The market consensus is that Analog Electronic Corporation has an ROE of 9% and a beta of 1.70. It plans to maintain indefinitely its traditional plowback ratio of 2/3. This year's earnings were $3.6 per share. The annual dividend was just paid. The consensus estimate of the coming year's market return is 15%, and T-bills currently offer a 5% return. Required:
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 Analog will announce momentarily that it will immediately reduce its plowback ratio to 1/3. Find the intrinsic value of the stock.

a $7.95

b. $2.21

c $16.36

d, $13.01

Explanation:

according to the constant dividend growth model

price = [d0 (1+g)] / (r - g)

d0 = recently paid dividend

Dividend = payout ratio x earnings

payout ratio = 1 - plowback rate

1 - 2/3 = 1/3

1/3 x 3.6 = $1.2

r = cost of equity

According to the capital asset price model: Expected rate of return = risk free + beta x (market rate of return - risk free rate of return)

5% + 1.7(15 - 5) = 22%

g = growth rate

g = plowback rate x ROE

2/3 X 9 = 6%

1. [1.2 x 1.06] / (0.22 - 0.06) = 1.272/ 0.16 = $7.95

2.

The price to earning ratio is a financial metric used to value a company. it compares the price of a stock to the earnings of the stock. the lower the metric is, the higher the valuation of the firm

price to earning ratio = market value per share / earnings

$7.95 /  $3.6 = $2.21

c. present value of growth opportunities = earnings / cost of equity

3.6 / 0.22 = $16.36

d.

price = [d0 (1+g)] / (r - g)

d0 = recently paid dividend

Dividend = payout ratio x earnings

payout ratio = 1 - plowback rate

1 - 1/3 = 2/3

2/3 x 3.6 = $2.40

r = cost of equity = 22%

g = plowback rate x ROE

1/3 X 9 = 3%

[2.4 x 1.03] / (0.22 - 0.03) = 2.472/ 0.19 = $13.01

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