Question

Suppose Stark Ltd. just issued a dividend of $1.59 per share on its common stock. The company paid dividends of $1.25, $1.33, $1.40, and $1.51 per share in the last four years. a. If the stock currently sells for $40, 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.)

Answer 1

Step-by-step explanation:

arithmetic average growth rate = {[(1.33 - 1.25)/1.25] + [(1.40 - 1.33)/1.33] + [(1.51 - 1.40)/1.40] + [(1.59 - 1.51)/1.51]} / 4 = {0.064 + 0.053 + 0.079 + 0.053} / 4 = 0.06225 x 100 = 6.225%

geometric growth rate = ⁴√{0.064 x 0.053 x 0.079 x 0.053} = 0.061%

a) using arithmetic average growth rate

Div₁ = $1.59 x 1.06225 = $1.689

P₀ = $40

g = 6.225%

40 = 1.689 / (Re - 0.06225)

Re - 0.06225 = 1.689 / 40 = 0.04222

Re = 0.04222 + 0.06225 = 0.10447 = 10.45%

b) using geometric average growth rate

Div₁ = $1.59 x 1.061 = $1.68699

P₀ = $40

g = 0.061%

40 = 1.68699 / (Re - 0.061)

Re - 0.061 = 1.68699 / 40 = 0.04217

Re = 0.04217 + 0.061 = 0.103174 = 10.32%