Chapter 15, Problem 18P

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.

a. How many shares of stock must be sold to net $\$$ 21,120,000? (Note: No out of-pocket costs must be considered in this problem.)

b. Why is the investment banker selling the stock at less than its current market price?

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?

d. Compute the EPS and the price (P/E stays constant) after the new production facility begins to produce a profit.

e. Are the shareholders better off because of the sale of stock and the resultant investment? What other financing strategy could the company have tried to increase earnings per share?

Summary Introduction

To calculate: The number of shares to be sold at $21,120,000 for Midland Corporation.

Introduction:

Share Price:

The highest price of one share of a company that an investor is willing to pay is termed as the share’s price. It is the current price used for the trading of such shares.

Answer to Problem 18P

The number of shares to be sold at $21,120,000 are 500,000 shares.

Explanation of Solution

The calculation of the number of shares:

$\begin{array}{c}\text{Number of shares}=\frac{\text{Net amount to be raised}}{\text{Net price}}\\ =\frac{\$21,120,000}{\$42.24}\\ =500,000\text{ shares}\end{array}$

Working Note:

The calculation of Net Price:

$\begin{array}{c}\text{Net price}=\text{Public Price}-\text{Spread Price}\\ =\$44-\left(4\%\times 44\right)\\ =\$44-1.76\\ =\$42.24\end{array}$

Summary Introduction

To explain: The reason as to why an investment banker would sell a stock at less than its market price at present for Midland Corporation.

Introduction:

Share Price:

The highest price of one share of a company that an investor is willing to pay is termed as the share’s price. It is the current price used for the trading of such shares.

Answer to Problem 18P

The investment banker is selling the stock at a price lesser than its market price at present for Midland Corporation so as to create a sufficient demand to sell all the shares. Thus, this method increases the demand among the shareholders.

Explanation of Solution

The new shares may increase the total number of outstanding shares and leads to the dilution of EPS. This dilution will reduce the stock price in the market until the income included from the new assets and the market will pay for the stock.

Summary Introduction

To calculate: The EPS and the P/E ratio before the issue and also calculate the price for each share right after the stock is sold, if P/E remains the same.

Introduction:

P/E ratio:

It is calculated by dividing a company’s share price at present by its EPS. It helps in valuing a company’s profitability in the present as well as in the future.

Earnings per share (EPS):

It is the profit per outstanding share of a public company. A higher EPS indicates higher value of the company because investors are ready to pay higher price for one share of the company.

Share Price:

The highest price of one share of a company that an investor is willing to pay is termed as the share’s price. It is the current price used for the trading of such shares.

Answer to Problem 18P

For Midland Corporation, the EPS is $4.75 and P/E ratio is 10.11 times and price per share after the sale of stock is $42.66.

Explanation of Solution

The calculation of EPS:

$\begin{array}{c}\text{EPS}=\frac{\text{Net Income}}{\text{Shares outstanding}}\\ =\frac{\$19,000,000}{\$4,000,000}\\ =\$4.75\end{array}$

The calculation of P/E ratio:

$\begin{array}{c}\text{P/E Ratio}=\frac{\text{Price}}{\text{EPS}}\\ =\frac{\$48}{\$4.75}\\ =10.11\end{array}$

The calculation of price per share:

$\begin{array}{c}\text{Price per share}=\text{P/E Ratio}\times \text{EPS after offering}\\ =10.11\times \$4.22\\ =\$42.66\end{array}$

Working Note:

The calculation of EPS after offering:

$\begin{array}{c}\text{EPS after offering}=\frac{\text{Net Income}}{\text{Total shares outstanding}}\\ =\frac{\$19,000,000}{\$4,500,000}\\ =\$4.22\end{array}$

Summary Introduction

To calculate: The EPS and the price after profit is produced by the new production facility, if the P/E remains the same.

Introduction:

P/E ratio:

It is calculated by dividing a company’s share price at present by its EPS. It helps in valuing a company’s profitability in the present as well as in the future.

Earnings per share (EPS):

It is the profit per outstanding share of a public company. A higher EPS indicates higher value of the company because investors are ready to pay higher price for one share of the company. 

Answer to Problem 18P

For Midland Corporation, the EPS after contribution will be $4.83 and the price per share will be $48.33.

Explanation of Solution

The calculation of EPS after contribution:

$\begin{array}{c}\text{EPS after contribution}=\frac{\text{Net Income after contribution}}{\text{Total shares outstanding}}\\ =\frac{\$21,745,600}{\$4,500,000}\\ =\$4.83\end{array}$

The calculation of Price per share:

$\begin{array}{c}\text{Price per share}=\text{P/E Ratio}\times \text{EPS after contribution}\\ =10.11\times \$4.83\\ =\$48.83\end{array}$

Working Note:

The calculation of net income after contribution:

$\begin{array}{c}\text{Net Income after contribution}=\text{Net Income before contribution}+\text{Earnings percentage}\\ =\$19,000,000+\left(\$21,120,000\times 13\%\right)\\ =\$19,000,000+\$2,745,600\\ =\$21,745,600\end{array}$

Summary Introduction

To determine: Whether the shareholders are at a better state after the sale of stock and the consequential investment. Explain the other financing strategies that can be used by the company in order to increase its EPS.

Introduction:

Earnings per share (EPS):

It is the profit per outstanding share of a public company. A higher EPS indicates higher value of the company because investors are ready to pay higher price for one share of the company.

Share Price:

The highest price of one share of a company that an investor is willing to pay is termed as the share’s price. It is the current price used for the trading of such shares.

Answer to Problem 18P

Yes, the shareholders appear better off because of the stock sale as it generates additional investment and the company could use the combination of debt and equity strategy for increasing its EPS.

Explanation of Solution

The shareholders would appear better in the long term due to the raising of additional investments to the company and if the debt financing or combination of debt and equity might be used by the firm then it may lead to the increment of the EPS of the firm.