Chapter 21, Problem 5QP

a.

Summary Introduction

To determine: The EPS of the merged firm.

Answer to Problem 5QP

The EPS of the merged firm is $4.20.

Explanation of Solution

Determine the EPS and total earnings of Company CS

$\begin{array}{c}EP{S}_{CompanyCS}=\left[\frac{Share\mathrm{Pr}ice}{PERatio}\right]\\ =\left[\frac{\$40}{\$10}\right]\\ =\$4\\ \\ TotalEarnings=\left[EPS\times SharesOuts\tan ding\right]\\ =\left[\$4\times 2,000,000\right]\\ =\$8,000,000\end{array}$

Therefore, the EPS is $4 and total earnings is $8,000,000.

Determine the EPS and total earnings of Company FF

$\begin{array}{c}EP{S}_{CompanyFF}=\left[\frac{Share\mathrm{Pr}ice}{PERatio}\right]\\ =\left[\frac{\$20}{\$8}\right]\\ =\$2.50\\ \\ TotalEarnings=\left[EPS\times SharesOuts\tan ding\right]\\ =\left[\$2.50\times 1,000,000\right]\\ =\$2,500,000\end{array}$

Therefore, the EPS is $2.50 and total earnings is $2,500,000.

Determine the EPS of the merged firm

$\begin{array}{c}EP{S}_{MergedFirm}=\left[\frac{TotalEarnings}{TotalShares}\right]\\ =\left[\frac{\$8,000,000+\$2,500,000}{2,000,000+\left(\frac{1,000,000}{2}\right)}\right]\\ =\left[\frac{\$10,500,000}{2,500,000}\right]\\ =\$4.20\end{array}$

Therefore, the EPS of merged firm is $4.20.

b.

Summary Introduction

To determine: The price per share of Company CS.

Answer to Problem 5QP

The price per share of Company CS is $40.

Explanation of Solution

Determine the price per share of Company CS

$\begin{array}{c}\mathrm{Pr}icepershar{e}_{CompanyCS}=\left[\frac{TotalValue}{TotalShares}\right]\\ =\left[\frac{\left(\$40\times 2,000,000\right)+\left(\$20\times 1,000,000\right)}{2,000,000+\left(\frac{1,000,000}{2}\right)}\right]\\ =\left[\frac{\$100,000,000}{2,500,000}\right]\\ =\$40\end{array}$

Therefore, the price per share of Company CS is $40.

c.

Summary Introduction

To discuss: The demonstration of Company CS or Company FF realize any change in wealth.

Answer to Problem 5QP

The value of Company CS and Company FF is Unchanged.

Explanation of Solution

• Company FF have a stock worth of $20,000,000 ($40*500,000 shares), so the wealth of Company FF is unchanged.
• The wealth of Company CS is also unchanged.

Therefore, the value of Company CS and Company FF is Unchanged.

d.

Summary Introduction

To determine: The P/E ratio of new firm if there are no economic gains.

Answer to Problem 5QP

The P/E ratio of new firm if there are no economic gains is 9.52.

Explanation of Solution

Determine the P/E ratio of new firm if there are no economic gains

The P/E ratio of the merged firm is between the P/E ratio of the two firms.

$\begin{array}{c}PEofMergedFirm=\left[\frac{TotalValue}{TotalEarnings}\right]\\ =\left[\frac{\$100,000,000}{\$10,500,000}\right]\\ =9.52381or9.52\end{array}$

Therefore, the P/E ratio of new firm if there are no economic gains is 9.52.

e.

Summary Introduction

To determine: The price per share of Company CS.

Answer to Problem 5QP

The price per share of Company CS is $42.

Explanation of Solution

If the P/E ratio of Company CS remains constant at 10, then the merged firm will the share price at $42 per share ($4.20*10). This will result in an increase in the firm value to $105,000,000 ($42*2,500,000).

Therefore, price per share of Company CS is $42.

f.

Summary Introduction

To determine: The gains from the merger split between shareholders of the two firms.

Answer to Problem 5QP

The gain of Company CS is $4,000,000 and Company CS is $1,000,000.

Explanation of Solution

Determine the gain of Company CS and Company FF

$\begin{array}{c}Gai{n}_{CompanyCS}=\left[\mathrm{Pr}icepershare\times SharesOuts\tan ding\right]\\ =\left[\$2\times 2,000,000\right]\\ =\$4,000,000\\ \\ Gai{n}_{CompanyFF}=\left[ValueofShares-ActualFirmValue\right]\\ =\left[\left(\$42\times 500,000\right)-\$20,000,000\right]\\ =\$1,000,000\end{array}$

Therefore, the gain of Company CS is $4,000,000 and Company CS is $1,000,000.