Question

2. The dividend just paid by Seattle Coffee Shops was $2.95 per share. The dividends are anticipated to maintain a growth rate of 6% forever. If the stock currently sells for $64 per share, what is the required return?

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 and g is the growth

First we will calculate next years' dividend (D1). Dividend will grow at the rate of 6% 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 = $2.95, r is the rate of interest = 6% and n is 1 years

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

FV = $2.95 * (1 + 6%)1

FV = $2.95 * (1 + 0.06)

FV = $2.95 * 1.06

FV = $3.127

So, value of D1 is $3.127

Now, we will calculate the required rate of return by the Gordon Model formula as below:

Share price = D1 / k -g

where, Share price = $64, D1 is next years' dividend = $3.127, k is the required rate of return  and g is the growth = 6%

Putting the values in the above formula, we get,

$64 = $3.127 / k - 6%

k - 6%= $3.127 / $64

k - 0.06 = 0.048859375

k = 0.048859375 + 0.06

k = 0.10885 or 10.88%

So, required rate of return is 10.88%