Value of Regional Bank's Common Stock

Explanation

In this example, the growth rate of dividends is assumed to remain stable, allowing the use of the Gordon Model. The Gordon Model is also known as the

"constant growth dividend discount model" and takes the following form:

P0 = [D1 / (r - g)]

Where -

P0 = the price of common stock X at time 0

D1 = the expected dividend at t1

r = the required rate of return on equity investments and g = the expected growth rate of dividends.

Since the dividend at t1 is not provided, we must calculate it manually by multiplying the dividend at t0 by (1 + g). This will produce an answer of $0.3857 at t1.

Now that the dividend at t1 has been determined, the given information can be put into the equation provided, leading to the following series of calculations:

P0 = [$0.3857 / (.1375 - .1020)] = $10.86.

When using the Gordon model, remember that the required rate of return "r" must be greater than the expected growth rate "g." Otherwise, the equation will produce a nonsensical answer.