Question

Suppose a firm will pay a $2 dividend next year and expects to increase dividends by 20%, 15%, and 10% over the following three years. After that, dividends will increase at a rate of 5% per year indefinitely. If the required return is 17%, what is the price of the stock today?

Group of answer choices

$22.14

$18.80

$19.21

$21.50

$20.98

Answer 1

This type of 2 stage dividend discount model can be solved using two steps:

Step 1: the forecast period, where the growth of dividends can be forecasted

Step 2: The horizon period, where we apply the constant growth DDM formula.

Let us create a table of dividend cashflows and find the present values of the dividends.

Particulars	Year 1	Year 2	Year 3	Year 4	Year 5
Grwoth rates (given)	-	20%	15%	10%	5%
Dividends	$2	2.4	2.76	3.036	3.188
PV factor @ 17%	0.8547	0.7305	0.6244	0.5337
Present Value	1.7094	1.7532	1.7233	1.6203

Sum of the dividends of the explicit forecast period = $1.7094 + 1.7532 + 1.7233 + 1.6203 = $6.8062

Step 2: we now find the value at the end of year 4 using the constant growth formula

The formula is: D1/(Re-g) , where D1 is the next dividend. Re is the required rate, g is the growth rate.

Therefore, substituting the values, we get,

3.188/(0.17-0.05)

= $26.57 --> This value is standing at the end of Year 4 and we need to pull it to today, hence we discount it 4 years back to get the present value today,

Hence, $26.57 x 0.5337 = $14.18

Hence, the price of the share today is the sum of Step 1 and Step 2

$6.8062 + $14.18

= $20.98