Question

World Enterprises is determined to report earnings per share of $2.05. It therefore acquires the Wheelrim and Axle Company. You are given the following facts:

	World Enterprises				Wheelrim and Axle				Merged Firm
Earnings per share		$	1.50			$	2.00			$2.05
Price per share		$	30.00			$	20.00			?
Price–earnings ratio			20				10			?
Number of shares			110,000				200,000			?
Total earnings		$	165,000			$	400,000			?
Total market value		$	3,300,000			$	4,000,000			?

There are no gains from merging. In exchange for Wheelrim and Axle shares, World Enterprises issues just enough of its own shares to ensure its $2.05 earnings per share objective.

Required:

1. Complete the below table for the merged firm.
2. How many shares of World Enterprises are exchanged for each share of Wheelrim and Axle?
3. What is the cost of the merger to World Enterprises?
4. What is the change in the total market value of the World Enterprises shares that were outstanding before the merger?

Answer 1

Q1. Complete the above table.

Ans.

World Enterprises

Wheelrim and Axle

Merged Firm

Earnings per share

$1.50

$2

$2.05

Price per share

$30

$20

$26.487   (refer note 4)

Price–earnings ratio

20

10

12.92     (refer note 5)

Number of shares

110,000

200,000

275,610 (refer note 2)

Total earnings

$165,000

$400,000

$565,000 (refer note 1)

Total market value

$3,300,000

$4,000,000

$7,300,000 (refer note 3)

Note 1 - As there are no gains from merging the total earnings of the merged firm would be $165,000 + $400,000 = $565,000

Note 2 - Total number of shares of the merged firm = Total Earnings / Earnings per share

=

565,000/2.05

=

275609.756

=

275610

Note 3 - Total market value of the merger firm = $3,300,000 + $4,000,000 = $7,300,000

Note 4 - Price per share of the merged firm = Total Value of the merged firm / Number of shares of the merged firm

=

$7300000/275610

=

26.487

Note 5 - Price Earning Ratio = Price per share/ Earnings per share

=

26.487/2.05

=

12.92

Q2. How many shares of World Enterprises are exchanged for each share of Wheelrim and Axle?

Ans.

Total number of shares of merged firm = 275,610

Shares held by shareholders of World enterprises = 110,000

Shares issued to shareholders of Wheelrim and Axle= 275,610-110,000

=

165,610

Exchange ratio = 165610/ 200000

=

82.8%

Q3. What is the cost of the merger to World Enterprises?

Ans.

Cost of merger = No of shares to be issued to vendor company/ Total number of shares of merged company * Value of merged firm - Value of Vendor firm

=

165610/275610*7,300,000- 4,000,000

=

$386,463

Q4. What is the change in the total market value of the World Enterprises shares that were outstanding before the merger?

Ans.

Change in Total market value of the shareholders of World Enterprises shares that were outstanding before the merger = 110,000 * (30-26.487)

=

386,430

Value of the shares that were outstanding before merger have been reduced by $386,430 after merger