Question

Suppose Stark Ltd. just issued a dividend of $2.57 per share on its common stock. The company paid dividends of $2.20, $2.31, $2.38, and $2.49 per share in the last four years.

1) If the stock currently sells for $65, what is your best estimate of the company’s cost of equity capital using the arithmetic average growth rate in dividends?

2) What if you use the geometric average growth rate?

Answer 1

Answer:

1)  The company’s cost of equity capital using the arithmetic average growth rate in dividends would be 8.08%

2) If the geometric average growth rate of the dividend was used, the cost of equity capital would be 8.07%

Explanation:

Hi, the formula that we need to use is as follows.

$r(e)=\frac{Do(1+g)}{Price} +g$

Where:

Do = Last dividend

g =growth rate

r(e) = cost of equity

Now, we need to find the average value of "g" in order to answer both questions. First, the arithmetic average.

We need to find the growth rate for every period, we can do that by using the following equation.

$g_{n} =\frac{Dividend_{n} -Dividend_{n-1} }{Dividend_{n-1} }$

So, let´s find out the 4 growth rate for all 5 dividends

$g_{1} =\frac{2.31 -2.20 }{2.20 } =0.05$

$g_{2} =\frac{2.38 -2.31 }{2.31 } =0.0303$

$g_{3} =\frac{2.49 -2.38 }{2.38 } =0.04622$

$g_{4} =\frac{2.57 -2.49 }{2.49 } =0.03213$

Now. we find the arithmetic average.

$g=\frac{0.03213+0.04622+0.03030+0.05000}{4} =0.0397$

So the arithmetic average growth rate is 3.97%

No, let´s find out the cost of equity

$r(e)=\frac{2.57(1+0.0397)}{65} +0.0397=0.0808$

So, the cost of equity r(e) = 8.08% if we use the arithmetic average.

For question 2), we have to find the geometric average, the formula is

$g=\sqrt[n]{(1+g_{1} )(1+g_{2} )(1+g_{3} )...(1+g_{n} )}$

In our case, "n" is equals to 4, for there are 4 growth rates to average, everything should look like this.

$g=\sqrt[4]{(1+0.03213 )(1+0.04622 )(1+0.0303 )(1+0.0500 )} =0.0396$

So, the cost of equity would be

$r(e)=\frac{2.57(1+0.0396)}{65} +0.0396=0.0807$

So, if we use the geometric average, the cost of equity would be 8.07%

Best of luck.