Chapter 15, Problem 10QP

Summary Introduction

To find: The book value for a share, the market value for a share, and the earnings per share. The net present value of the investment and also determine whether the dilution takes place.

Introduction:

Dilution refers to the loss for the existing shareholders value in respect of percentage ownership, market value of the shares they hold, or, reduction in the book value or earnings per share.

Answer to Problem 10QP

The book value for a share is $135.85, the market value for a share is $0.5478, the earnings per share is $26.58, and the net present value is - $384,348.

Explanation of Solution

Given information:

Company M wishes to diversify their operation. The company is looking at an investment that has the similar price earnings ratio as the company. The investment cost is $850,000 and it is funded with the new equity issue. The return on investment is equal to the return on equity (ROE) of the company. The recent financial information of the company are as follows:

• The price of the stock is $85
• The number of shares is 30,000
• The total liabilities is $3,400,000
• The total assets is $8,000,000
• The net income is $900,000

Explanation:

Formula to calculate the owner’s equity:

$\text{Owners' equity = Total assets - Total liabilities }$

Note: The owner’s equity is calculated in order to determine the return on equity (ROE)

Computation of the owner’s equity:

$\begin{array}{c}\text{Owners' equity = Total assets - Total liabilities }\\ \text{= \$8,000,000 - \$3,400,000 }\\ \text{= \$4,600,000}\end{array}$

Hence, the owner’s equity is $4,600,000.

Formula to calculate the return on equity:

$\text{ROE}=\frac{\text{Net income}}{\text{Owners' equity}}$

Computation of the return on equity (ROE):

$\begin{array}{c}\text{ROE}=\frac{\text{Net income}}{\text{Owners' equity}}\\ =\frac{\$900,000}{\$4,600,000}\\ =\text{ 0}\text{.1957 }\end{array}$

Hence, the ROE is 0.1957 or 19.57%.

Computation of the new net income:

Since the return on investment will be the same as the current ROE, compute the new net income below using the formula of the ROE used above:

The owners’ equity will comprise the new investment for the calculation of the ROE

$\begin{array}{c}\text{ ROE}\text{}\text{ = }\frac{\text{Net income}}{\text{Owners' equity}}\\ \text{ Net income = ROE}\times \text{Owners' equity }\\ \text{Net income = }\text{.1957}\times \left(\$4,600,000+\$850,000\right)\\ \text{ Net income = \$1,066,304}\end{array}$

Hence, the new net income $1,066,304.

Formula to compute the current earnings per share:

$\text{EPS}=\frac{\text{Net income}}{\text{Shares outstanding}}$

Computation of the earnings per share:

$\begin{array}{c}\text{EPS}=\frac{\text{Net income}}{\text{Shares outstanding}}\\ =\frac{\$900,000}{30,000}\\ =\text{\$30}\text{.00 per share}\end{array}$

Hence, the earnings per share is $30 for a share.

Formula to calculate the number of the new shares to be issued:

$\text{New shares to be issued}=\frac{\text{Required investment}}{\text{Current market price per share}}$

Note: The required investment is $850,000.

Computation of the number of the new shares to be issued:

$\begin{array}{c}\text{New shares to be issued}=\frac{\text{Required investment}}{\text{Current market price per share}}\\ =\frac{\$850,000}{\$84}\\ =\text{10,119 shares}\end{array}$

Hence, the new shares to be issued is 10,119 shares.

Computation of the earnings per share after the stock issue:

$\begin{array}{c}\text{EPS}\text{}=\frac{\text{New net income}}{\text{Total outstanding shares}}\\ =\frac{\$1,066,304}{\left(30,000+10,119\right)}\\ \text{= }\frac{\$1,066,304}{40,119}\\ \text{ = \$26}\text{.58 }\end{array}$

Hence, the earnings per share after the stock issue is $26.58.

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

$\text{Price Earnings ratio}=\frac{\text{Current market price of the share}}{\text{EPS}}$

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

$\begin{array}{c}\text{P/E ratio = }\frac{\text{Current market price per share}}{\text{Current EPS}}\\ \text{= }\frac{\$84}{\$30}\\ \text{= 2}\text{.800}\end{array}$

Hence, the price earnings ratio is 2.800.

Formula to calculate the new stock price for a share:

$\text{Current market price per share}=\text{P/E ratio}\times \text{Post stock offer EPS}$

Computation of the new stock price for a share:

The price earnings ratio remains the same and the new stock price of the company after the stock offer is calculated as follows:

$\begin{array}{c}\text{Current market price per share}=\text{P/E ratio}\times \text{Post stock offer EPS}\\ =\text{2}\text{.800}\times \text{ \$26}\text{.58}\\ =\text{\$74}\text{.42}\end{array}$

Hence, the new price of the stock is $74.42.

Formula to calculate the current book value for a share:

$\text{Current book value = }\frac{\text{Owners' equity}}{\text{Number of outstanding shares}}$

Computation of the current book value for a share:

$\begin{array}{c}\text{Current book value = }\frac{\text{Owners' equity}}{\text{Number of outstanding shares}}\\ =\frac{\$4,600,000}{30,000}\\ =\text{\$153}\text{.33 per share}\end{array}$

Hence, the current book value of a share is $153.33.

Formula to calculate the new book value for a share:

$\text{New book value per share}=\frac{\text{Owners' equity}}{\text{Number of outstanding shares}}$

Computation of the new book value for a share:

$\begin{array}{c}\text{New book value per share}=\frac{\text{Owners' equity}}{\text{Number of outstanding shares}}\\ =\frac{\$4,600,000+\$850,000}{40,119}\\ =\frac{\$5,450,000}{40,119}\\ =\text{\$135}\text{.85 per share}\end{array}$

Hence, the new book value of a share is $135.85.

Formula to calculate the market to book value before the stock offer:

$\text{ Market-to-book value}=\frac{\text{Market value per share}}{\text{Book value per share}}$

Computation of the market to book value after the stock offer:

$\begin{array}{c}\text{ Market-to-book value}=\frac{\text{Market value per share}}{\text{Book value per share}}\\ =\frac{\$74.42}{\$135.85}\\ =\text{\$}\text{.5478}\end{array}$

Hence, the market to book value after the stock offer is $0.5478.

Computation of the net present value of the new investment:

The net present value is determined by adding the cost of the new investment with the difference between the new market value of the company and the current market value of the company.

$\begin{array}{l}\text{NPV }=-\text{850,000}+\left\{\left(\$74.42\times 40,119\right)-\left(\$84\times 30,000\right)\right\}\\ \text{NPV }=-\text{\$384,348}\end{array}$

Hence, the net present value is - $384,348.

Explanation:

In this case of Company M, the dilution had taken place after the investment made in the diversification projects due to the following reasons:

• The market-to-book ratio is less than one.
• The NPV of the new project investment for Company M is negative.