Galaxy Air,previously a no-growth firm,has two million shares outstanding.Until now,it consistently earned $20 million per year on its assets.(It has no debt and pays out all earnings as dividends.Its cost of capital is 10%.)Due to its newly appointed CEO,Galaxy Air is now able to squeeze out 1% annual growth by plowing back 5% of earnings.Calculate its stock price per share.

Question

Quizplus · Accepted Answer

Firstly, we need to calculate the new earnings per share (EPS) after 1% growth:
EPS = (Previous Earnings + Plowback Earnings) / Number of Shares
EPS = [(2 million shares x $20 million) + (5% x $20 million)] / 2 million shares
EPS = $21 per share
Next, we need to calculate the new dividend per share (DPS):
DPS = Previous Earnings per Share - Plowback Earnings per Share
DPS = $20 - (5% x $20) = $19
To calculate the new stock price, we can use the constant growth model:
Price per Share = DPS / (Cost of Capital - Growth Rate)
Price per Share = $19 / (10% - 1%) = $212.22
However, since we are asked to calculate the stock price after the growth, we need to subtract the plowback earnings from the new stock price:
Price per Share = [$19 + (1% x $21)] / (10% - 1%) - (5% x $21)
Price per Share = $106.61
Therefore, the correct answer is B).

Galaxy Air,previously a No-Growth Firm,has Two Million Shares Outstanding