Cost of equity r(e)

CFA Level I Corporate Finance
#1

Hi,

Just got stuck with a question on calculating cost of equity r(e). Please help.

Given information in the book are:

Stock price = $30

Next year’s dividend = $1.5

Estimated growth rate = 7%

When I did the question, I used formula #1 as shown below, my answer was wrong.

So my question is, under what circumstances would you use formula #1 and #2?

#1. r(e) = [D(1+g) / P] + g

and

#2. r(e) = [D / P] + g

Your help is greatly appreciated.

Thanks

#2

Hello,

Formula (1) is basically Gordon Growth formula whereby the D is referring to current period dividend, Do.

The data available from the book stated that ’ next period’ dividend which means D1 not Do.

Hence,

P = Do(1+g) / (r-g) --------------------------(1)

Rearranging (1): P(r-g) = Do(1+g)

r = [Do(1+g) /P] +g --------------(2) _ which is the same as your #1 _

Inserting the given data into equation (2) will give:

r = [1.5/30] + 0.07 , noting that Do(1+g) is next period dividend i.e. $1.50, which is already given

r = 0.12 ( or 12%)

Hope it helps a bit.

Cheers,

Ernest

#3

You use eqn 1 if it was this year’s dividend.

but because they give you next year’s dividend there is no need to apply the growth factor so you can use eqn 2

you don’t have to memorise two equations, current price is based on next year’s dividend divided by the difference in cost of equity and the growth rate as you assume that the coy is an ongoing concern and its future dividend growth is an indicator of its value

#4

Thanks for your prompt reply.

#5

You can solve it like this . Lets arrange the data as following :

D1 = Dividend next year

P0 = Price

g= growth rate

The formula says : Ke = D1/P0 + g Which equals

1.5/30+.07 . Sol is 12%