Question

Given the information below, if the required rate of return for the stock is 15%, the security is overvalued. Do you agree? Why?

P₀ = $40

D₀=$2

g₁=10%

g₂=15%

g₃=20%

g₄=25%

Growth rate after year 4 is expected to be 5%.

The implied rate of return (discount rate) should be positively related to the implied beta of a stock. Do you agree? Why?

Answer 1

Let us first calculate the price of the stock in a multi stage growth model:

D0 = $2,

D1= 2*1.1 = $2.2

D2 = $2.2*1.15 = $2.53

D3 = $2.53*1.2 = $3.036

D4 = $3.036*1.25 = $3.79

P4 = D5/Re - G

= 3.79*1.05/0.15-0.05

= $39.795

Now, let us calculate the present value,

2.2/1.15 + 2.53/1.15^2 + 3.036/1.15^3 + 3.79/1.15^4 + 39.795/1.15^4

= 1.913 +1.913 +1.996+2.1660 +22.7529

= $30.7409

YES, the stock is not overvalued because the intrinsic value of the stock is $30.7409 (as per the multi stage model) but the value of the stock is $40. So, the stock is above the intrinsic value so it is overvalued.

Yes, the required return is positively related to beta as as increase in beta will result in the increase in the required return by the investors.

Re = RF + BETA (Rm - Rf)

So, the required return is