Question

ABC, Inc. just paid its annual dividend yesterday of $9 per share, and it is widely expected that the dividend will increase by 5% per year indefinitely. If the discount rate is 12%, what price should the stock sell at? A. $134.00 B. $135.00 C. $136.00 D. $137.00 E. None of the above

Answer 1

Option (B) is correct

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 = 12% and g is the growth rate = 5%

First we will calculate next years' dividend. Dividend will grow at the rate of 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 current years' dividend = $9, r is the rate of interest = Growth rate = 5% and n is 1 years

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

FV = $9 * (1 + 5%)1

FV = $9 * (1 + 0.05)

FV = $9 * 1.05

FV = $9.45

So, value of D1 is $9.45

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

Share price = $9.45 / 12% - 5%

Share price = $9.45 / 7%

Share price = $135