Chapter 15, Problem 9QP

a)

Summary Introduction

To find: The effect on issuing the new equity to fund the investment by assuming the constant price-earnings ratio.

Introduction:

Dilution is the loss in present shareholders value with respect to percentage ownership, market value of the shares they hold, or, reduction in the book value or earnings per share.

Answer to Problem 9QP

The new book value of a share is $12.41, the new total earnings is $0.64 per share, the new earnings per share is $0.64, the new price of the stock is $30.78, the new market to book ratio is 2.481, and the net present value is - $1,419,354.85.

Explanation of Solution

Given information:

Company T wants to expand their facilities. The current outstanding shares of the company is 5 million with no debts. The selling price of the share is $31 for a share and the book value of the share is $7. The current net income is $3.2 million. The cost of the new facility is $45 million and will rise the net income by $900,000.

Explanation:

In this case of Company E, the company already has 5,000,000 outstanding shares and wishes to raise $45,000,000 to finance the new facility. The market value of the share is $31 per share.

Hence, at this price per share, Company E will add 1,451,612.903 $\left(\frac{\$45,000,000}{\$31}\right)$ number of new shares and therefore the total number of outstanding shares after rights offering would be 6,451,612.903 $\left(5,000,000+1,451,612.903\right)$.

Hence, the total number of new shares after the rights offering is 6,451,612.903.

Formula to calculate the new book value after the rights offering:

$\text{New book value per share}=\frac{\left(\begin{array}{l}\text{Pre-rights offering share value}\\ +\text{Share value of rights offerings}\end{array}\right)}{\text{Ex-rights outstanding shares}}$

Note: The ex-rights outstanding shares are the total number of new shares after the rights offering.

Computation of the new book value after the rights offering:

$\begin{array}{c}\text{New book value per share}=\frac{\left(\begin{array}{l}\text{Pre-rights offering share value}\\ +\text{Share value of rights offerings}\end{array}\right)}{\text{Ex-rights outstanding shares}}\\ =\frac{\left\{\left(5,000,000\times \$7\right)+\left(1,451,612.903\times \$31\right)\right\}}{6,451,612.903}\\ =\text{\$12}\text{.41}\end{array}$

Hence, the new book value after the rights offering is $12.41.

Formula to compute the current earnings per share:

$\text{Curent EPS}=\frac{\text{Current net income}}{\text{Current outstanding share numbers}}$

Computation of the current earnings per share:

$\begin{array}{c}\text{Curent EPS}=\frac{\text{Current net income}}{\text{Current outstanding share numbers}}\\ =\frac{\$3,200,000}{5,000,000}\\ =\text{\$0}\text{.64 per share}\end{array}$

Hence, the current earnings per share is $0.64.

Formula to calculate the P/E (price earnings) ratio:

$\text{Price earnings ratio}=\frac{\text{Market price of the share}}{\text{EPS}}$

Computation of the P/E (price earnings) ratio:

$\begin{array}{c}\text{Price earnings ratio}=\frac{\text{Market price of the share}}{\text{EPS}}\\ =\frac{\$31}{\$.64}\\ =\text{48}\text{.44 times}\end{array}$

Hence, the P/E ratio is 48.44 times.

Computation of the new earnings per share if there is an increase in the net income by $900,000:

Now, when the net income rises by $900,000, the earnings per share (EPS) would vary. The new net income would be $4,100,000 $\left(\$3,200,000+\$900,000\right)$ which is the total of the current net income and the rise in the net income. The total outstanding shares would be 6,451,612.903. Compute the new EPS as follows:

$\begin{array}{c}\text{New EPS}=\frac{\text{Increased net income}}{\text{Total number of outstanding shares}}\\ =\frac{\$4,100,000}{6,451,612.903}\\ =\text{\$0}\text{.64 per share}\end{array}$

Hence, the new earnings per share is $0.64.

Formula to calculate the new price of the share:

$\text{New share price}=\text{P/E}\times \text{New EPS}$

Note: The price earning ration is constant.

Computation of the new price of the share:

$\begin{array}{c}\text{New share price}=\text{P/E}\times \text{New EPS }\\ =\text{48}\text{.44}\times \text{\$0}\text{.64 }\\ =\text{\$30}\text{.78}\end{array}$

Hence, the new price of the share is $30.78.

Formula to calculate the current market-to-book ratio:

$\text{ Current market-to-book ratio}=\frac{\text{Current market value of the share}}{\text{Book value of the share}}$

Computation of the current market to book ratio:

$\begin{array}{c}\text{ Current market-to-book ratio}=\frac{\text{Current market value of the share}}{\text{Book value of the share}}\\ =\frac{\$31}{\$7}\\ \text{= 4}\text{.4286}\end{array}$

Hence, the market-to-book ratio is 4.4286.

Formula to compute the new market to book ratio:

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

Computation of the new market to book ratio:

$\begin{array}{c}\text{New market-to-book ratio}=\frac{\text{New share price }}{\text{New book value of the share}}\\ =\frac{\$30.78}{\$12.41}\\ =\text{2}\text{.481}\end{array}$

Hence, the new market-to-book ratio is 2.481.

Computation of the net present value:

The operating performance after the new facility financing seems to be unsatisfactory for Company E as it gives a negative net present value (NPV). Compute this by adding the cost of the new facility to the difference between the new market value of the company and the current market value of the company, which is as follows:

$\begin{array}{l}\text{Net Present Value}\left(\text{NPV}\right)=-\text{Cost of the new facility}+\\ \left(\text{New market value}-\text{Current market value of the company}\right)\\ \text{Or, NPV}\text{}=-\text{\$45,000,000}+\left\{\left(6,451,612.903\times \$30.78\right)-\left(5,000,000\times \$31\right)\right\}\\ \text{Or, NPV}\text{}=\text{ -\$1,419,354}\text{.85}\end{array}$

Hence, the net present value is - $1,419,354.85.

b)

Summary Introduction

To find: The new net income of the company.

Introduction:

Dilution is the loss in present shareholders value with respect to percentage ownership, market value of the shares they hold, or, reduction in the book value or earnings per share.

Answer to Problem 9QP

The new net income of the company is $4,129,032.26.

Explanation of Solution

Given information:

Company T wants to expand their facilities. The current outstanding shares of the company is 5 million with no debts. The selling price of the share is $31 for a share and the book value of the share is $7. The current net income is $3.2 million. The cost of the new facility is $45 million and will rise the net income by $900,000.

Formula to calculate the net income:

$\text{Net income}=\text{Total number of shares}\times \text{EPS }$

Computation of the new net income:

For Company E, since the price earnings ratio remains the same, the earnings per share must also remain unchanged. With the total number of outstanding shares of 6,551,724 and with the EPS of $0.64(unchanged), the new net income is calculated as follows:

$\begin{array}{c}\text{Net income}=\text{Total number of shares}\times \text{EPS }\\ =\text{6,451,612}\text{.903}\times \text{\$}\text{.64 }\\ =\text{ \$4,129,032}\text{.26}\end{array}$

Hence, the new net income is $4,129,032.26.