This article has been adapted from  Fool UK , our sister site across the pond.

You could almost hear shareholders of Royal Bank of Scotland (NYSE: RBS) breathing a collective sigh of relief yesterday.

The 83% state-owned bank reported a first-quarter operating profit of 1.053 billion pounds (ignoring tax and charges) as bad loan charges fell. Total income was down to 7.6 billion pounds from 8.2 billion pounds last year -- mainly because market conditions weren't as favorable for RBS's investment-banking arm, Global Banking and Markets.

But there was still an overall net loss of 528 million pounds, in large part because of a charge of 469 million pounds from a market valuation of credit insurance provided to RBS by taxpayers under the Asset Protection Scheme (APS). Such is the penalty for previous misdeeds, as the banks must stump up more for funding and hold more liquidity.

The bank also suffered impairment charges of 2.0 billion pounds, including 1.3 billion pounds in relation to its Ulster Bank subsidiary, though its insurance business, which it plans to sell off, returned to profit.

RBS's chief executive, Stephen Hester, reckons that the bank is showing continuing progress, and the market seems to agree so far. The shares have responded positively to the results.

What RBS didn't do was to set aside any cash to meet its probable obligations from mis-sold payment protection insurance, unlike Lloyds Banking Group (NYSE: LYG), which put a jaw-dropping 3.2 billion pounds to the side. It seemed to concede defeat over the legal case brought by the banking-industry body, the British Bankers' Association. 

Meanwhile, RBS says the eventual cost could prove to be "material" -- no kidding!

Overall, the results have been welcomed by the market mainly because RBS is seeing improvement in its core business and gradually reducing its exposure to riskier non-core operations as part of its five-year recovery strategy.

Value now?
What we're really interested in trying to decide is whether the shares are a buy. As our Stephen Bland has pointed out, RBS's main attraction is in its discount to book value -- an area in which it is pleasingly out of kilter with the other banks.

Hester has previously promised that RBS will turn a profit this year, and analysts seem to agree. It may well be that the recovery in RBS shares has finally begun in earnest.

The main concern, though, is the state ownership and how and when that situation will be resolved. 

Hester has said he hopes a part sell-down by the UK government will become "increasingly visible and appealing," but it may take time. He has also said the bank doesn't expect to exit the scheme until next year. 

The government paid an average of 50.2 pence per share -- and may wish to see a return on its investment. But given the current political hue, I imagine the government will want out sooner rather than later.

The LSE-listed RBS shares went over 58 pence last April, but full-year figures were generally disappointing, and the shares have been falling from a recent high of 49 pence in February. (On the NYSE, the shares fetch close to $14.)

Trying to value RBS is no easy task for traders. When I wrote about RBS a year ago, I thought the shares were a buy (at 35 pence in London), though I was deliberately short on reasoning; the bank is a difficult company to value accurately, and it's as much art as it is science.

But most Fools see themselves as longer-term investors, and on that score, I imagine anyone buying the shares around their current level and forgetting about them for a decade or so should have a pleasant surprise. It's really all about patience.

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