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 $1.23. The dividends are expected to grow at 18 percent over the next five years. In five years, the estimated payout ratio is 30 percent and the benchmark PE ratio is 18. After five years, the earnings are expected to grow at 7 percent per year. The required return is 14 percent.

Required:
What is the target stock price in five years?(Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)
Stock price in 5 years $
What is the stock price today?(Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)
Stock price today $

Answer 1

a)$168.48

b)$48.51

Step-by-step explanation:

D0 = $1.23

g = 18%

PR = 30%

PE = 18%

E(growth) =7%

RR = 14%

Find the dividend in year five

D1 = 1.23*1.18=1.45, D2 =1.45 *1.18 =1.71, D3= 1.71*1.18 =2.02, D4 = 2.02*1.18 =2.38, D5 = 2.38*1.18=2.81

PR = DPS/EPS

30= 2.81/EPS

EPS=2.81/30%

=$9.36

to find stock price use the benchmark PE

9.036*18 = $168.48

b) After 5 years earnings to grow at 7%

Discount the dividends at 14 %

1.45/1.14)+1.71/1.14^2 +2.02/1.14^3 +2.38/1.14^4+2.81*1.07/0.14-0.07

=$48.51

Answer 2

Step-by-step explanation:

Calculation for 5th year dividend.

Year Dividend Growth Dividend

1 1.23 1.18 1.45

2 1.45 1.18 1.71

3 1.71 1.18 2.02

4 2.02 1.18 2.38

5 2.38 1.18 2.81

Now we find EPS for 5th year through payout ratio.

EPS5 = D5 / Payout ratio

EPS5 = $2.81 / 0.30

EPS5 = $9.37

Calculation for price.

P0 = Benchmark PE ratio x EPS5

P0 = 18 ($9.37)

P0 = $168.66

B. What is the stock price today.

Year Dividend Table value at 14% PV of dividend

1 1.45 0.8771 1.27

2 1.71 0.7694 1.32

3 2.02 0.6749 1.36

4 2.38 0.5920 1.41

5 171.47 0.5193 89.04

Total 94.40

Stock price today = $94.40