Chapter 26, Problem 8QP

a)

Summary Introduction

To compute: The NPV (Net Present Value) of the merger

Introduction:

A merger is the total absorption of one company by another, where the firm that is acquiring retains its uniqueness and it terminates the other to exist as an individual entity.

Answer to Problem 8QP

The NPV of the merger is $5,200.

Explanation of Solution

Given information: Pre-merger details about Firm B, the bidding firm and Firm T, the targeted firm provides the following information:

• The outstanding shares of Firm B and Firm T are $5,400 and $1,400 respectively.
• The prices for one share of Firm B and Firm T are $47 and $18 respectively.

The synergistic value benefits of Firm T from acquiring Firm B is $9,400.

Formula to calculate the NPV:

$\text{NPV cash}=\text{Value of the target firm}+\text{Synergy value}-\text{Cost of acquistion}$

Calculate the NPV if the price per share for acquisition is $21:

$\begin{array}{c}\text{NPV}=\left(\begin{array}{l}\text{Value of the target firm}\left(\text{Price per share}\right)+\text{Synergy value}-\\ \text{Cost of acquistion}\left(\text{Acquisition price per share}\right)\end{array}\right)\\ =\$1,400\left(\$18\right)+\$9,400-\$1,400\left(\$21\right)\\ =\$5,200\end{array}$

Hence, the NPV is $5,200.

b)

Summary Introduction

To calculate: The price per share

Introduction:

A merger is the total absorption of one company by another, where the firm that is acquiring retains its uniqueness and it terminates the other to exist as an individual entity.

Answer to Problem 8QP

The price per share is $47.96.

Explanation of Solution

Given information: Pre-merger details about Firm B, the bidding firm and Firm T, the targeted firm provides the following information:

• The outstanding shares of Firm B and Firm T are $5,400 and $1,400 respectively.
• The prices for one share of Firm B and Firm T are $47 and $18 respectively.

The synergistic value benefits of Firm T from acquiring Firm B is $9,400.

Formula to calculate the share price:

$\text{Share price}=\frac{\left[\begin{array}{l}\text{Market value of the merger company}\left(\text{Price per share for Firm B}\right)+\\ \text{NPV of the acquisition}\end{array}\right]}{\text{Number of oustanding shares}}$

Calculate the share price:

$\begin{array}{c}\text{Share price}=\frac{\left[\begin{array}{l}\text{Market value of the merger company}\left(\text{Price per share for Firm B}\right)+\\ \text{NPV of the acquisition}\end{array}\right]}{\text{Number of oustanding shares}}\\ =\frac{\left[\$5,400\left(\$47\right)+\$5,200\right]}{\$5,400}\\ =\$47.96\end{array}$

Hence, the share price $47.96.

c)

Summary Introduction

To calculate: The merger premium.

Introduction:

A merger is the total absorption of one company by another, where the firm that is acquiring retains its uniqueness and it terminates the other to exist as an individual entity.

Answer to Problem 8QP

The merger premium is $4,200.

Explanation of Solution

Given information: Pre-merger details about Firm B, the bidding firm and Firm T, the targeted firm provides the following information:

• The outstanding shares of Firm B and Firm T are $5,400 and $1,400 respectively.
• The prices for one share of Firm B and Firm T are $47 and $18 respectively.

The synergistic value benefits of Firm T from acquiring Firm B is $9,400.

Formula to calculate the merger premium:

$\text{Merger premium}=\left[\text{Outstanding shares of Target firm}\left(\begin{array}{l}\text{Cost per share for the target firm}-\\ \text{Price per share for the target firm}\end{array}\right)\right]$

Calculate the merger premium:

$\begin{array}{c}\text{Merger premium}=\left[\text{Outstanding shares of Target firm}\left(\begin{array}{l}\text{Cost per share for the target firm}-\\ \text{Price per share for the target firm}\end{array}\right)\right]\\ =\$1,400\left(\$21-\$18\right)\\ =\$4,200\end{array}$

Hence, the merger premium is $4,200

d)

Summary Introduction

To calculate: The price per share if the merger takes place through the exchange of stock and if the bidding firm offers one share for each of the two target firm’s shares.

Introduction:

A merger is the total absorption of one company by another, where the firm that is acquiring retains its uniqueness and it terminates the other to exist as an individual entity.

Answer to Problem 8QP

The price for one share in the merged firm is $47.28.

Explanation of Solution

Given information: Pre-merger details about Firm B, the bidding firm and Firm T, the targeted firm provides the following information:

• The outstanding shares of Firm B and Firm T are $5,400 and $1,400 respectively.
• The prices for one share of Firm B and Firm T are $47 and $18 respectively.

The synergistic value benefits of Firm T from acquiring Firm B is $9,400.

Formula to calculate the new shares:

$\text{New shares created}=\left(\begin{array}{l}\text{Number of shares of the target firm}\times \\ \text{Exchange ratio}\end{array}\right)$

Calculate the new shares:

$\begin{array}{c}\text{New shares created}=\left(\begin{array}{l}\text{Number of shares of the target firm}\times \\ \text{Exchange ratio}\end{array}\right)\\ =\$1,400\times \frac{1}{2}\\ =\$700\end{array}$

Hence, the created new shares is $700.

Formula to calculate the value of the merged firm:

$\text{Value of the merged firm}=\left[\begin{array}{l}\text{Outstanding shares of the bidding firm}\\ \left(\text{Price per share of bidding firm}\right)+\\ \text{Outstanding shares of the target firm}\\ \left(\text{Price per share of target firm}\right)+\\ \text{Synergistic benefits}\end{array}\right]$

Calculate the value of the merged firm:

$\begin{array}{c}\text{Value of the merged firm}=\left[\begin{array}{l}\text{Outstanding shares of the bidding firm}\\ \left(\text{Price per share of bidding firm}\right)+\\ \text{Outstanding shares of the target firm}\\ \left(\text{Price per share of target firm}\right)+\\ \text{Synergistic benefits}\end{array}\right]\\ =\$5,400\left(\$47\right)+\$1,400\left(\$18\right)+\$9,400\\ =\$2,88,400\end{array}$

Hence, the value of the merged firm is $288,400.

Formula to calculate the price for one share for a merged firm:

$\text{Price per share}=\frac{\text{Value of the merged firm}}{\text{Total shares of new firm}}$

Calculate the price for one share for a merged firm:

$\begin{array}{c}\text{Price per share}=\frac{\text{Value of the merged firm}}{\text{Total shares of new firm}}\\ =\frac{\$288,400}{\$5,400+\$700}\\ =\$47.28\end{array}$

Hence, the price for one share is $47.28.

e)

Summary Introduction

To calculate: The NPV of the merger if the merger takes place through the exchange of stocks and if the bidding firm offers one share for each of the two target firms’ shares

Introduction:

A merger is the total absorption of one company by another, where the firm that is acquiring retains its uniqueness and it terminates the other to exist as an individual entity.

Answer to Problem 8QP

The NPV of the merger is $1,504.92.

Explanation of Solution

Given information:

Pre-merger details about Firm B, the bidding firm and Firm T, the targeted firm provides the following information:

• The outstanding shares of Firm B and Firm T are $5,400 and $1,400 respectively.
• The prices for one share of Firm B and Firm T are $47 and $18 respectively.

The synergistic value benefits of Firm T from acquiring Firm B is $9,400.

Formula to calculate the NPV:

$\text{NPV}=\left[\begin{array}{l}\text{Outstanding shares of the target firm}\\ \left(\text{Price per share of target firm}\right)+\text{Synergistic benefits}-\\ \text{Cost of acquisition }\left(\text{Price per share for the merged firm}\right)\end{array}\right]$

Calculate the NPV:

$\begin{array}{c}\text{NPV}=\left[\begin{array}{l}\text{Outstanding shares of the target firm}\\ \left(\text{Price per share of target firm}\right)+\text{Synergistic benefits}-\\ \text{Cost of acquisition }\left(\text{Price per share for the merged firm}\right)\end{array}\right]\\ =\$1,400\left(\$18\right)+\$9,400-\$700\left(\$47.2786885245901\right)\\ =\$1,504.92\end{array}$

Hence, the NPV is $1,504.92.