Question

You are considering an investment in Justus Corporation's stock, which is expected to pay a dividend of $3.00 a share at the end of the year (D1 = $3.00) and has a beta of 0.9. The risk-free rate is 4.6%, and the market risk premium is 4.5%. Justus currently sells for $44.00 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 ?) Do not round intermediate calculations. Round your answer to the nearest cent

Answer 1

Cost of Equity- Cost of Equity is what it costs the company to maintain its share price to the satisfaction level of its equity shareholders. There are two approaches for calculation of Cost of Equity-

1) DDM or Dividend Discount model- As per this model, the value of equity is equal to the present value of all Future dividends that is expected to provide over an indefinite period. Depending upon growth forecasts, there can be two cases:

a) Constant Rupee Dividend- It is also called No growth in dividends. when company provides same amount of dividend year after year

K_e = D/ P_O where K= cost of equity   D= annual dividend P_O= Current market price

b) Constant Growth rate in dividend- In this, it is assumed that the dividends will grow at a constant rate forever

   K_e = D/ P_{O +} g

2) CAPM - it is an equilibrium model used to predict expected return on a security or portfolio.

K_e = R_f + B( R_M - R_f) where R_f= Risk free rate B= Beta( systematic risk)

R_m= Return on market R_m- R_f = Market risk premium

Given, D₁ = $3 B= 0.9 R_f= 4.6% or 0.046 R_m- R_f = 4.5% or 0.045 P0 = $44 g= ? Time= 3 years

First we will calculate the cost of equity

K_e = R_f + B( R_M - R_f)

K_e = 0.046 + 0.9 (0.045) = 0.0865 or 8.65%

Now we will calculate the growth rate or g

P₀ = D_1/ K_{e -} g

44= 3/ 0.0865 - g

3.806- 44g = 3

g= 3.806-3 / 44 = 0.0183 or 1.83%

Now we will calculate the value of stock after 3 years

P₃ = P₀ ( 1+g )³

P₃ = 44 (1+ 0.0183)³

P₃ = 44 (1.0183)³  = 44* 5.890 = 44 * 1.0559 = $46.46