Question

1. Given the information below, please estimate the constant required rate of return.

P₀ = $30

D₀=$2

g₁=2%

g₂=4%

g₃=6%

g₄=8%

g₅=10%

g₆=12%

Growth rate after year 6 is expected to be 3.5% and stay constant forever.

2. Given the risk-free rate is 3% and the equity risk premium is 4%, the stock is overvalued if the actual beta for the security is 1.8. Do you agree? Why?

Answer 1

a. The cost of equity/ constant required return of return is :

Re = Rf + beta (Rm - Rf)

= 3 + 4*1.8

=10.2%

The stock price according to the multi stage growth model is :

D1 = $2*1.02

=$2.04

D2 = $2.12 (2.04*1.04)

D3= $2.25 (2.12 *1.06)

D4 =$2.43 (2.25*1.08)

D5 =$2.67 (2.43*1.1)

D6 = $2.99 ($2.67*1.12)

P6 = D7/ Re - g

= $3.09/( 0.102 - 0.035)

=3.09/0.067

=$46.12

The stock price today is :

$2.04/1.102 + 2.12 /1.102^2 + 2.25 /1.102^3 + 2.43 /1.102^4+ 2.67 /1.102^5+ 2.99/1.102^6 + $46.12/1.102^6

=1.85 + 1.75 + 1.68 + 1.65 + 1.64 + 1.67 + 25.75

=$36

b. So, according to the Model the share price should be $36, but the stock price is $30. So, IT IS UNDERVALUED AND NOT OVERVALUED. As the share price is less than the intrinsic value determined by the model. SO I DO NOT AGREE.