Chapter 20, Problem 10QP

Dilution Teardrop, Inc., wishes to expand its facilities. The company currently has 6.8 million shares outstanding and no debt. The stock sells for S65 per share, but the book value per share is $20. Net income for Teardrop is currently $11.5 million. The new facility will cost $30 million, and it will increase net income by $675,000. The par value of the stock is $1 per share.

1. a. Assuming a constant price-earnings ratio, what will the effect be of issuing new equity to finance the investment? To answer, calculate the new book value per share, the new total earnings, the new EPS, the new stock price, and the new market-to-book ratio. What is going on here?
2. b. What would the new net income for Teardrop have to be for the stock price to remain unchanged?

Summary Introduction

To determine: The effect of issuing new equity to investment, new book value per share, new total earnings, new earnings per share, new stock price, new market-to-book ratio.

Dilution:

The dilution is a process or action, where the ownership percentage of a shareholder gets reduced due to the issue of new shares. As the number of outstanding shares gets increased, the par value of the company gets decreased.

Explanation of Solution

Given,

The number of outstanding shares is 6,800,000.

The price at which company wants to sell the outstanding share is $65.

The book value is $20.

The net income is $11.5 million.

The cost of the new facility is $30 million.

The net income increases by $675,000.

The par value of the stock is $1 per share.

Calculation of the new book value per share:

The formula to calculate the new book value per share is,

$\text{New}\text{book}\text{value}\text{per}\text{share}=\frac{\left(\begin{array}{l}\text{Value}\text{of}\text{shares}\text{outstanding}\\ +\text{Value}\text{of}\text{shares}\text{to}\text{sell}\end{array}\right)}{\text{The}\text{number}\text{of}\text{shares}\text{after}\text{offering}}$  

Substitute $136,000,000 for the value of shares outstanding , $29,999,970 for value of shares to sell  and 7,261,538 for the number of shares after offering (refer working note) in the above formula.

$\begin{array}{c}\text{New}\text{book}\text{value}\text{per}\text{share}=\frac{\left(\$136,000,000+\$29,999,970\right)}{7,261,538}\\ =\frac{\$165,999,970}{7,261,538}\\ =\$22.86\end{array}$

The new book value per share is $22.86.

Calculation of the new earnings per share:

The formula to calculate the new earnings per share is,

$\text{New}\text{earnings}\text{per}\text{share}=\frac{\text{New}\text{net}\text{income}}{\text{Shares}\text{outstanding}}$

Substitute $12,175,000 $\left(\$11,500,000+\$675,000\right)$ for the new net income and 7,261,538 for the number of shares in the above formula.

$\begin{array}{c}\text{New}\text{earnings}\text{per}\text{share}=\frac{\$12,175,000}{7,261,538}\\ =\$1.68\text{per}\text{share}\end{array}$

The new earnings per share are $1.68 per share.

Calculation of the price-earnings ratio:

The formula to calculate the price/earnings ratio is,

$\text{Price-earnings ratio}=\frac{\text{Price}\text{of}\text{each}\text{share}}{\text{Earning}\text{per}\text{share}}$

Substitute $65 for the price of each share and $1.68 for earning per share (refer working note) in the above formula.

$\begin{array}{c}\text{Price}\text{earnings}=\frac{\$65}{\$1.68}\\ =\$38.69\end{array}$

The price-earnings are $38.69.

Calculation of the new stock price:

The formula to calculate the new stock price is,

$\text{New}\text{stock}\text{price}=\left(\begin{array}{l}\text{New}\text{earnings}\text{per}\text{share}\\ \times \text{Price}\text{earnings}\end{array}\right)$

Substitute $1.68 for the new earnings per share and $38.69 for the price-earnings in the above formula.

$\begin{array}{c}\text{New}\text{stock}\text{price}=\left(\$1.68\times \$38.69\right)\\ =\$65\end{array}$

The new stock price will be same as before that is $65.

Calculation of the new market-to-book ratio:

The formula to calculate the new market-to-book ratio is,

$\text{New}\text{market-to-book}\text{ratio}=\frac{\text{New}\text{share}\text{price}}{\text{New}\text{book}\text{value}\text{per}\text{share}}$

Substitute $64.61 for the new share price and $22.86 for the new book value per share in the above formula.

$\begin{array}{c}\text{New}\text{market-to-book}\text{ratio}=\frac{\text{New}\text{share}\text{price}}{\text{New}\text{book}\text{value}\text{per}\text{share}}\\ =\frac{\$64.61}{\$22.86}\\ =2.82\end{array}$

The new market-to-book ratio is 2.82.

Calculation of the net present value:

The formula to calculate the net present value is,

$\text{Net}\text{present}\text{value}=\left(\begin{array}{l}\text{New}\text{market}\text{value}\text{of}\text{firm}\\ -\text{Current}\text{market}\text{value}\text{of}\text{firm}\end{array}\right)$

Substitute $30,000,000 for the new market value and $27,167,970 for the current market value of the firm (refer working note) in the above formula.

$\begin{array}{c}\text{Net}\text{present}\text{value}=\left(-\$30,000,000-\$27,167,970\right)\\ =-\$57,167,970\end{array}$

The net present value of the firm is ($57,167,970).

Working note:

Calculation of the current value of outstanding shares,

$\begin{array}{c}\text{Current}\text{value}\text{of}\text{outstanding}\text{shares}=\left(\begin{array}{l}\text{Number}\text{of}\text{shares}\\ \times \text{Price}\text{of}\text{each}\text{outstanding}\text{share}\end{array}\right)\\ =6,800,000\times \$20\\ =\$136,000,000\end{array}$

The current value of outstanding shares is $136,000,000.

Calculation of the number of shares issue,

$\begin{array}{c}\text{Number of Shares Issue}=\frac{\text{Amount Required}}{\text{Market Price of Share}}\\ =\frac{30,000,000}{\$65}\\ =461,538.5\text{shares}\end{array}$

The number of shares to be issued is 461,538.5 shares.

Calculation of the value of shares to be sold:

$\begin{array}{c}\text{Values}\text{of}\text{shares}\text{to}\text{be}\text{sold}=\left(\begin{array}{l}\text{Number}\text{of}\text{shares}\text{to}\text{be}\text{sold}\\ \times \text{Price}\text{per}\text{share}\end{array}\right)\\ =461,538\times \$65\\ =\$29,999,970\end{array}$

The value of shares to be sold is $29,999,970.

Calculation of the number of shares after offering,

$\begin{array}{c}\text{Number}\text{of}\text{shares}\text{after}\text{offering}=\left[\begin{array}{l}\text{Current}\text{shares}\text{outstanding}\\ +\text{Number of shares issued}\end{array}\right]\\ =6,800,000+461,538\\ =7,261,538\end{array}$

Calculation of the current earnings per share,

$\begin{array}{c}\text{Current}\text{earnings}\text{per}\text{share}=\frac{\text{Net}\text{income}}{\text{Shares}\text{outstanding}}\\ =\frac{11,500,000}{6,800,000}\\ =\$1.69\text{per}\text{share}\end{array}$

The current earnings per share are $1.69 per share.

Calculation of the current market-to-book ratio,

$\begin{array}{c}\text{Market-to-book}\text{ratio}=\frac{\text{Current}\text{price}\text{of}\text{share}}{\text{Book}\text{value}\text{per}\text{share}}\\ =\frac{\$65}{\$20}\\ =3.25\end{array}$

The current market-to-book ratio is 3.25.

Calculation of the current market value of the firm,

$\begin{array}{c}\text{Current}\text{market}\text{value}\text{of}\text{the}\text{firm}=\left[\begin{array}{l}\left(\begin{array}{l}\text{Number}\text{of}\text{shares}\\ \text{after}\text{offering}\times \text{New}\text{share}\text{price}\end{array}\right)\\ -\left(\text{Outstanding}\text{shares}\times \text{Price}\text{of}\text{each}\text{share}\right)\end{array}\right]\\ =\left[\left(7,261,538\times \$64.61\right)-\left(6,800,000\times \$65\right)\right]\\ =\$469,167,970.18-\$442,000,000\\ =\$27,167,970\end{array}$

The current market value of the firm is $27,167,970.

Conclusion

Thus, the new book value per share is $22.86, new earnings per share are $1.68 per share, new price earnings is $38.46, the new stock price is $64.61, a new market to book ratio is 2.82 and new net present value is ($57,167,970).

Summary Introduction

To determine: The new net income if the stock price remains unchanged.

Explanation of Solution

Given,

The number of outstanding shares is 7,261,538.

The earning per share is $1.69.

Calculation of the new net income:

The formula to calculate the new net income is,

$\text{New}\text{net}\text{income}=\left(\begin{array}{l}\text{Number}\text{of}\text{outstanding}\text{shares}\\ \times \text{Earning}\text{per}\text{share}\end{array}\right)$

Substitute 7,261,538 for the number of outstanding shares and $1.69 for the earning per share in the above formula.

$\begin{array}{c}\text{New}\text{net}\text{income}=7,261,538\times \$1.69\\ =\$12,271,999.22\end{array}$

The new net income is $12,271,999.22.

Conclusion

Thus, the new net income is $12,271,999.22.