Question

Common stock value—Constant growth   

McCracken​ Roofing, Inc., common stock paid a dividend of ​$1.41 per share last year. The company expects earnings and dividends to grow at a rate of 5​% 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 11​%, what required rate of return would result in a price per share of ​$28​?

Answer 1

Information provided:

Last year’s dividend= $1.41

Growth rate= 5%

Current stock price= $28

The question is solved using the dividend discount model.

a.The stock’s required rate of return is calculated using the dividend discount model. It is calculated using the below formula:

Ke=D1/Po+g

Where:

D1= Next year’s dividend

Po=Current stock price

g=Firm’s growth rate

Ke= $1.41*(1+0.05)/ $28 + 0.05

     = $1.48/ $28 + 0.05

     = 0.0529 + 0.05

     = 0.1029*100

     =10.29%.

Therefore, the stock’s required rate of return is 10.29%.

b.Information provided:

Last year’s dividend= $1.41

Growth rate= 11%

Current stock price= $28

Required rate of return= 11%

The question is solved using the dividend discount model.

The stock’s required rate of return is calculated using the dividend discount model. It is calculated using the below formula:

Ke=D1/Po+g

Where:

D1= Next year’s dividend

Po=Current stock price

g=Firm’s growth rate

Ke= $1.41*(1+0.11)/ $28 + 0.11

     = $1.57/ $28 + 0.11

     = 0.0561 + 0.11

     = 0.1661*100

     = 16.61%.

Therefore, the stock’s required rate of return is 16.61%.

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