Recall that the prior year's earnings is the prior year's total return on equity multiplied by the prior year's equity.
NI.t-1 = ROE.t-1*equity.t-1
And earnings growth is this year's earnings divided by last year's earnings, minus 1.
g.t = NI.t/NI.t-1 - 1
Therefore, earnings growth can also be expressed as
g.t = (ROEE.t*equity.t-1 + ROIE.t*NI.t-1*b) / (ROE.t-1*equity.t-1) - 1
g.t = (ROEE.t*equity.t-1) / (ROE.t-1*equity.t-1) + (ROIE.t*NI.t-1*b) / (ROE.t-1*equity.t-1) - 1
g.t = ROEE.t / ROE.t-1 + (ROIE.t*NI.t-1*b) / (ROE.t-1*equity.t-1) - 1
g.t = ROEE.t / ROE.t-1 - 1 + (ROIE.t*NI.t-1*b) / (ROE.t-1*equity.t-1)
Again recall that
NI.t-1 = ROE.t-1*equity.t-1
Therefore
g.t = (ROEE.t / ROE.t-1 - 1) + ROIE.t*b
So, earnings growth equals the change in the return on existing equity, plus the return on incremental equity multiplied by the retention ratio. In other words, a company can grow earnings either by getting more efficient (improving the return on existing equity) or reinvesting at a positive rate of return.
You may now be wondering why I started off this post, and have claimed in other posts, that earnings growth is just equal to the return on incremental equity times the retention ratio.
g = ROIE * b
This is because I have been assuming that a steady-state company has already gotten as efficient as possible. Therefore, the return on existing equity doesn't change and earnings can only be increased through reinvestment.
Is it realistic to assume steady-state companies can no longer increase the efficiency (ROE) of their existing operations?
In my original post on earnings growth, I used the example of a lemonade stand. I pretended each lemonade stand cost $10 to set up and generated $2 in profit each year for an ROE of 20%. Implicit in my analysis was that the existing lemonade stands never got any more profitable. The only way to increase profits is by investing in new lemonade stands, with each new stand increasing profit by $2.
Profit is revenue minus costs. So with the lemonade stand I'm assuming revenue per lemonade stand maxes out at a certain point (in real dollars) and cost per lemonade stand bottom out. While the lemonade stand is a simplified version of reality, I think this assumption is generally pretty reasonable for a steady state firm. Basically, I assume that at a steady state, the opportunity in the firm's existing markets is tapped out (revenues in real dollars can't get any higher, costs in real dollars can't get any lower), so the only way to grow is by expanding the market through reinvestment. Therefore, in general I think it is indeed realistic, as a baseline rule, to assume steady-state companies can't increase the ROE of their existing operations.
A question one could then ask is, what if expanding the market doesn't require any reinvestment? If this were true, earnings could increase (in real dollars) with zero reinvestment (allowing the firm to simultaneously increase real earnings while paying out all earnings as dividends or share repurchases). The steady-state earnings multiple...
payout*(1+g)/(r-g)
… would then be significantly higher because the payout ratio would be 100% instead of say 60% or 80%.
Exceptions to the Rule
One company that can or could possibly increase earnings without reinvestment is Netflix. Recall from my post on Free Cash Flow to Equity that reinvestment is (ignoring non-cash working capital) capex minus depreciation and amortization. For Netflix, capex is its cash spending on content for future periods, and D&A is Netflix's guess of how much it spent on content for the current period. So for Netflix to no longer be reinvesting, its content spend for future periods will have to equal its content spend for the current period -- in other words, its content spend will have to plateau.
Since Netflix is distributed over the internet, it doesn't really have to invest money to reach new customers (unlike the lemonade stand business, which requires building new stands to enter new markets). In addition, customers across the world watch many of the same TV shows and movies. So Netflix's customer count could keep increasing even if Netflix's content costs plateaued and hence Netflix was no longer reinvesting. The increase in customers with no increase in costs would increase net income, and since no earnings would be retained, the prior year book equity would equal the current year book equity and ROE would increase, all without Netflix reinvesting a dime.
So, yes I do think it's possible for companies to increase earnings without reinvestment. The question I would then ask would be -- is the company really in a steady state at that point? For example, with Netflix, is the steady state when they cash content spend equals content amortization? Have they reached a steady state just because earnings are growing without reinvestment?
Personally I would define a steady state as when it's reasonable to assume earnings growth stabilizes at some certain level less than the growth of the economy (since we can't assume than earnings grow bigger than the economy). I think this definition makes sense because the terminal value calculation requires assuming a perpetual growth rate. And then the growth rate has to be lower than the economy, so a steady state is when earnings growth stabilizes at 4% or less. The question with Netflix or any other grow-earnings-with-no-reinvestment company is whether it is possible to grow earnings forever at 4% or so (not just a few years or a decade or two) without reinvesting.
As long as the population in the company's market continues to grow, I think it's possible. For example, if the global population continues to grow forever, then Netflix can increase revenue in real dollars without increasing costs in real dollars and as such increase ROE forever without retaining any earnings.
However, I do think potential infinite economies of scale businesses like Netflix (or, at least what Netflix could be) are the exception to the rule. For most businesses I think it's reasonable to assume steady-state growth requires reinvestment.
Further Reading
https://pages.stern.nyu.edu/~adamodar/New_Home_Page/valquestions/growth.htm