Question

Midland Corporation has a net income of \(19 million and 4 million shares outstanding. Its common stock is currently selling for \)48 per share. Midland plans to sell common stock to set up a major new production facility with a net cost of \(21,120,000. The production facility will not produce a profit for one year, and then it is expected to earn a 13 percent return on the investment. Stanley Morgan and Co., an investment banking firm, plans to sell the issue to the public for \)44 per share with a spread of 4 percent.

c. What are the earnings per share (EPS) and the price-earnings ratio before the issue (based on a stock price of $48)? What will be the price per share immediately after the sale of stock if the P/E stays constant?

Short answer

The EPS before the issue is $4.75 and the PE ratio is 10.1 times. The EPS after the issue is $4.22.

Step-by-step solution

Information provided in the question

Net income = $19,000,000

Shares outstanding = $4,000,000

Present selling price = $48 per share

ROI =13 %

Selling price for public issue = $44 per share

Spread = 4%

Calculation of earnings per share before issue

The earnings per share is $4.75.

$\begin{array}{rcl}\mathrm{EPS}& =& \frac{\mathrm{Earnings}}{\mathrm{Stock}\mathrm{outstanding}}\\ & =& \frac{\$19,000,000}{4,000,000}\\ & =& \$4.75\end{array}$

Calculation of PE ratio before issue

The PE ratio is 10.1 times.

$\begin{array}{rcl}\mathrm{PE}& =& \frac{\mathrm{Price}\mathrm{per}\mathrm{share}}{\mathrm{Earning}\mathrm{per}\mathrm{share}}\\ & =& \frac{\$48}{\$4.75}\\ & =& 10.1\mathrm{times}\end{array}$

Calculation of earnings per share after issue

The earnings per share is $4.22.

$\begin{array}{rcl}\mathrm{EPS}& =& \frac{\mathrm{Earnings}}{\mathrm{Stock}\mathrm{outstanding}}\\ & =& \frac{\$19,000,000}{4,000,000+500,000}\\ & =& \$4.22\end{array}$

Calculation of stock price after issue

The stock price with PE ratio of 10.1 times is $42.66.

$\begin{array}{rcl}\mathrm{Price}\mathrm{per}\mathrm{share}& =& \mathrm{PE}\times \mathrm{Earnings}\mathrm{per}\mathrm{share}\\ & =& 10.1\times \$4.22\\ & =& \$42.66\end{array}$