Question

4. (Merger and acquisition): Energy-USA plans to acquire Energy-Brazil. It offers X million shares of Energy-USA for all of Energy-Brazil’s shares. The exchange rate is R$1.7200/$ around the acquisition. P/E ratio for energy brazil=20, for energy USA=30, # of Shares for energy Brazil=200million, for energy USA=250, (after-tax) Earnings Energy-Brazil R$172 million Energy-USA $200 million .

(a) Find the lower bound of X (4 decimal places) such that original Energy-Brazil shareholders would agree with the merger (assume the P/E ratio is 30 after the merger)? (b) Find the upper bound of X (4 decimal places) such that original Energy-USA shareholders would benefit from the merger (assume the P/E ratio is 30 after the merger)? (c) If the merger adds no extra value to both original firms, find P/E (after the merger), the value of X (4 decimal places), and the exchange ratio (4 decimal places) of the merger per Energy-Brazil share in this scenario. (d) If X=90, and P/E=30 after the merger, calculate the value ($million) of the synergies created by the merger and the stock return (%) of Energy-USA to the original Energy-USA shareholders.

Answer 1

Evaluation of Merger

Particulars	Energy USA	Energy Brazil
(a)P/E ratio	30	20
(b) Outstanding number of share	250m	200m
(c) After tax Earnings (PAT)	$200m	172m/1.72 = $100m
(d) Current EPS	$0.8	$0.5
(e) Current MPS = (a) * (d)	$24	$10
(f) Current market value = (b) *(e)	$6000	$2000

(a) The shareholders of Energy Brazil will get ready for merger if at least their Post merger MPS remain intact, if not improve.

Post Tax MPS = Post Tax PE ratio * Total Earnings /Total number of share post merger

$10 = 30 * ($200+$100)m/250m+x

2500m + 10x = 9000m

10x = 6500m

x= 650m

(b) The shareholders of Energy USA will want merger if their post merger MPS remain intact if not improve.

Using the same formula

$24 = 30 * ($200+$100)m/250m+x

$6000m + 24x = $9000m

24x = $3000m

x = 125m

(c) For no synergy to any company Earnings post merger shall be equal to earnings prior to merger of both companies and Exchange Ratio shall be based on EPS

Exchange Ratio= EPS of amalgamated Company/EPS of amalgamating Company

Exchange Ratio =0.5/0.8 i.e, 0.625

Value of x = 200m*0.625 i.e, 125m

Post Merger EPS = ($200+$100)m/250m + 200m*0.628

= $300/375 i.e, $0.8

(d) x=90m

P/E ratio = 30

Post merger EPS = ($200+$100)m/250m + 90m

= 0.88235

Post Merger MPS=0.88235*30

= 26.4705

Particulars	Energy USA	Energy Brazil
Post Merger number of share	250	90
Post Merger market value	$6617.625	$2382.345
Pre Merger market value	$6000	$2000
Synergy	$617.625	$382.345
Synergy in percentage	10.2938%	19.1173%