The market consensus is that Analog Electronic Corporation has an ROE = 9% and a beta of 1.25. It plans to maintain indefinitely its traditional plow-back ratio of 2/3. This year's earnings were $3 per share. The annual dividend was just paid. The consensus estimate of the coming year's market return is 14% and T-bills currently offer a 6% return.

a) Find the price at which Analog stock should sell?

b) Calculate the P/E ratio.

c) Calculate the present value of growth opportunities.

d) Suppose your research convinces you that Analog will announce momentarily that it will immediately reduce its plow-back ratio to 1/3, then find the intrinsic value of the stock.

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

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.