Question

Firm B Firm T Shares outstanding 4,800 1,800 Price per share $ 47 $ 20 Firm B has estimated that the value of the synergistic benefits from acquiring Firm T is $9,100. Firm T can be acquired for $22 per share in cash or by exchange of stock wherein B offers one of its shares for every two of T's shares. Are the shareholders of Firm T better off with the cash offer or the stock offer? Cash offer is better Share offer is better At what exchange ratio of B shares to T shares would the shareholders in T be indifferent between the two offers? (Do not round intermediate calculations and round your answer to 4 decimal places, e.g., 32.1616.)

Answer 1

A. Share Offer Is Better

B. .4569

Step-by-step explanation:

A. Based on the information given the shareholders of Firm T will be better off with the STOCK OFFER because cash offer is the amount of $22 per share.

B. Calculation to determine the exchange ratio of B shares to T shares

First step is to calculate the New shares created

New shares created = 1,800(1/2)

New shares created = 900 new shares

Second step is to calculate the value of the merged firm

Value of the merged firm= 4,800($47) + 1,800($20) + $9,100

Value of the merged firm= $270,700

Third step is to calculate the price per share of the merged firm

Price= $270,700/(4,800 + 900)

Price= $270,700/5,700

Price= $47.49

Fourth step is to calculate the Equity offer value

Equity offer value = (1/2)($47.49)

Equity offer value = $23.75 per share

Fifth step is to calculate the post merger share price

Value of the merged firm= $270,700

Shares in new firm = 4,800 + 1,800x

Hence:

Post merger share price:

P= $270,700/(4,800 + 1,800x)

Sixth step

For the target firm’s shareholders to be indifferent which means they have to receive the same wealth

Hence;

1,800(x)P= 1,800($22)

Let solve this equation for P

P= $22/x

Now Let Combine the two equations

$270,700/(4,800 + 1,800x) = $22/x

x= .4569

Seventh step is to calculate the NPV

NPV = 1,800($20) + $9,100 – 1,800($22)

NPV = $5,500

Eight step is to calculate the Share price

Share price = [4,800($47) + $5,500]/4,800

Share price = $48.15

Now let calculate the Exchange ratio

Exchange ratio = $22/$48.15

Exchange ratio = .4569

Therefore the exchange ratio of B shares to T shares that the shareholders in T would be indifferent between the two offers is .4569