Question

Suppose Blue Jay Enterprises is all equity financed (they have no outstanding debt), has asset worth $200 million and an ROE of 7%. 

Blue Jay also has $2 million shares outstanding and a plowback ratio of b = 60%. Suppose its market capitalization rate is 5% (k = 0.05).

(a) What is Blue Jay's earnings per share? What is the price of Blue Jay's

stock?

(b) What is its dividend growth rate, g?

(c) What is its price one year from now (assume dividends are paid annually)?

(d) What plowback ratio would maximize Blue Jay's stock price?

Answer 1

A)
Since the firm is all equity financed, Value of Equity = Value of Assets = $200 million
Share Price = Value of Equity / Shares Outstanding
= 200 / 2
= $100

Share Price = Dividend in year 1 / (k - g)
g = ROE x b = 7% x 0.6 = 4.2%
Dividend in year 1 = Earnings per Share x b x (1 + g)
Share Price = EPS x b x (1 + g) / (k - g)
100 = EPS x 0.6 x (1 + 0.042) / (0.05 - 0.042)
EPS = $1.28

B)
Growth rate = 4.2%

C)
Price one year from now = Dividend in Year 2 / (k - g)
D2 = EPS0 x (1 + g)2 x b (Where EPS0 is the current EPS)
D2 = 1.28 x (1 + 0.042)2 x 0.6 = $0.8336
Price in one year = 0.8336 / (0.05 - 0.042)
= $104.20

D)
Price = Dividend next year / (k - g)
From the formula, the price is maximized when the denominator is minimized. When the denominator is 0, the maximum theoretical price is infinity.
k - g = 0
g = k
g = 5%

g = ROE x b
5% = ROE x b
5% = 7% x b
b = 5% / 7% = 0.7143 or 71.43%
For a plowback ratio of 71.43%, the price could be maximized.

E)
ROE = 4%,
growth rate, g = 4% x 0.6 = 0.024 or 2.4%

To find EPS,
100 = EPS x 0.6 x (1 + 0.024) / (0.05 - 0.024)
EPS = $4.23

To find price one year from now,
D2 = EPS0 x 0.6 x (1 + 0.024)2 = $2.66
Price in 1 year = D2 / (k - g)
= 2.66 / (0.05 - 0.024)
= $102.4

Since the ROE is less than the capitalization rate, investing the earnings would not be as profitable as paying off dividends, The share value would be maximized when the plowback ratio is 0%