Question

Suppose Powers Ltd. just issued a dividend of $1.20 per share on its common stock. The company paid dividends of $.85, $.92, $.99, and $1.09 per share in the last four years.

Required:

If the stock currently sells for $53, what is your best estimate of the company’s cost of equity capital using arithmetic and geometric growth rates? (Do not round intermediate calculations. Enter your answers as a percentage rounded to 2 decimal places (e.g., 32.16).)

	Cost of equity
Arithmetic dividend growth rate	%
Geometric dividend growth rate	%

Answer 1

	Cost of equity
Arithmetic dividend growth rate	11.48%
Geometric dividend growth rate	11.47%

Explanation;

1. Cost of equity (Arithmetic dividend growth rate);

First of all let’s calculate growth rate;

g1 = ($.92 – $.85) / $.85 = 8.24%

g2 = ($.99 – $.92) / $.92 = 7.61%

g3 = ($1.09 – $.99) / $.99 = 10.10%

g4 = ($1.20 – $1.09) / $1.09 = 10.09%

Average arithmetic growth rate will be (8.24 + 7.61 + 10.10 + 10.09) / 4 = 9.01%

Now let’s calculate cost of equity;

Cost of equity [$1.20 (1.0901) / $53] + 0.0901

Cost of equity = 11.48%

2. Cost of equity (Geometric growth rate);

First of all let’s calculate growth rate;

$1.20 = $.85(1 + g)4

On solving this equation growth rate comes to .0900

Thus, growth rate (g) = 9%

Now let’s calculate cost of capital;

Cost of equity;

Cost of equity [$1.20 (1.09) / $53] + 0.09

Cost of equity = 11.47%