Answer:
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
