JPMorgan Chase (JPM -0.12%), the largest bank in the U.S. by assets, recently purchased most of the assets of First Republic (FRCB) from the Federal Deposit Insurance Corp. (FDIC) after First Republic was seized by regulators.

The deal comes with a number of benefits and is expected to immediately boost JPMorgan Chase's annual profit by $500 million a year. That seems like a pretty modest gain considering that JPMorgan generated close to $42 billion of net income over the last year.

But management's estimates on the earnings accretion from First Republic seem quite conservative. Here's why.

The acquisition gets earnings back on track

Because the bank was seized and then sold pretty much right away, management did not have a lot of time to do due diligence on First Republic. Even so, JPMorgan has likely been thinking about this possibility for longer than just a few days, because First Republic has been struggling since March.

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First Republic experienced more than $100 billion of deposit outflows in the first quarter, which forced the bank to replace the lost deposits with higher-cost borrowings that would cut into its earnings. But First Republic still generated $269 million of net income in the first quarter, and that's after seeing the average cost of its interest-bearing liabilities rise from 1.76% to 2.73%.

The first-quarter results put First Republic on track to generate over $1 billion in net income on an annualized basis. Now, obviously, if the bank had not been sold, its earnings would have nose-dived in the quarters ahead. That's because the cost of the bank's interest-bearing liabilities is on an average basis and not period end, so funding costs likely continued to balloon toward the end of the first quarter and into the second. I think First Republic would have started seeing losses.

But JPMorgan Chase should be able to use deposits from its own customer base to stop the bleeding and get the First Republic back on track. JPMorgan Chase's Chief Financial Officer, Jeremy Barnum, said on the bank's earnings call that the bank is trying to stay very conservative right now on its earnings estimates because "there are open questions about deposit retention" in regard to the remaining clients at First Republic. However, I would think that JPMorgan would reassure current clients and maybe even bring back some old ones.

I'm also not anticipating that JPMorgan Chase will see material losses on First Republic's securities or loan books. Yes, First Republic's mortgage book and securities book are underwater due to higher interest rates. However, JPMorgan Chase should be able to grind down these losses and wait until the assets mature or the unrealized losses come down as the Federal Reserve slows or pauses its interest rate hikes.

From a credit perspective, First Republic has always maintained pristine credit quality. And JPMorgan Chase secured a loss-sharing agreement with the FDIC that will cover 80% of losses on First Republic's mortgage holdings for the first seven years and 80% on the bank's commercial portfolio for the first five years.

Execution is key, but the deal looks attractive

How beneficial this acquisition will be for JPMorgan depends on management's execution as well as on how the bank maintains and scales First Republic's wealth franchise, which I think is the real prize of the acquisition. But JPMorgan Chase should be able to replace a lot of the higher-cost funding and borrowings with its own funding base, limit losses from the bank's loan book, and derive value from the wealth franchise.

Banks with more than 10% U.S. deposit market share, like JPMorgan, are not normally able to make whole-bank acquisitions, so this is a rare opportunity. JPMorgan has bought distressed banks before, and I have confidence in management to extract good long-term value from the deal.