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 percent.)Due to its newly appointed CEO, Galaxy Air is now able to squeeze out 1 percent annual growth by plowing back 5 percent of earnings. Calculate its stock price per share.

Question

Quizplus · Accepted Answer

Galaxy Air's earnings before growth are $20 million, which results in an earnings per share (EPS) of $10 ($20 million divided by 2 million shares). 
With a growth of 1 percent, Galaxy Air's new earnings are $20.2 million ($20 million x 1.01). 
They are keeping back 5% of earnings for investment ($1.01 million) which leaves a payout of $19.19 million ($20.2 million - $1.01 million). 
The new EPS is $9.595 ($19.19 million divided by 2 million shares). 
Since Galaxy Air's required return (cost of capital) is 10 percent, the price-to-earnings (P/E) ratio is 1/(0.10-0.01) = 11.11. 
The stock price per share is $9.595 x 11.11 = $106.61. Therefore, the correct choice is B.

Galaxy Air, Previously a No-Growth Firm, Has Two Million Shares