Question

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

Year	Earnings Per Share
20X1	$	7.00
20X2		7.42
20X3		7.87
20X4		8.34
20X5		8.84

   
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.)

Earnings for 20X6 9.37

Dividend 3.75

How do I work part B.

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.)
  

Anticipated stock price?

Answer 1

Place yourself at beginning of 20X6. So, what they are asking is stock price today. Stock price under the constant dividend growth model is computed as follows -

P0 = D1 / (ke - g)

where, P0 = stock price today, D1 = expected dividend next year (20X6), Ke = required return, g = growth rate

growth rate = ($8.84 - $8.34) / $8.34 = 0.05995 or 6%

Expected dividend in 20X6 (D1) = Earnings next year x dividend payout ratio = $8.84 x (1 + 0.06) x 0.4 = $3.74816

P0 = $3.74816 / (0.13 - 0.06) = $53.54514 or $53.55 (or $53.54)