Question

A company recently paid a $0.55 dividend. The dividend is expected to grow at a 12.1 percent rate. At a current stock price of $63.45, what return are shareholders expecting? (Do not round intermediate calculations. Round your answer to 2 decimal places. (e.g., 32.16))

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 = 12.1%

First we will calculate next years' dividend. Dividend will grow at the rate of 12.1% 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 = $0.55, r is the rate of interest = 12.1% and n is 1 years

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

FV = $0.55 * (1 + 12.1%)¹

FV = $0.55 * (1 + 0.121)

FV = $0.55 * 1.121

FV = $0.61655

So, value of D1 is $0.61655

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

$63.45 = $0.61655 / k - 12.1%

k - 12.1% = $0.61655 / $63.45

k - 0.121 = 0.0097171

k = 0.0097171 + 0.121

k = 0.1307 or 13.07%

So, required rate of return is 13.07%