Question

Jennifer Davis is interested in buying the stock of Pharoah, Inc., which is increasing its dividends at a constant rate of 9.5 percent. Last year the firm paid a dividend of $2.65. The required rate of return is 17.00 percent. What is the current value of this stock?

Answer 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 = 17% and g is the growth = 9.5%

First we will calculate next years' dividend. Dividend will grow at the rate of 9.5% annually. So we will calculate the D1 by future value formula as per below:

FV = P * (1 + r)10

where, FV = Future value, which is the dividend next year,  P is last years' dividend = $2.65, r is the rate of interest = 9.5% and n is 2 years ( here we will take it as 2 years because we have taken P as dividend of last year. So, while calculating the value of dividend next year, we will take it as 2, meaning current and next year).

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

FV = $2.65 * (1 + 9.5%)2

FV = $2.65 * (1 + 0.095)2

FV = $2.65 * (1.095)2

FV = $2.65 * 1.199025

So, value of D1 is $3.17741625

Now, we will calculate the share price: putting the values in the Gordon Model formula:

Share price = D1 / k -g

putting the values in the above formula,

Share price = $3.17741625 / 17% - 9.5%

Share price = $3.17741625 / 7.5%

Share price = $42.37