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 6.0%, and the market risk premium is 5.5%. Justus currently sells for $28.00 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? Round your answer to two decimal places. Do not round your intermediate calculations.

Answer 1

SOLUTION :

THE VALUES PROVIDED IN THE QUESTION ARE AS FOLLOWS:

expected to pay a dividend at the end of the year (D1 )= $2.00

beta of stock =0.9.

(Rf ) risk-free rate = 6.0%

(Rm-Rf ) market risk premium =5.5%

(Po ) Justus currently sells = $28.00 per share

dividend is expected to grow at some constant rate, g. ( Given )

Assuming the market is in equilibrium

  ( P3 )stock price at the end of 3 years =?

The formula to calculate the   Required rate of return ( Ke ) as per (CAPM ) CAPITAL ASSETS PRICING MODEL

Required rate of return =risk-free rate + beta *market risk premium

Ke =Rf +beta*Rm-Rf

Using the values provided in the question are as follows

Ke = 6 + 0.9 * 5.5

Ke =6 +4.95

Required rate of return ( Ke ) =10.95 % or 0.1095

The formula to calculate the growth rate ( g ) as per Gorden growth Model

Po= D1 / Ke-g

Using the values provided in the question are as follows

$28 = $2.00 / 0.1095-g

$28 ( 0.1095 - g ) = $ 2.00

$ 3.066 - $28 g = $ 2.00

$3.066 - $ 2.00 = $ 28 g

$1.066 = $ 28 g

g =$1.066 /$ 28

g =0.03807

g =0.0381 or 3.81 %

The formula to calculate the ( D4 ) = expected value of dividend at the end of 4 th year

D4 = D1 * (1+ g1-4 )3

D4 = $2.00 * ( 1+ 0.0381 ) 3

D4 = $2.00 *1.11871013634

D4 =$ 2.23742027268

expected value of dividend at the end of 4 th year ( D4 )=$ 2.23742027268

The formula to calculate the   ( P3 )stock price at the end of 3 years

  ( P3 )stock price at the end of 3 years =D4 /Ke –g

Where,

( D4 ) = expected value of dividend at the end of 4 th year

( Ke ) = Required rate of return as per (CAPM ) CAPITAL ASSETS PRICING MODEL

(g ) = Growth Rate

  ( P3 )stock price at the end of 3 years =$ 2.23742027268 / 0.1095- 0.0381

( P3 )stock price at the end of 3 years =$ 2.23742027268 / 0.0714

( P3 )stock price at the end of 3 years =$ 31.336

( P3 )stock price at the end of 3 years =$ 31.34

Hence, reqired answer i.e ( P3 )stock price at the end of 3 years =$ 31.34