Costs and Benefits of Merger

When a company ‘A’ acquires another company say ‘B’, then it is a capital investment decision for company ‘A’ and it is a capital disinvestment decision for company ‘B”. Thus, both the companies need to calculate the Net Present Value (NPV) of their decisions. 

To calculate the NPV to company ‘A’ there is a need to calculate the benefit and cost of the merger. The benefit of the merger is equal to the difference between the value of the combined identity (PV_AB) and the sum of the value of both firms as a separate entity. It can be expressed as Benefit = (PV_AB) – (PV_A+ PV_B)

Assuming that compensation to firm B is paid in cash, the cost of the merger from the point of view of firm A can be calculated as 

Cost= Cash - PV_B

Thus NPV for A = Benefit –Cost
                       = (PV_AB – (PV_A + PV_B)) – (Cash – PV_B)

the net present value of the merger from the point of view of firm B is the same as the cost of the merger for ‘A’. Hence,
NPV to B = (Cash - PV_B)

NPV of A and B in case the compensation is in stock

In the above scenario we assumed that compensation is paid in cash, however in real life compensation is paid in terms of stock. In that case, cost of the merger needs to be calculated caarefully. It is explained with the help of an illustration –
Firm A plans to acquire firm B. Following are the statistics of firms before the merger –  

	A	B
Market price per share	Rs.50	Rs.20
Number of Shares	500,000	250,000
Market value of the firm	Rs.25 million	Rs.5 million

The merger is expected to bring gains, which have a PV of Rs.5 million. Firm A offers 125,000 shares in exchange for 250,000 shares to the shareholders of firm B. 

The cost in this case is defined as – 

Cost = aPV_AB  - PV_B

Where a represents the fraction of the combined entity received by shareholders of B.
In the above example, the share of B in the combined entity is –
a = 125,000 / (500,000 + 125,000) = 0.2

assuming that the market value of the combined entity will be equal to the sum of present value of the separate entities and the benefit of merger. Then, 

PV_AB  = PV_A+ PV_B+ Benefit = 25 + 5 + 5 = Rs.35 million

Cost = aPV_AB  - PV_B = 0.2 x 35 – 5= Rs.2 million

thus

NPV to A =Benefit – Cost
= 5 –2 = Rs.3 million
NPV to B = Cost to A = Rs 2 million.

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