Answer:
a. Ke = Rf + β(Rm – Rf)
Ke = 6 + 1.25(14-6)
Ke = 6 + 10
Ke = 16%
b = 2/3
Do = 1/3 x $3 = $1
g = b x r
g = 2/3 x 9
g = 6%
Po = Do(1+g)/ke - g
Po = $1(1+0.06)/0.16-0.06
Po = $10.60
b. P/E ratio = Market price per share/Earnings per share
P/E ratio = $10.60/$3
P/R ratio = 3.53
c. Present value of growth opportunities = Market price - Value without growth
Present value of growth opportunities = $10.60 - $6.25
Present value of growth opportunities = $4.35
Value without growth = Do/Ke
= $1/0.16
= $6.25
d. b = 1/3
Do = 2/3 x $3 = $2
g = 1/3 x 9
g = 3%
Intrinsic value = Do(1+g)/Ke-g
= 2(1+0.03)/0.16-0.03
= $15.85
Step-by-step explanation:
In this scenario, we need to determine cost of equity based on capital asset pricing model. Then, we will calculate the growth rate by multiplying the plow-back ratio by return on equity. Thereafter, the price of the stock will be computed based on dividend growth model as shown above. P/E ratio is the ratio of market price per share to earnings per share.
The present value of growth opportunities is the difference between market price and the value without growth as calculated above.