A local bank pays 100% of its earnings out in dividends. If earnings continue to grow at 2% per year and the most recent annual dividend is $0.88. How much would you be willing to pay for this stock if you expect the return on the market portfolio to be 10%, the risk-free rate to be 3%, and the company’s beta to be 0.7?

The maximum price per share that should be paid today is $15.21

Explanation:

We first need to calculate the required rate of return (r) on this stock. The required rate of return can be calculated using the CAPM approach.

r = rRF + Beta * (rM - rRF)

Where,

r = 0.03 + 0.7 * (0.1 - 0.03)   =  0.079 or 7.9%

The fair price per share of this stock can be calculated using the constant growth model of DDM as the earnings, which will all be paid out as dividend, are expected to grow at a constant rate of 2%. The formula for price per share today under this model is,

P0 = D0 * (1+g)  /  (r - g)

P0 = 0.88 * (1+0.02) / (0.079 - 0.02)

P0 = $15.21

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