"The retention ratio and the payout ratio are two sides of the same coin" — Aswath Damodaran
In Security Analysis (BSF311) I briefly showed on the whitedboard Prof. Damodaran's calculation of the growth rate in earnings per share when applying the Dividend Discount Model (DDM). It was a bit fast, a perhaps a little confusing. So here it goes again (*). First, state the growth rate g where NI stands for Net Income and ROE stands for Return on Capital:
g = (NIt - NIt-1)/Nt-1
Then use the book value of equity to compute ROE (remember that we use book values when assessing past performance, and market values when valuing assets today):
ROEt = NIt / Equityt <=> NIt = ROEt * Equityt-1 [1] and NIt-1 = ROEt-1 * Equityt-2 [2]
Now let us define Equityt-1 as the sum of Equityt-2 and retained earnings in period t-1 (REt-1):
Equityt-1 = Equityt-2 + REt-1 [3]
We can now re-write [1] using [3]:
NIt = ROEt * Equityt-2 + ROEt * REt-1 [4]
If we assume that the return on equity is unchanged, then ROEt = ROEt-1 = ROE. Therefore we can rewrite [4] as:
NIt = ROEt-1 * Equityt-2 + ROEt-1 * REt-1 [5]
Because the first term of [5] is just NIt-1 as defined in [2], the growth rate is:
g = ROE * (REt-1/NIt-1)
Where (REt-1/NIt-1) is the retention rate. Says Prof. Damodaran: "The growth rate in earnings per share of a firm can be written as the product of two variables—the percentage of the net income retained in the firm to generate future growth (retention ratio) and the return earned on equity in these new investments [...] Firms that have higher retention ratios and earn higher returns on equity should have much higher growth rates in earnings per share than firms that do not share these characteristics".
Stay tuned for more on this from Prof. Damodaran.
(*) Aswath Damodaran. Applied Corporate Finance, Fourth Edition (New York: John Wiley & Sons, 2015), p. 523 and Investment Valuation, Third Edition (New York: John Wiley & Sons, 2012), pp. 285-287.
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