Question

1. Plastic First is engaged in the manufacturing of plastic materials. It is an allequity firm with 80 million shares outstanding, currently trade at $20 per share. It is considering acquiring My Toys to expand its business into the final products. My Toys currently has 30 million shares outstanding with a market price of $22 per share. The merger is expected to generate synergistic gains of $35 million in the first year. These gains are expected to grow at rate of 4% per year thereafter forever. Cash flows can be discounted at a nominal rate of 12.0%.

a). If Plastic First make a cash offer for the shares of My Toys with a premium of 40% on the prevailing market price of My Toys, what is the NPV of the merger to MMG shareholders?

b). If, instead a stock offer is made such that the NPV of the merger to Plastic First shareholders is the same as in (a), what is the appropriate exchange ratio for the acquisition of the acquirer after the acquisition?

c). What is the maximum exchange ratio that the management of Plastic First can pay (on a per share basis) for a share of My Toys without hurting its own shareholders?

Answer 1

(a) Plastic First Value = V(A) = Number of shares outstanding x Price per share = 80 x 20 = $ 1600 million

My Toy Value = V(B) = Number of shares outstanding x Price per share = 30 x 22 = $ 660 million

Synergistic Gain = $ 35 in first year which grows at a perpetual rate of 4 % per annum thereafter.

Discount Rate = 12 %

PV of Synergistic Gains = 35 / (0.12 - 0.04) = $ 437.5 million

Combined Firm Value = V(C) = 1600 + 660 + 437.5 = $ 2697.5 million

Acquisition Premium = 40 %

Cost of Merger to First Plastic = Cash Paid - V(B) = 1.4 x V(B) - V(B) = $ 264 million

Megrer Gain to First Plastic = V(C) - V(A) - V(B) = 2697.5 - 1600 - 660 = $ 437.5 million

Merger NPV = Merger Gain - Cost of Merger = 437.5 - 264 = $ 173.5 million

(b) Let the number of shares offered be K

Cost of Merger = K x 20 - 660

Merger Gain = $ 437.5 million

Merger NPV = 437.5 - (20 x K - 660)

173.5 = (20K - 660)

K = 41.675 million

Hence, Plastic First offers 41.675 million shares in return for 30 million shares of My Toy

Therefore, exchange ratio = 41.675 / 30 = 1.39 approximately.

(c) Let the number of shares offered be N

The shareholders of Plastic First get hurt only when their merger NPV becomes less than zero. Hence, the limiting case is when merer NPV is zero.

Cost of Merger = N x 20 - 660

Merger Gain = $ 437.5 million

Merger NPV = 437.5 - (20N - 660)

20N = 660 + 437.5

N = 54.875 millon shares

Hence, the limiting case involves exchanging 54.875 million shares of First Plastic for 30 million shares of My Toy.

Maximum Exchange Ratio = 54.875 / 30 = 1.83

Maximum Price offered per Share = 1.83 x 20 = $ 36.6