Question

Company A has a market value of equity of $2,000 million and 80 million shares outstanding. Company B has a market value of equity of $400 million and 25 million shares outstanding. Company A announces at the beginning of 2019 that is going to acquire Company B.

The projected pre-tax gains in operating income (in millions of $) from the merger are:

	2019	2020	2021	2022	2023
Pre-tax Gains in Operating Income	12	16	28	38	45

The projected pre-tax gains in operating income are expected to grow at 4% after year 2023. The company is using a discount rate of 8% to value the synergies. The marginal corporate tax rate is 35%.

Company A has decided to pay a $300 million premium for Company B. Assume that capital markets are efficient and that there is a 100% probability the deal will be closed.

If Company A were to make a 100% stock offer for Company B, what would the exchange ratio be? Remember that the exchange ratio is the number of Company A’s shares that the shareholders of Company B will receive in exchange for each of their shares.

Answer 1

Total value to be paid to shareholders of Company B = Current Market Value B + Premium = 400+ 300 = 700

Price Per Share = 700 / 25 = 28

We find the benefit from the merger:

Terminal Value = Last Cashflow (1+ Growth)/ (Discount Rate - Growth Rate)

Out of 586.23 benefit from merger, 300 benefit as premium is given to Co B. Hence net benefit with Co A = 286.23

Hence Market Value of Company A= 2000+286.23 = 2286.23

Price per share = 2286.23 / 80= 28.58

Hence Exchange ratio for each share of B = Price of share B/ Price of Share A = 28 / 28.58 = 0.98

Hence for every 1 share of Co B, shareholders will get 0.98 shares of Co A.