When two listed companies merge, what is the effect on the shares of both companies?

This would depend on the swap ratio (read more by clicking the hyperlink) of the merger. Suggest you also read this article on Business Standard to understand a bit more on swap ratios. The article talks about the Pfizer - Wyeth merger deal and the swap ratio. 

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Let me try to explain what I understand.

ACQUISITION
Assume both acquiree and target are listed companies.
The acquiree which acquires target (either through auction when the company is for sale/bankrupt or by slowly acquiring majority shares) is said to have won an acquisition.
The ownership of the target is transferred to the acquiree.
Both the companies will continue to trade on their own scripcode in the stock exchanges.
The two company operations will be separate even though some board members are common.
Sometimes the name of the target would be changed as per the decision taken by acquiree.

Example: Mahindra group (NSE:M&M) acquired though auction Satyam computer services ltd. (NSE:SATYAMCOMP) when Satyam indulged in the finance scandal during 2009. Satyam shares fell as low as 11.5 rupees from 500+. M&M bid for a share price of 58.90 for 31% of total shares and acquired Satyam. The name is then changed to Mahindra Satyam (but scrip is same NSE:SATYAMCOMP). Both NSE:M&M and NSE:SATYAMCOMP continued its trading as usual in stock exchange

MERGER
Assume company1 and company2 are listed companies.
company1 and company2 make a joint decision to merge their busineses for various financial reasons.
They combine and become a single entity, either under the name of company1 or company2. Usually it will be named after the company which is having upper hand.

Example: MahindraSatyam (NSE:SATYAMCOMP) merged with TechMahindra (NSE:TECHM) and continued as a single entity TechMahindra during 2013.
Trading ceased on SATYAMCOMP and continues on TECHM.
In this case, TechMahindra offered 1 share of TECHM for every 8.5 shares of SATYAMCOMP to all the shareholders of SATYAMCOMP and annexed all the MahindraSatyam shareholders into its own shareholders pool. This ratio 1:8.5 (or 2:17) is called the Swap Ratio. While SATYAMCOMP ceased to trade, it was trading closing to 120 rupees and TECHM was trading close to 1000 rupees. Almost 1:8.3 in the ratio, you see.

Summary 

  • So in case of acquisition and running as independent bodies, no effect of shareholders, except the sentimental values.
  • But in case of annexure/merger, the annexing company will issue shares or sometimes cash to the shareholders of the ceasing company.

Praveen, if it’s a short question, you should just put it in the title instead of putting two words. Please check the edit that’s just been made.

Karthik, would be nice if you could summarise how the swap ratio calculation is applied.

Its a bit of a lengthy discussion hence provided the link with an intention of providing a quick and dirty understanding :-)… Will try and summarize it as and when possible.