Question

Sierra Corporation has just paid a dividend of $2 per share, and its dividends are expected to grow at a steady rate of 7% for the foreseeable future. The firm’s shares are currently selling for $30 per share, with an equity beta of 1.2. The risk-free rate is 5% and expected market return is 13%. What is the firm’s estimated cost of equity if we were to calculate it as the average of the costs of equity from the dividend growth model and the security market line?

Select one:

a. 14.13%

b. 14.20%

c. 14.37%

d. 14.60%

e. 14.89%

Answer 1

Solution:
	Answer is C. 14.37%
Working Notes:
	Costs of equity from the dividend growth model
	Ke = D1/P0 + g
	Cost of common equity (Ke) = ??
	Po=current share price = $30 per share
	g= growth rate= 7%
	D0= Current Dividend=$2 per share
	D1 = D0(1+g)
	=$2 (1+ 0.07)
	=$2.14
	Ke = D1/P0 + g
	=$2.14/$30 + 0.07
	=0.0713333 + 0.07
	=0.14133333
	=14.133333333%
	=14.1333333 %
	Costs of equity from the security market line
	Using SML return on stock
	ri = rf + (rm-rf) Bi
	here
	ri= return of the stock   = ??
	rf= risk free rate = 5%
	rm= return of market = 13%
	Bi= beta of the stock = 1.2
	ri = rf + (rm-rf) Bi
	= 5% + (13% - 5%) x 1.2
	=5% + 8% x 1.2
	=5% + 9.60 %
	=14.60%
	Average of the costs of equity from the dividend growth model and the security market line
	= (Cost of Equity as per dividend growth model + Cost of Equity as per security market line)/2
	=(14.133333% + 14.60%)/2
	=28.7333333% /2
	=14.3666666 %
	14.37%
Please feel free to ask if anything about above solution in comment section of the question.