You consider buying a share of stock. The stock is expected to pay a dividend of $1.50 next year, and dividends are expected to grow by 5% per year forever. What is the stock price now if the stock's beta is 1.1, rf is 6%, and E[rm]

Question

The question is incomplete. The complete question is given as follows:

You consider buying a share of stock. The stock is expected to pay a dividend of $1.50 next year, and dividends are expected to grow by 5% per year forever. What is the stock price now if the stock's beta is 1.1, rf is 6%, and E[rm] = 16%.

Answer

 Stock price  =  $12.5

Explanation:

Using the dividend valuation model, the value of a stock can be determined using this model:

Price = D(1+g)/(r-g)

D- dividend payable now, g- growth rate in dividend, r-return on equity

Return on equity

Re= Rf + β(Rm -Rf)

Rf- risk-free rate, Rm - Return on market portfolio, β- Beta factor

To determine the Stock price we follow the steps below

Step 1

Determine the cost of equity

r = 6% + 1.1 *(16%-6%)

  = 17%

Step 2

Determine the stock price

Stock price = 1.50/(0.17-0.05)

                  =  $12.5

Stock price = $12.5

Note

D*(1+g) = Dividend next year. And this has been given as $1.50. So there is no need to apply the growth rate.