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.