The market consensus is that Analog Electronic Corporation has an ROE = 9%, a beta of 1.25, and plans to maintain indefinitely its traditional plowback 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. (Do not round intermediate calculations. Round your answer to 2 decimal places.) b. Calculate the P/E ratio. (Do not round intermediate calculations. Round your answer to 2 decimal places.) c. Calculate the present value of growth opportunities. (Negative amount should be indicated by a minus sign. Do not round intermediate calculations. Round your answer to 2 decimal places.) 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. Stock Price is $10.60.

b. Trailing P/E ratio is 3.53, while Leading P/E ratio is 3.33.

c. Present value of growth opportunitiesis -$9.28.

d .Stock Price is $15.85.

Explanation:

The following are given in the question:

ROE = 9%

b = beta = 1.25

pr = Plowback ratio = 2/3 = 0.67

dpr = dividend payout ratio = 1- pr = 1/3 = 0.33

e0 = This year’s earnings per share = $3

mr = The coming year’s market return = 14%

tr = T-bills return = 6%

We can now proceed as follows:

a. Find the price at which Analog stock should sell. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

The stock price can be calculated using the following formula:

P0 = Stock Price = d * (1 + g) / (r - g) …………………………. (1)

Where;

d = dividend per share = e0 / dpr = $3 / (1 / 3) = $1

g = Sustainable growth rate = ROE * pr = 9% * 2/3 = 0.06

rf = Risk free rate = Return on T-bills = 6%

b = Beta = 1.25

mr = Market return = 14%

r = Required return on Equity = rf + b * (mr - rf) = 6% + 1.25 * (14% - 6%) = 0.16

Substituting the values into equation (1), we have:

Stock Price = $1 * (1 + 0.06) / (0.16 – 0.06)

Stock Price = $1 * 1.06 / 0.10

Stock Price = $1 * 10.60

P0 = Stock Price = $10.60

b. Calculate the P/E ratio. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Trailing P/E ratio = P0/E0 = $10.60 / $3 = 3.53

Leading P/E ratio = P0/e1 ………………………………………. (2)

Where;

e1 = e0 * (1 + g) = $3 * (1 + 0.06) = 3.18

Substituting the values into equation (2), we have:

Leading P/E ratio = $10.60 / 3.18 = 3.33

c. Calculate the present value of growth opportunities. (Negative amount should be indicated by a minus sign. Do not round intermediate calculations. Round your answer to 2 decimal places.)

P0 = e1 / r + pvgo …………………………………… (3)

Where pvgo denotes present value of growth opportunities, and P0, e1 and r are as already obatained in part a and b.

Substituting the values into equation (2) and solve for pvgo, we have:

$10.60 = $3.18 / 0.16 + pvgo

$10.60 = $19.875 + pvgo

pvgo = $10.60 - 19.875

pvgo = -$9.28

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.

g = ROE * pr = 9% * (1 / 3) = 3%

dpr = 1 – pr = 1 - 1/3 = 2/3

d = dividend per share = e0 / dpr = $3 / (2 / 3) = $2

Stock Price = d * (1 + g) / (r - g) = $2 * (1 + 3%) / (0.16 – 3%)

Stock Price = $2 * (1 + 3%) / (0.16 – 3%)

Stock Price = $15.85

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