Question

You are considering an investment in Justus Corporation's stock, which is expected to pay a dividend of $2.25 a share at the end of the year (D₁ = $2.25) and has a beta of 0.9. The risk-free rate is 4.8%, and the market risk premium is 4.5%. Justus currently sells for $40.00 a share, and its dividend is expected to grow at some constant rate, g. 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

Risk free rate = 4.8%, Beta = 0.9 , Market risk premium = 4.5%

Since market is in equilibrium, therefore cost of equity = expected rate return of stock

We can use CAPM to find the expected rate of return on stock

Expected return on stock = Cost of equity = r = Risk free rate + Beta x market risk premium = 4.8% + 0.9 x 4.5% = 4.8% + 4.05% = 8.85%

Dividend at end of year 1 = Dividend for year 1 = D1 = 2.25, Current price of stock = P₀ = 40

Let g = Constant growth rate of dividends

According of constant growth rate model

P₀ = D1 / (r - g)

40 = 2.25 / (8.85% - g)

40 (8.85% - g ) = 2.25

g = 8.85% - (2.25 / 40)= 8.85% - 5.625% = 3.225%

Dividend at end of year 4 = Dividend in year 4 = D4 = D1 x (1 + g)³ = 2.25 x (1 + 3.225%)³ = 2.25 x (1.03225)³ = 2.25 x 1.099903 = 2.4747

Now using constant growth model , Let P₃ = Price of stock at end of 3 years, then

P₃ = D4 / ( r - g) = 2.4747 / (8.85% - 3.225%) = 2.4747 / 5.625% = 43.9946 = $43.99

Hence Price of stock at end of 3 years = $43.99