# Grinold-Kroner Model

The Grinold-Kroner model states that the expected return of a stock is its dividend yield, plus the inflation rate, plus the real earnings growth rate, minus the change in stock outstanding, plus changes in the P/E ratio:

• E(Re)≈ D/P + (%ΔE − %ΔS) + %ΔP/E

where:

E(Re) = expected equity return

D/P = dividend yield

%ΔE = expected percentage change in total earnings

%ΔS = expected percentage change in shares outstanding

%ΔP/E = expected percentage change in the P/E ratio

A share repurchase is a reduction in shares outstanding, which means the company buys back shares and pays cash to investors. This cash payment is a form of positive return and increases cash flow to investors, EPS, and expected return (mathematically, a share repurchase is a negative %ΔS term, so subtracting a negative term becomes a positive number).

The variables of the Grinold-Kroner model can be regrouped into three components: the expected income return, the expected nominal growth in earnings, and the expected repricing return.

The expected cash flow return (income return):

• D/P – %ΔS = income return

D/P is the current yield as seen in the constant growth dividend discount model. It is the expected dividend expressed as a percentage of the current price. The Grinold-Kroner model goes a step further in expressing the expected current yield by considering any repurchases or new issues of stock.

The expected nominal earnings growth is the real growth in earnings plus expected inflation:

• expected nominal earnings growth return = %ΔE

The expected repricing return is captured by the expected change in the P/E ratio:

• expected repricing return = %ΔP/E

It is helpful to view the Grinold-Kroner model as the sum of the (1) expected cash flow return, (2) expected nominal earnings growth rate, and (3) expected repricing return.

• E(Re) ≈ (D/P − %ΔS) + %ΔE + %ΔP/E

It is important to understand that the assumptions of the Grinold-Kroner model may lead to irrational results. Because the model assumes an infinite time horizon, it ignores an investor’s time horizon.

Most of the inputs to the Grinold–Kroner model are fairly readily available. Economic growth forecasts can easily be found in investment research publications, reports from such agencies as the IMF, the World Bank, and the OECD, and likely from the analyst firm’s own economists. Data on the rate of share repurchases are less straightforward but are likely to be tracked by sell-side firms and occasionally mentioned in research publications. The big question is how to gauge valuation of the market in order to project changes in the P/E.

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