Question

You are considering an investment in Justus Corporation's stock, which is expected to pay a dividend of $2.00 a share at the end of the year (D1 = $2.00) and has a beta of 0.9. The risk-free rate is 4.2%, and the market risk premium is 4.5%. Justus currently sells for $28.00 a share, and its dividend is expected to grow at some constant rate, g. The data has been collected in the Microsoft Excel Online file below. Open the spreadsheet and perform the required analysis to answer the question below.

Assuming the market is in equilibrium, what does the market believe will be the stock price at the end of 3 years? (That is, what is ?) Round your answer to two decimal places. Do not round your intermediate calculations.

Answer 1

Explanation:

Using the dividend discount model and the information given:

D1 = $2.00

beta = 0.9

risk-free rate = 4.2%

market risk premium = 4.5%

current stock price = $28.00

First, we need to find the required rate of return for the stock using the capital asset pricing model (CAPM):

r = r_rf + beta * (r_m - r_rf)

r = 0.042 + 0.9 * 0.045

r = 0.0831 or 8.31%

Next, we can use the dividend discount model to find the expected stock price at the end of 3 years:

D1 = D0 * (1 + g)

D0 = D1 / (1 + g)

P0 = D1 / (r - g)

P3 = D3 / (r - g)

P0 = current stock price = $28.00

D0 = D1 / (1 + g) = $2.00 / (1 + g)

D3 = D0 * (1 + g)^3

Substituting these values and solving for P3:

$28.00 = $2.00 / (1 + g) / (0.0831 - g)

$28.00 * (0.0831 - g) = $2.00 / (1 + g)

0.002343 - 0.028g + 0.0831g - 0.0831g^2 = 0.002343 + 0.002g

0.0831g^2 - 0.026g - 0.002343 = 0

g = 0.069 or 6.9%

Now we can use the dividend discount model again to find the expected stock price at the end of 3 years:

P3 = $2.00 * (1 + 0.069) ^ 3 / (0.0831 - 0.069)

P3 = $38.81

Therefore, the market believes the stock price at the end of 3 years will be $38.81