Question

Common stock valuelong dashConstant growth   McCracken​ Roofing, Inc., common stock paid a dividend of ​$1.48 per share last year. The company expects earnings and dividends to grow at a rate of 6​% per year for the foreseeable future.  

a.  What required rate of return for this stock would result in a price per share of ​$28​?

b. If McCracken expects both earnings and dividends to grow at an annual rate of 12​%, what required rate of return would result in a price per share of ​$28​?

Answer 1

a.	Required rate of return	=	(D0*(1+g)/P0)+g		Where,
		=	(1.48*(1+0.06)/28.00)+0.06		D0	=	$       1.48
		=	11.60%		g	=	6%
					P0	=	$    28.00
b.	Required rate of return	=	(D0*(1+g)/P0)+g		Where,
		=	(1.48*(1+0.12)/28.00)+0.12		D0	=	$       1.48
		=	17.92%		g	=	12%
					P0	=	$    28.00

Answer 2

SOLUTION :

a.

Dividend paid last year, D0 = 1.48 ($)

Growth rate for dividend and earnings, g = 6% = 0.06 (constant)

=> 1 + g = 1.06

=> Divided for year 1, D1 = D0(1+g) = 1.48*1.06 = 1.5688 

Let required rate of return be r to get price of share at 28 ($)

As per CAPM :

Required rate of return, r : 

= D1/P + g 

= 1.5688/28 + 0.06

= 0.1160

= 11.60% (ANSWER).

b.

If g = 12% = 0.12

=> 1+g = 1.12

=> D1 = Do(1+g) = 1.48*1.12 = 1.6576 

So,

Required rate of return, r : 

= D1/P + g 

= 1.6576/28 + 0.12

= 0.1792

= 17.92% (ANSWER).