Question

Firm X and Firm Y are both 100% equity-financed. Firm X wants to acquire Firm Y for $165,000 in the form of either cash or stock. The synergy value of the deal is $25,000. You are given the following additional information:


Firm X Firm Y Number of Shares 20,000 $37.50 9,750 $15.00 Price per Share

1. What is the merger premium expressed as a percent of Firm Y's stock price?
2. What is the NPV of the acquisition if cash is used?
3. What is the price per share of the post-merger firm following a cash acquisition?
4. What is the price per share of the post-merger firm if payment is made in stock?

What is the NPV of acquiring Firm Y when stock financing is used?

Answer 1

Part a

Meger premium = purchase consideration paid - value of shares of the traget company

=165000-(9750×15)=18750

Premium per share of target company = 18750/9750=1.923

As a % of share price = 1.923/15=12.82%

Part b

NPV of merger= value of target company + synergy -merger premium

=(9750×15)+25000-18750=152500$

Part c

Price per after merger= (Vx +NPVm)/Nm

Where

Vx = value of x before merger = 20000×37.5=750000$

NPVm= NPV of merger =152500

Nm= number of shares after merger= 20000 since it is a cash deal

Price after merger = (750000+152500)/20000=45.125

Part d and e

In case if a stock deal we need a swap ratio but in question we are not given any ddetails of the same so we have to assume that swap ratio is calculated on the basis of share price of both the company

SR= price of Y/ price of X= 15/37.5=.40 which means company X will issue .4 of its shares to the shareholders of Y company for every shares held by the of the Y company.

So no. Of shares after merger (Nm)=20000 +.4×9750 =23900

NPV of merger = purchase consideration paid +synergy premium

= (no of X shares given to Y's shareholders ×price of x company shares) +25000-0

=((.4×9760)×37.5)+25000-0=171250$

Here premium will be zero because we have calculated the swap ratio on price basis

Let us check, premium=.4×9750×37.5 -15×9750=0 yes!

Price per share= (750000+171250)/23900= 38.55

Hence cash deal is better.