Question

In practice, a common way to value a share of stock when a company pays dividends is to value the dividends over the next five years or so, then find the “terminal” stock price using a benchmark PE ratio. Suppose a company just paid a dividend of $1.15. The dividends are expected to grow at 10 percent over the next five years. The company has a payout ratio of 40 percent and a benchmark PE of 19. The required return is 11 percent.

a. What is the target stock price in five years? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

b. What is the stock price today? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

first we need to find the dividends paid over five years:

year 1 =1.15*1.10	1.265
year 2= 1.265*1.10	1.3915
year 3=1.3915*1.10	1.53065
year 4=1.53065*1.10	1.683715
year 5=1.683715*1.10	1.8520865

a.target stock price in five years:

EPS of year 5 = dividend / (payout ratio)

=>1.8520865/ 0.40

=>4.63021625.

stock price in five years = EPS * PE ratio

=>4.6302165*19

=>$87.97.

b.stock price today:

year	value (dividend / price)	pv factor	value * PV factor
1	1.265	(1/1.11)=0.9009	1.265*0.9009=>1.1396385
2	1.3915	1/(1.11)^2=>0.81162	1.3915*0.81162=>1.2936923
3	1.53065	1/(1.11)^3=>0.73119	1.53065*0.73119=>1.11919597
4	1.683715	1/(1.11)^4=>0.65873097	1.683715*0.65873097=>1.10911522
5	1.8520865	1/(1.11)^5=>0.59345133	1.8520865*0.59345133=>1.0991232
5	87.97	1/(1.11)^5=>0.59345133	87.97*0.59345133=>52.2059135
		current price	57.97