Question

Suppose Stark, Ltd., just issued a dividend of $2.51 per share on its common stock. The company paid dividends of $2.01, $2.17, $2.25, and $2.36 per share in the last four years.

a.	If the stock currently sells for $43, 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.)
b.	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.)

Answer 1

a). To use the dividend growth model, we first need to find the growth rate in dividends. So, the increase in dividends each year was:

g1 = ($2.17 - $2.01)/$2.01 = 0.0796 or 7.96%

g2 = ($2.25 - $2.17)/$2.17 = 0.0369 or 3.69%

g3 = ($2.36 - $2.25)/$2.25 = 0.0489 or 4.89%

g4 = ($2.51 - $2.36)/$2.36 = 0.0636 or 6.36%

So, the average arithmetic growth rate in dividends was:

g = (0.0796 + 0.0369 + 0.0489 + 0.0636)/4 = 0.0572 or 5.72%

Using this growth rate in the dividend growth model, we find the cost of equity is:

RE = [{D0(1 + g)} / P0] + g

= [$2.51(1.0572)/$43.00] + 0.0572 = 0.0617 + 0.0572 = 0.1189, or 11.89%

b).  Calculating the geometric growth rate in dividends, we find:

$2.51 = $2.01(1 + g)⁴

g = [$2.51 / $2.01]^1/4 - 1 = 1.0571 - 1 = 0.0571, or 5.71%

The cost of equity using the geometric dividend growth rate is:

RE = [{D0(1 + g)} / P0] + g

= [$2.51(1.0571)/$43.00] + 0.0571 = 0.0617 + 0.0571 = 0.1188, or 11.88%