Pre-deal situation:
BuyCo plans to acquire 100% shares of SellCo in a stock-for-stock transaction.
BuyCo has a net income of $300,000 and 100,000 shares outstanding
Market shareprice of BuyCo is $50.0
Pre-deal EPS = $3.0
Pre-deal P/E = 16.7x
SellCo has a net income of $100,000 and 50,000 shares outstanding
Market shareprice of SellCo is $60.0
Pre-deal EPS = $2.0
Pre-deal P/E = 30.0x
The deal:
BuyCo agrees to pay a premium for control of 30%, so the offer price for one SellCo share is 1.3*$60.0 = $78.0
Stock-for-stock exchange ratio is $78/$50 = 1.56 of BuyCo shares for one SellCo share
BuyCo issues 1.56*50,000 = 78,000 new shares to exchange them for all the SellCo shares outstanding
Total shares of NewCo = 100,000(pre-deal shares of BuyCo) + 78,000 (new shares) = 178,000 shares
NewCo expected EPS = Total net income/Total shares outstanding = ($300,000+$100,000)/178,000 = $2.25
NewCo expected shareprice = (P/E of BuyCo)*(expected EPS) = 16.7x*$2.25 = $37.45
Post-deal situation:
EPS of NewCo falls from $3.0 to $2.25, so the deal is 25% dilutive for BuyCo shareholders
BuyCo shareholders own 100,000/178,000 = 56.18% of NewCo (so they retain control)
SellCo shareholders own 78,000/178,000 = 43.82% of NewCo

[2]Accretion/dilution analysis is a type of M&A financial modelling performed in the pre-deal phase to evaluate the effect of the transaction on shareholder value and to check whether EPS for buying shareholders will increase or decrease post-deal.[2] Generally, shareholders do not prefer dilutive transactions; however, if the deal may generate enough value to become accretive in a reasonable time, a proposed combination is justified.

Aside is a simplified example. A real-life accretion/dilution analysis may be much more complex if the deal is structured as cash-and-stock-for-stock, if preferred shares and dilutive instruments are involved, if debt and transaction fees are substantial, and so on. Generally, if the buying company has a higher P/E multiple than that of the target, the deal is likely to be accretive. The reverse is true for a dilutive transaction.

See also