Chapter 29, Problem 8QP

Cash versus Stock as Payment Consider the following premerger information about a bidding firm (Firm B) and a target firm (Firm T). Assume that both firms have no debt outstanding.

	Firm B	Firm T
Shares outstanding	8.300	3,400
Price per share	$46	$21

Firm B has estimated that the value of the synergistic benefits from acquiring Firm T is $12,600.

1. a. If Firm T is willing to be acquired for $24 per share in cash, what is the NPV of the merger?
2. b. What will the price per share of the merged firm be assuming the conditions in (a)?
3. c. In part (a), what is the merger premium?
4. d. Suppose Firm T is agreeable to a merger by an exchange of stock. If B offers one of its shares for every two of T s shares, what will the price per share of the merged firm be?
5. e. What is the NPV of the merger assuming the conditions in (d)?

Summary Introduction

To calculate: The NPV of the merger.

Merger:

Merger occurs when the shareholders of two or more companies pool the resources of their company into one separate legal entity and as a result a new company comes into existence. Merger is basically the result of merge of two or more companies into one.

Synergy:

Synergy is a state in which two or more companies are combined to perform better than the sum of their individual efforts in terms of productivity, revenue and so forth.

Net Present Value (NPV):

Net present value is one of the techniques of capital budgeting. Net present value is used to find out the difference between the present value of cash inflow and present value of cash outflow.

Cash vs. Stock Payment Method:

Cash versus stock payment method is one of the methods of payment where the acquiring firm has to decide when do the acquiring firm have to pay with cash or when do the acquiring firm have to pay with stock to the target company.

Purchase Accounting Method for Mergers:

In the purchase accounting method, the assets of the targeted company have to be recorded into the current market value in the books of acquiring company and goodwill assets account have to be created. Goodwill is the difference of current market value and purchase price.

Explanation of Solution

Given,

Synergistic benefits from the acquiring firm T is $12,600.

Calculated,

Market value of the target firm (firm T) is $71,400.

Cost of acquisition is $81,600.

Formula to calculate NPV is as follows:

$\text{NPV}=\text{Market}\text{value}\text{of}\text{target}\text{firm}+\text{Synergistic}\text{benefits}-\text{Cost}\text{of}\text{acquisition}$

Substitute $71,400 for the market value of target firm, $12,600 for synergistic benefits and $81,600 for the cost of acquisition.

$\begin{array}{c}\text{NPV}=\$71,400+\$12,600-\$81,600\\ =\$2,400\end{array}$

The NPV of the merger is $2,400.

Working Notes:

Calculation of market value of target firm (firm T) is as follows:

The given information:

Shares outstanding of firm T are 3,400.

Price per share of firm T is $21.

Formula to calculate the market value of target firm is follows:

$\text{Market}\text{value}\text{of}\text{target}\text{firm}=\text{Shares}\text{outstanding}\times \text{Price}\text{per}\text{share}$

Substitute 3,400 for shares outstanding and $21 for price per share as follows:

$\begin{array}{c}\text{Market}\text{value}\text{of}\text{target}\text{firm}=3,400\times 21\\ =\$71,400\end{array}$

Calculation of cost of acquisition is as follows:

The given information:

Shares outstanding of firm T are 3,400.

Price offer for buying shares of firm T is $24 per share.

Formula to calculate cost of acquisition is as follows:

$\text{Cost}\text{of}\text{acquisition}=\mathrm{Outstanding}shares\times \text{share}\text{price}\text{offered}$

Substitute 3,400 for shares outstanding and $24 for shares price offered as follows:

$\begin{array}{c}\text{Cost}\text{of}\text{acquisition}=3,400\times \$24\\ =\$81,600\end{array}$

Conclusion

Conclusion:-The NPV of the merger is $2,400.

Summary Introduction

To calculate:-The price per share of the merged firm be assuming the condition in (a).

Explanation of Solution

The given information:

Shares outstanding of acquiring firm (firm B) is 8,300.

Calculated as follows:

NPV of the merger is $2,400.

Market value of the acquiring firm (firm B) is $381,800.

Formula to calculate share price of the merged firm is as follows:

$\text{Share}\text{price}\text{of}\text{merged}\text{firm}=\frac{\text{Market}\text{value}\text{of}\text{acquiring}\text{firm}+\text{NPV}\text{of}\text{acquisition}}{\text{Shares}\text{outstanding}\text{of}\text{acquiring}\text{firm}}$

Substitute $381,800 for market value of acquiring firm, $2,400 for NPV of acquisition and 8,300 for shares outstanding.

$\begin{array}{c}\text{Share}\text{price}\text{of}\text{merged}\text{firm}=\frac{\$381,800+\$2,400}{8,300}\\ =\$46.29\end{array}$

The share price of merged firm is $46.29.

Working notes:

Calculation of the market value of acquiring firm is as follows:

The given information:

Shares outstanding of firm B are 8,300.

Price per share of firm B is $46.

Formula to calculate the market value of target firm is as follows:

$\text{Market}\text{value}\text{of}\text{target}\text{firm}=\text{Shares}\text{outstanding}\times \text{Price}\text{per}\text{share}$

Substitute 8,300 for shares outstanding and $46 for price per share as follows:

$\begin{array}{c}\text{Market}\text{value}\text{of}\text{target}\text{firm}=8,300\times 46\\ =\$381,800\end{array}$

Conclusion

Conclusion:- The share price of merged firm is $46.29.

Summary Introduction

To calculate:-The merger premium.

Explanation of Solution

The given information:

Shares outstanding of target firm (firm T) is 3,400

Calculated as follows:

Premium per share is $3.

Formula to calculate merger premium is as follows:

$\text{Merger}\text{premium}=\text{Outstanding}\text{shares}\times \text{Premium}\text{per}\text{share}$

Substitute 3,400 for outstanding shares and $3 for premium per share as follows:

$\begin{array}{c}\text{Merger}\text{premium}=3,400\times \$3\\ =\$10,200\end{array}$

The merger premium is $10,200.

Working notes:

Calculation of premium per share is as follows:

The given information:

Price per share of firm T is $21.

Price offer for buying shares of firm T is $24 per share.

Formula to calculate premium per share is as follows:

$\text{Premium}\text{per}\text{share}=\text{Price}\text{offered}\text{per}\text{share}-\text{Market}\text{price}\text{per}\text{share}$

Substitute $24 for price offered per share and $21 for market price per share as follows:

$\begin{array}{c}\text{Premium}\text{per}\text{share}=\$24-\$21\\ =\$3\end{array}$

Conclusion

The merger premium is $10,200.

Summary Introduction

To compute:-The price per share of merged firm.

Explanation of Solution

Calculated as follows:

Value of merged firm is $465,800.

No of shares outstanding of the merged firm is 10,000.

Formula to calculate price per share of merged company is as follows:

$\text{Price}\text{per}\text{share}\text{of}\text{merged}\text{firm}=\frac{\text{Value}\text{of}\text{merged}\text{firm}}{\text{No}\text{of}\text{shares}\text{outstanding}\text{of}\text{merged}\text{firm}}$

Substitute $465,800 for value of merged firm and 10,000 for no of shares outstanding of merged firm as follows:

$\begin{array}{c}\text{Price}\text{per}\text{share}\text{of}\text{merged}\text{firm}=\frac{\$465,800}{10,000}\\ =\$46.58\end{array}$

The price per share of merged firm is $46.58.

Working notes:

Calculation of value of merged firm is as follows:

The given information:

Synergistic benefits are $12,600.

Calculated as follows:

Market value of acquiring firm (firm B) is $381,800.

Market value of target firm is (firm T) is $71,400.

Formula to calculate the value of merged firm is as follows:

$\text{Value}\text{of}\text{merged}\text{firm}=\left[\begin{array}{l}\text{Market}\text{value}\text{of}\text{acquiring}\text{firm}\\ +\text{Market}\text{value}\text{of}\text{target}\text{firm}\\ \text{+Synergistic}\text{benefits}\end{array}\right]$

Substitute $381,800 for market value of acquiring firm, $71,400 for market value of target firm and $12,600 for synergistic benefits.

$\begin{array}{c}\text{Value}\text{of}\text{merged}\text{firm}=\$381,800+\$71,400+\$12,600\\ =\$465,800\end{array}$

Calculation of no of outstanding shares of merged firm is as follows:

The given information:

Shares outstanding of acquiring firm (firm B) are 8,300.

Shares outstanding of target firm (firm T) are 3,400.

Firm B offers one of its shares for every two of T’s share, therefore the exchange ratio will be 1:2.

Formula to calculate total no of shares outstanding of merged firm is as follows:

$\text{Total}\text{no}\text{of}\text{shares}\text{outstanding}=\left[\begin{array}{l}\text{Shares}\text{outstanding}\text{of}\text{acquiring}\text{firm}\\ +\left(\begin{array}{l}\text{Shares}\text{outstanding}\text{of}\text{target}\text{firm}\\ \times \text{Exchange}\text{ratio}\end{array}\right)\end{array}\right]$

Substitute 8,300 for shares outstanding of acquiring firm, 3,400 for shares outstanding of target firm and 1:2 as exchange ratio.

$\begin{array}{c}\text{Total}\text{no}\text{of}\text{shares}\text{outstanding}=8300+\left(3400\times \frac{1}{2}\right)\\ =10,000\end{array}$

Conclusion

The price per share of merged firm is $46.58.

Summary Introduction

To calculate:-NPV of merger assuming conditions in (d).

Explanation of Solution

The given information:

Synergistic benefits from acquiring firm T is $12,600.

Calculated as follows:

Market value of the target firm (firm T) is $71,400.

Cost of acquisition is $79,186.

Formula to calculate NPV is as follows:

$\text{NPV}=\text{Market}\text{value}\text{of}\text{target}\text{firm}+\text{Synergistic}\text{benefits}-\text{Cost}\text{of}\text{acquisition}$

Substitute $71,400 for the market value of target firm, $12,600 for synergistic benefits and $81,600 for the cost of acquisition.

$\begin{array}{c}\text{NPV}=\$71,400+\$12,600-\$79,186\\ =\$4,814\end{array}$

The NPV of the merger is $4,814.

Working Notes:

Calculation of market value of target firm (firm T) is as follows:

The given information:

Shares outstanding of firm T are 3,400.

Price per share of firm T is $21.

Formula to calculate market value of target firm is as follows:

$\text{Market}\text{value}\text{of}\text{target}\text{firm}=\text{Shares}\text{outstanding}\times \text{Price}\text{per}\text{share}$

Substitute 3,400 for shares outstanding and $21 for price per share as follows:

$\begin{array}{c}\text{Market}\text{value}\text{of}\text{target}\text{firm}=3,400\times 21\\ =\$71,400\end{array}$

Calculation of cost of acquisition is as follows:

The given information:

B offers one of its shares for every two of T’s share, therefore the exchange ratio will be 1:2.

Shares outstanding of firm T are 3,400.

Shares offer to firm T will be 1700(3400*1/2)

Price offer for buying shares of firm T is $46.58 per share.

Formula to calculate cost of acquisition is as follows:

$\text{Cost}\text{of}\text{acquisition}=\mathrm{Outstanding}shares\times \text{share}\text{price}\text{offered}$

Substitute 1,700 for shares outstanding and $46.58 for shares price offered as follows:

$\begin{array}{c}\text{Cost}\text{of}\text{acquisition}=1,700\times \$46.58\\ =\$79,186\end{array}$

Conclusion

The NPV of the merger is $4,814.