Question

Justin Cement Company has had the following pattern of earnings per share over the last five years:    
   

Year	Earnings Per Share
20X1	$	12.00
20X2		12.60
20X3		13.23
20X4		13.89
20X5		14.58

   
The earnings per share have grown at a constant rate (on a rounded basis) and will continue to do so in the future. Dividends represent 40 percent of earnings.     
   
a. Project earnings and dividends for the next year (20X6). (Round the growth rate to the nearest whole percent. Do not round any other intermediate calculations. Round your answers to 2 decimal places.)
  

     
        
b. If the required rate of return (K_e) is 13 percent, what is the anticipated stock price (P₀) at the beginning of 20X6? (Round the growth rate to the nearest whole percent. Do not round any other intermediate calculations. Round your answer to 2 decimal places.)
  

Answer 1

(a)

Year	EPS	Growth (in %)	DPS (40% of EPS)
2011	12		(12 x 0.4) = $ 4.8
2012	12.6	[(12.6 -12)/12] x100 = 5	(12.6 x 0.4) = $ 5.04
2013	13.23	[(13.23 -12.6)/12.6] x 100 = 5	(13.23 x 0.4) = $ 5.292
2014	13.89	[(13.89 - 13.23)/13.23] x 100 = 4.988 or 5 %	(13.89 x 0.4) = $ 5.556
2015	14.58	[(14.58 - 13.89)/13.89] x 100 = 4.967 or 5%	(14.58 x 0.4) = $ 5.832
2016	15.31	[(15.31-14.58)/14.58] x 100 = 5.006 or 5 %	(15.31 x 0.4) = $ 6.124

* DPS is Dividend Per Share and EPS is Earnings Per Share

(b) As the EPS and DPS figures given are the end of year figures, the 2016 EPS and DPS come in at the end of that year. Hence, stock price at beginning of 2016 or end of year 2015 would be the discounted value of 2016 DPS.

Required Rate of Return = K(e) =13 % and Growth Rate = g = 5 %

Therefore, P0 = 2016 DPS / (K(e) - g) = 15.31 / (0.13 - 0.05) = $ 191.375