**Earning-Price Ration and the Cost of Equity**

As a general rule, it is not theoretically correct to use the ration of earnings to price as a measure of the cost of equity. The earnings-price ratio (E/P ratio) does not reflect the true expectations of the ordinary shareholders.

For example, if the current market price of a share is 500$ (face value being 100$) and the earning per share is 10$, the E/P ratio will be, 10/500=0.02. Does this mean that the expectation of shareholders is 2%? They would, in fact, expected to receive a stream of dividends and a final price of the share that would result in a return significantly greater than the E/P ratio. Thus, the dividend valuation model gives the most of valid measure of the cost of equity.

There are expectations, however. One expectation that we have already pointed out is the no-growth firms. The cost of equity in the case of no-growth firms is equal to the expected E/P ratio:

**Ke = (DIV1 / Po) + g**

**Ke = (EPS1 (1-b) / Po) + br**

**Ke = EPS1 / Po**

Where b is the earnings retention rate, EPS1 is the expected earnings per share and r is the return investment (equity).

Another situation where the expected earnings-price ration may be used as a measure of the cost of equity is expansion, rather than growth faced by the firm. A firm is said to be expanding, not growing, if the investment opportunities available to it are expected to earn a rate of return equal to the cost of equity.

For example, above equation may be written as follows:

**Po = (EPS1 (1-b))/ (Ke –rb)**

**If r = Ke, then**

**Po = (EPS1 (1-b))/ (Ke –rb) = (EPS1 (1-b) / Ke(1-b)) = EPS1 / Ke**

And solving for Ke, w get

**Ke = EPS1 / Po**

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