CPU Company currently (t = 0) pays a dividend of $2.50 per share on its common stock. Dividends are expected to increase at the rate of $0.25 per share for the next several years. Determine the current value of CPU's common stock to an investor who expects to be able to sell the stock for $35 per share after 3 years, given that the investor requires a 14 percent rate of return on this security.

Question

Quizplus · Accepted Answer

We can use the dividend discount model to calculate the current value of the stock:

D1 = $2.50 + $0.25 = $2.75 (next year's dividend)
D2 = $2.75 + $0.25 = $3.00 (dividend in two years)
D3 = $3.00 + $0.25 = $3.25 (dividend in three years)

Next, we can calculate the expected price of the stock at the end of year 3 using the dividend discount model:

P3 = D4 / (r - g) = $3.50 / (0.14 - 0.25) = -$70.00 (note that the negative value indicates an unrealistic assumption - the growth rate cannot be higher than the required rate of return)

Since the expected price of the stock is unrealistic, we cannot use the dividend discount model to calculate the current value of the stock based on the expected price at the end of year 3. Instead, we can use the formula for the present value of a growing perpetuity to calculate the current value of the stock based on the expected dividends:

PV = D1 / (r - g) = $2.75 / (0.14 - 0.25) = $30.54

Therefore, the current value of CPU's common stock to an investor who expects to be able to sell the stock for $35 per share after 3 years, given that the investor requires a 14 percent rate of return on this security, is $30.54.

CPU Company Currently (T = 0) Pays a Dividend of $2.50