Question

1. You think CCLC will pay dividend next year and the first dividend will be $20 a share. You expect GOOG to grow dividend at 9% a year. If your required return for GOOD is 11.3%, what would be the price in 7 years?

2. CCLC will pay an annual dividend of $2 next year. The company just announced that future dividends will be increasing by 8% annually. Would you buy this stock at $42 a share if your required return is 12%?

Answer 1

1. As per Gordon model, share price is given by:

Share price = D1 / k -g

where, D1 is next years' dividend, k is the required rate of return = 11.3% and g is the growth rate = 9%

For calculating the share price 7 years from now, we will amend the formula to below:

Share price (after 7 years) = D8 / k -g

where, D8 is the dividend after 7 years

First we will calculate dividend after 7 years. Dividend will grow at the rate of 9% annually. So we will calculate the D8 by future value formula as per below:

FV = P * (1 + r)⁷

where, FV = Future value, which is the dividend after 8 years,  P is next years' dividend = $20, r is the rate of interest = 11.3% and n is 7 years

Now, putting these values in the above formula, we get,

FV = $20 * (1 + 11.3%)⁷

FV = $20 * (1 + 0.1130)⁷

FV = $20 * (1.113)⁷

FV = $20 * 2.11576

FV = $42.32

So, the value of D8 is $42.32

Now, we will calculate the share price after 7 years by putting the values in the below formula:

Share price (after 7 years) = D8 / k -g

Share price (after 7 years) = $42.32/ 11.3% - 9%

Share price (after 7 years) = $42.32 / 2.3%

Share price (after 7 years) = $1840

2. As per Gordon model, share price is given by:

Share price = D1 / k -g

where, D1 is next years' dividend = $2, k is the required rate of return = 12% and g is the growth rate = 8%

Putting the values in the above formula, we get,

Share price = $2 / 12% - 8%

Share price = $2 / 4%

Share price = $50

As per the Gordon model, share price should be $50. So we can buy this share at $42 as the share is underpriced.