Suppose Stark Ltd. just issued a dividend of $2.24 per share on its common stock. The company paid dividends of $1.80, $1.98, $2.05, and $2.16 per share in the last four years. a. If the stock currently sells for $45, what is your best estimate of the company’s cost of equity capital using the arithmetic average growth rate in dividends? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) a. What if you use the geometric average growth rate? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Question

09-10-2019
Business

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Suppose Stark Ltd. just issued a dividend of $2.24 per share on its common stock. The company paid dividends of $1.80, $1.98, $2.05, and $2.16 per share in the last four years. a. If the stock currently sells for $45, what is your best estimate of the company’s cost of equity capital using the arithmetic average growth rate in dividends? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) a. What if you use the geometric average growth rate? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

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Answer:

Ans, The cost of the company’s cost of equity capital using the arithmetic average growth rate is 10.63% and using the geometric average of the growth rate is 10.60%

Explanation:

Hi, this is the equation we need to solve in order to find the company’s cost of equity capital.

[tex]r=\frac{Dividend}{Price} +g[/tex]

As you can see, we almost have everything, the only problem here is "g", its growth rate, so let´s find "g" using the arithmetic average, but first, we need to find the growth rate for every period, the formula is

[tex]g=\frac{(FinalDividend-PastDividend}{PastDividend} [/tex]

Therefore, we need to find 4 g´s, let´s call them g1, g2, g3 and g4:

[tex]g1=\frac{(1.98-1.80)}{1.80} =0.10[/tex]

[tex]g2=\frac{(2.05-1.98)}{1.98} =0.0354[/tex]

[tex]g3=\frac{(2.16-2.05)}{2.05} =0.0537[/tex]

[tex]g4=\frac{(2.24-2.16)}{2.16} =0.0370[/tex]

So the average is:

[tex]Average(g)=\frac{0.10+0.0354+0.0537+0.0370}{4} =0.0565[/tex]

Therefore, the average growth rate is 5.65%

And the company’s cost of equity is:

[tex]r=\frac{2.24}{45} +0.0565=0.1063[/tex]

so, if the average growth rate is found by using the arithmetic average is 10.63%.

Now, let´s find the geometric average

[tex]g(average)=\sqrt[4]{(1+0.10)(1+0.0354)(1+0.0537)(1+0.0370)} -1=0.0562[/tex]

therefore, using the geometric average to find the growth rate, the company’s cost of equity is:

[tex]r=\frac{2.24}{45} +0.0562=0.1060[/tex]

using the geometric average, the company’s cost of equity is 10.60%

Best of luck.