Question

Suppose hornsby ltd. just issued a dividend of $2.56 per share on its common stock. the company paid dividends of $2.06, $2.13, $2.30, and $2.40 per share in the last four years. if the stock currently sells for $75, what is your best estimate of the company's cost of equity capital using arithmetic and geometric growth rates?

Answer 1

divide both sides by the $2.06 which gets you 2.56/2.06 = (1+g)4
Then you just take the fourth root of both sides and you're left with 1-g on the right. I'm sure you can isolate for g from there on.
Substitute x = 1+g , and solve it like any other equation involving x.
2.56/2.06 = x4
4sqrt(2.56/2.06) = x
x = 1.055828, however, x = 1+g, so g = x-1, g = 1.055828-1 = 0.055828