Chapter 20, Problem 11QP

Dilution The all-equity firm Metallica Heavy Metal Mining (MHMM) Corporation wants to diversify its operations. Some recent financial information for the company is shown here:

Stock price	$75
Number of shares	65,000
Total assets	$9,400,000
Total liabilities	$4, 100,000
Net income	$980,000

MHMM is considering an investment that has the same PE ratio as the firm. The cost of the investment is $l,500,000, and it will be financed with a new equity issue. The return on the investment will equal MHMM's current ROE. What will happen to the book value per share, the market value per share, and the EPS? What is the NPV of this investment? Does dilution take place?

Summary Introduction

To determine: The effect on the book value per share, market value per share and the earnings per share, the net present value of the investment and do dilution takes place.

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.

Return on Equity:

The return on equity refers to the part of net income, where the company gets profits from the amount invested by the shareholders. The return on equity is a measure of the profitability of a company.

Earning per share:

The earning per share is a measure of the profitability of a company. It represents the portion of the profit of the company which is allocated to each outstanding share of the stock.

Explanation of Solution

Given,

The stock price is $75.

The number of shares is 65,000.

The value of total assets is $9,400,000.

The value of total liabilities is $4,100,000.

The net income is $980,000.

Calculation of the current earnings per share:

The formula to calculate the earnings per share is,

$\text{Current}\text{earnings}\text{per}\text{share}=\frac{\text{Net}\text{income}}{\text{Outstanding}\text{shares}}$

Substitute $980,000 for net income and 65,000 for outstanding shares in the above formula.

$\begin{array}{c}\text{Current}\text{earnings}\text{per}\text{share}=\frac{\$980,000}{65,000}\\ =\$15.08\text{per}\text{share}\end{array}$

Hence, the current earnings per share are $15.08 per share.

Calculation of the new earnings per share:

The formula to calculate the new earnings per share is,

$\text{New}\text{earnings}\text{per}\text{share}=\frac{\text{New}\text{net}\text{income}}{\text{Total}\text{number}\text{of}\text{shares}}$

Substitute $1,257,358 for the net income and 85,000 $\left(65,000+20,000\right)$ for the number of shares in the above formula.

$\begin{array}{c}\text{Earnings}\text{per}\text{share}=\frac{\$1,257,358}{85,000}\\ =\$14.79\text{per}\text{share}\end{array}$

Hence, the earnings per share is $14.79 per share.

The earnings per share decreases by $0.29 $\left(\$15.08-\$14.79\right)$

Calculation of the current book value per share:

The formula to calculate the current book value per share,

$\text{Book}\text{value}\text{per}\text{share}=\frac{\text{Total}\text{equity}}{\text{Total}\text{number}\text{of}\text{shares}}$

Substitute $5,300,000 $\left(\$9,400,000-\$4,100,000\right)$ for the total equity and 65,000 for the total number of shares in the above formula.

$\begin{array}{c}\text{Book}\text{value}\text{per}\text{share}=\frac{\text{Total}\text{equity}}{\text{Total}\text{number}\text{of}\text{shares}}\\ =\frac{\$5,300,000}{65,000}\\ =\$81.54\text{per}\text{share}\end{array}$

The current book value per share is $81.54 per share.

Calculation of the new book value per share:

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

$\text{New}\text{book}\text{value}\text{per}\text{share}=\frac{\text{Total}\text{equity}}{\text{Total}\text{number}\text{of}\text{shares}}$

Substitute $6,800,000 $\left(\$5,300,000+\$1,500,000\right)$ for the total equity and 85,000 for the number of shares in the above formula.

$\begin{array}{c}\text{New}\text{book}\text{value}\text{per}\text{share}=\frac{\$6,800,000}{85,000}\\ =\$80\text{per}\text{share}\end{array}$

Hence, the new book value per share is $80 per share.

The book value per share decreases by $1.54 $\left(\$81.54-\$80\right)$

Calculation of the current market-to-book ratio:

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

$\text{Market-to-book}\text{ratio}=\frac{\text{Current}\text{price}\text{of}\text{share}}{\text{Book}\text{value}\text{per}\text{share}}$

Substitute $75 for the current stock price and $81.54 for the book value per share in the above formula.

$\begin{array}{c}\text{Market-to-book}\text{ratio}=\frac{\text{Current}\text{price}\text{of}\text{share}}{\text{Book}\text{value}\text{per}\text{share}}\\ =\frac{\$75}{\$81.54}\\ =\$0.9198\end{array}$

Hence, the current market-to-book ratio is $0.9198.

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 $73.58 for the new share price and $80 for the new book value per share in the above formula.

$\begin{array}{c}\text{New}\text{market-to-book}\text{ratio}=\frac{\$73.58}{\$80}\\ =\$0.9198\end{array}$

Hence, the new market-to-book ratio is.$0.9198.

The new market to book ratio is same.

Calculation of the net present value:

The formula to calculate the net present value is,

$\text{Net}\text{present}\text{value}=\left(\begin{array}{l}\text{Change in}\text{market}\text{value}\text{of}\text{firm}\\ -\text{Cost of the project}\end{array}\right)$

Substitute $1,379,300 for the change in market value (refer working note) and $1,500,000 for the cost of project in the above formula.

$\begin{array}{c}\text{Net}\text{present}\text{value}=\left(\$1,379,300-\$1,500,000\right)\\ =-\$120,700\end{array}$

Hence, the net present value of the firm is −$120,700.

As the market to book ratio is less than one, Accounting dilution takes place. Also, the firm is investing in a project whose net present value is negative, so the market dilution will take place.

Working note:

Calculation of the total equity:

Calculation of the total equity:

$\begin{array}{c}\text{Total}\text{equity}=\left(\begin{array}{l}\text{Total}\text{assets}\\ -\text{Total}\text{liabilities}\end{array}\right)\\ =\$9,400,000-\$4,100,000\\ =\$5,300,000\end{array}$

The total equity is $5,300,000.

Calculation of the return on equity:

$\begin{array}{c}\text{Return}\text{on}\text{equity}=\frac{\text{Net}\text{income}}{\text{Total}\text{equity}}\\ =\frac{\$980,000}{\$5,300,000}\\ =0.1849\text{or}18.49\%\end{array}$

Hence, the return on equity is 18.49%.

Calculation of the new net income:

$\begin{array}{c}\text{New}\text{net}\text{income}=\frac{\text{Net}\text{income}}{\text{Total}\text{equity}}\times \text{Total}\text{new}\text{equity}\\ =\frac{\$980,000}{\$5,300,000}\times \text{\$6,800,000}\\ =\text{\$1,257,358}\end{array}$

Hence, the new net income is $1,257,358.

Calculation of the number of new shares:

$\begin{array}{c}\text{Number}\text{of}\text{new}\text{shares}=\frac{\text{Cost}\text{of}\text{investment}}{\text{Current}\text{share}\text{price}}\\ =\frac{\$1,500,000}{\$75}\\ =20,000\end{array}$

Hence, the number of new shares is 20,000.

Calculation of the price-earnings ratio:

$\begin{array}{c}\text{Price}\text{earnings}\text{ratio}=\frac{\text{Current}\text{share}\text{price}}{\text{Earnings}\text{per}\text{share}}\\ =\frac{\$75}{\$15.08}\\ =4.974\end{array}$

Hence, the price-earnings ratio is 4.974.

Calculation of the new stock price:

The formula to calculate the new stock price is,

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

Substitute $14.79 for the new earnings per share and 4.974 for the price-earnings (refer working note) in the above formula.

$\begin{array}{c}\text{New}\text{stock}\text{price}=\left(\$14.79\times 4.974\right)\\ =\$73.58\end{array}$

Hence, the new stock price is $73.58.

Calculation of the change in market value of firm:

$\begin{array}{c}\text{Change in}\text{market}\text{value}=\left[\begin{array}{l}\left(\text{Total}\text{number}\text{of}\text{shares}\times \text{New}\text{price}\text{per}\text{share}\right)\\ -\left(\text{Total}\text{number}\text{of}\text{shares}\times \text{Price}\text{per}\text{share}\right)\end{array}\right]\\ \text{=}\left[\left(\text{85,000}\times \text{\$73}\text{.58}\right)-\left(\text{65,000}\times \text{\$75}\right)\right]\\ \text{=\$6,254,300}-\$\text{4,875,000}\\ =\$1,379,300\end{array}$

Hence, the new market value is $1,379,300.

Thus, the book value per share decreases by $1.54, the earnings per share decreases by $0.29 and the market-to-book ratio remains the same. The dilution takes place as the net present value is negative.