# How to Calculate the Exchange Ratio in Mergers and Acquisitions

![Exchange Ratio](https://www.investopedia.com/thmb/_G8B7hVUdOlqQwFnksMScQb_Gss=/1500x0/filters:no_upscale():max_bytes(150000):strip_icc()/Exchange-Ratio-Final-f528b8276c4945f7a02e0af6f1bd2264.jpg)

*— Investopedia / Yurle Villegas*

> **Definition**
>
> The exchange ratio represents the relative number of shares an acquiring company issues to the shareholders of a target company during a merger or acquisition.

## What Is the Exchange Ratio?

The exchange ratio is the relative number of new shares that will be given to existing [shareholders](https://www.investopedia.com/terms/s/shareholder.asp) of a company that has been acquired or that has [merged](https://www.investopedia.com/terms/m/merger.asp) with another. It ensures shareholders keep the same relative value in the new entity. Exchange ratios play an important role in stock-based deals, determining how shares are distributed. They can be fixed or floating, depending on the terms of the merger or acquisition.

### Key Takeaways

*   The exchange ratio determines the number of new shares an investor receives post-merger or acquisition.
*   Two types of exchange ratios exist: fixed, with a known number of shares, and floating, ensuring a fixed value.
*   Fixed exchange ratios give acquirers certainty on control, while floating ratios ensure value for target companies.
*   Caps and floors on exchange ratios help prevent significant valuation disparities during mergers.
*   Merger arbitrage exploits valuation gaps, offering opportunities for investors betting on deal completions.

## How the Exchange Ratio Works in Mergers and Acquisitions

An exchange ratio ensures shareholders receive stock in the acquiring company that equals the value of their previous shares in the [target](https://www.investopedia.com/terms/t/targetfirm.asp) company. The target company share price is typically increased by the amount of a "takeover premium," or an additional amount of money an acquirer pays for the right to buy 100% of the company's outstanding shares and have a 100% controlling interest in the company.

Relative value does not mean, however, that the shareholder receives the same number of shares or same dollar value based on current prices. Instead, the exchange ratio considers both the [intrinsic value](https://www.investopedia.com/terms/i/intrinsicvalue.asp) of shares and the company's overall value.

## Calculating Exchange Ratios: A Guide for Investors

The exchange ratio only exists in deals that are paid for in stock or a mix of stock and cash as opposed to just cash. The calculation for the exchange ratio is:

$\begin{aligned} &\text{Exchange Ratio} = \frac{ \text{Target Share Price} }{ \text{Acquirer Share Price} } \\ \end{aligned}$

The target [share price](https://www.investopedia.com/ask/answers/061615/how-companys-share-price-determined.asp) is the price offered for the target shares. Because both share prices can change from the time the initial numbers are drafted to when the deal closes, the exchange ratio is usually structured as a fixed exchange ratio or a floating exchange ratio.

A fixed exchange ratio stays constant until the deal is complete. The number of shares is known, but the deal's value remains uncertain. The acquiring company prefers this method as the number of shares is known therefore the percentage of control is known.

With a floating exchange ratio, the target company gets a set value regardless of share price changes. In a floating exchange ratio, the shares are unknown but the value of the deal is known. The target company, or seller, prefers this method as they know the exact value they will be receiving.

## Illustrating an Exchange Ratio: A Practical Example

Imagine that the buyer of a company offers the seller two shares of the buyer's company in exchange for one share of the seller's company. Prior to the announcement of the deal, the buyer's or acquirer's shares may be trading at $10, while the seller's or target's shares trade at $15. Due to the 2 to 1 exchange ratio, the buyer is effectively offering $20 for a seller share that is trading at $15.

Fixed exchange ratios are usually limited by caps and floors to reflect extreme changes in stock prices. Caps and floors prevent the seller from receiving significantly less consideration than anticipated, and they likewise prevent the buyer from giving up significantly more consideration than anticipated.

Post announcement of a deal, there is usually a gap in valuation between the seller's and buyer's shares to reflect the [time value of money](https://www.investopedia.com/terms/t/timevalueofmoney.asp) and risks. Some of these risks include the deal being blocked by the government, shareholder disapproval, or extreme changes in markets or economies.

Taking advantage of the gap, believing that the deal will go through, is referred to as [merger arbitrage](https://www.investopedia.com/terms/m/mergerarbitrage.asp) and is practiced by [hedge funds](https://www.investopedia.com/terms/h/hedgefund.asp) and other investors. Leveraging the example above, assume that the buyer's shares stay at $10 and the seller's shares jump to $18. There will be a $2 gap that investors can secure by buying one seller share for $18 and shorting two buyer shares for $20.

If the deal closes, investors will receive two buyer shares in exchange for one seller share, closing out the short position and leaving investors with $20 in cash. Minus the initial outlay of $18, investors will net $2.

## The Bottom Line

The exchange ratio determines how many new shares shareholders receive in a merger or acquisition, ensuring they retain equivalent relative value. Ratios can be fixed or floating, influencing risks, premiums, and shareholder value.

Determining the ratio requires considering the intrinsic value of both companies' shares. For example, if Company A offers 0.5 of its shares for each share of Company B, investors can gauge potential gains or risks, key for strategies like merger arbitrage.