A commonly spread myth (along with “if you do not pass ethics, you will not pass the CFA”) is that for analyst and associate interviews outside of M&A, the only expected accretion/dilution question will be “in an all-stock transaction, is it accretive if company A (10x P/E) purchases company B (5x P/E)?”

This is not true, and accretion/dilution problems are a great way to weed out candidates who are not serious about investment banking.

Accretion/Dilution Plus/Minus Math

Beyond knowing whether a transaction is accretive or dilutive, the extent to which it is accretive or dilutive is also important. The following examples are theoretical examples of accretion/dilution math without factoring in how shares will react in the market post transaction and ignoring the effects of synergies and dilutive securities (physically settled stock units, convertibles, stock options and stock warrants).

Accretion/Dilution Example 1: The All-Stock Transaction with Differing Price-to-Earnings

$100 million Company A purchases Company B for $100 million. Company A has a price/earnings of 10x and Company B has a price/earnings of 5x. Company A has 1 million shares. How accretive is the transaction?

First, the analyst must find out the value of Company A’s shares. $100 million represents the market capitalization (although for an interview, an interviewee should ask if it is market capitalization or enterprise value to see if extra steps need to be taken), so market capitalization divided by shares outstanding is the share price.

($100 million in equity value)/(1 million shares outstanding) = $100 per share

Company A has Earnings Per Share (EPS) of $10, as the price/earnings is 10x.

P/E = 10.0x = Share Price/EPS = $100/$10

In order for Company A to purchase Company B, it has to issue 1 million additional shares to provide the consideration for the $100 million in Company B equity value.

After the transaction, there are 2 million company A shares outstanding. Company A’s earnings contribution is $10 million and Company B’s earnings contribution is $20 million.

$100 million/(10.0x price/earnings) = $10 million
$100 million/(5.0x price/earnings) = $20 million

Collectively, the new company has earnings of $30 million. Now that there are 2 million shares outstanding, earnings per share has risen to $15. This transaction was 50% accretive to earnings.

Assuming the company’s price/earnings rerates to reflect the separate valuation of the two segments, the new price earnings is 6.67x (closer to the 5x given the greater proportion of earnings from Company B).

Now to explore the relationship more in depth, we should consider the relative scale of the acquirer and target as well as the difference in price/earnings.

The larger the acquirer versus the target, the less influential the target’s P/E will be for the new pro-forma earnings per share (and assuming no rerating. For smaller acquisitions (“bolt-on” or “tuck-in” acquisitions), the post-transaction earnings per share and price/earnings will closely resemble the acquirer’s pre-merger ratios. For a larger, transformative transaction, effects are more ambiguous.

Similarly, a large difference in multiples will result in a more prominent change to the P/E and EPS post transaction.

Accretion/Dilution Example 2: Accretion/Dilution Breakeven Premium in an All-Stock Transaction

In evaluating a potential merger, breakeven analysis is conducted to see what transaction premium can be paid before the acquisition becomes dilutive to earnings (which is psychologically important). In an all-stock transaction, this is fairly simple – the breakeven is the price which makes the price/earnings of the target and the acquirer equal.

As such, if Company A trades at 10x and is purchasing Company B for 5x, they can pay a 100% premium before the acquisition becomes dilutive.

Assume Company B is $50 million with $10 million in earnings. Company A can pay $100 million for Company B before the transaction is dilutive.

One takeaway after all of this accretion/dilution math in an all-stock transaction is that financial engineering based on accretion/dilution without sound strategic rationale usually results in negative sentiment from the open market. A large takeover premium for a competitor will make the market think the company is overpaying due to a variety of factors including management ego, compensation (executive compensation is often justified by benchmarking to similar size peers – the larger the company the larger the salary), quixotic synergy assumptions and poor corporate finance advice from investment bankers.

Conversely, a dilutive transaction may result in a positive re-rating should analysts see tangible synergies (proximity, supply chain, cross-selling, scale, buyer power, elimination of redundancies in corporate head office and financial reporting requirements, superior management, cheaper cost of debt).

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