Question

6. (Merger and acquisition):Energy-USA plans to acquire Energy-Brazil. It offers X millionsharesof Energy-USA for all of Energy-Brazil’s shares. The exchange rate is R$4.07/$ around the acquisition. Also, there are no expected synergies from the transaction.

	P/E ratio	# of Shares	(after-tax) Earnings
Energy-Brazil	20	200 million	R$407 million
Energy-USA	30	250 million	$200 million

(a) If Energy-USA pays no premium to acquire Energy-Brazil, what will be the EPSof Energy-USA after the​ merger?

(b) What will be the P/E ratio (4 decimal places)of Energy-USA after the merger​ (if no​ premium is paid)?

(c) In part (b), find the value of Xand the exchange ratio (4 decimal places).

(d) (new part) Suppose Energy-USA offers an exchange ratio such​ that, at current​ pre-announcement stock prices ($) for both​ firms, the offer represents a 20% premium to acquire Energy-Brazil. What will be the EPSof Energy-USA after the​ merger?

Answer 1

(a) Energy - Brazil : PE Ratio = 20, Number of Shares = 200 million, After-Tax Earnings= R$ 407 million

Earnings per Share= 407 / 200 = R $ 2.035

Price per Share = P(Br) = 2.035 x 20 = R $ 40.7

Energy - USA: PE Ratio = 30, Number of Shares = 250 million and Earnings = $ 250 million

Earnings per Share = 200 / 250 = $ 0.8

Price per Share = P(Us) = 30 x 0.8 = $ 24

Current Exchange Rate = R$ 4.07 / $

As there are no synergies in the merger, the following equation should help:

X x 24 x 4.07 = 200 x 40.7

X = 83.33 million

Number of Shares Post Merger = 250 + 83.33 = 333.33 million

Earnings per Share = 200 / 333.33 = $ 0.6

(b) Earnings per Share = $ 0.6 and Price per Share = 24

PE Ratio = 24/0.6 = 40

(c) X = 83.33 million (as calculated in part(a))

Exchange Ratio = Number of Shares Issed / Number of Shares of USA-Brazil = 83.33 / 200 = 0.41665 ~ 0.42

(d) Actual Non-Premium Price per Share offered in $ = 83.33 x 24 / 200 = $ 10

20% Premium would imply a $ Price per Share = 1.2 x 10 = $ 12

Let the number of shares to be issued in case of a 20% premium buy be N million

Therefore, N x 12 x 4.07 = 200 x 40.7

N = (200 x 40.7) / (12 x 4.07) = 166.67 million

New EPS = 200 / (250 + 166.67) = $ 0.48