LONDON -- The FTSE 100 has risen by 25% over the last year, and many top shares are beginning to look quite expensive.

I'm on the hunt for companies that still look cheap, based on their long-term earnings potential. To help me hunt down these bargains, I'm using a special version of the price to earnings ratio called the PE10, which is one of my favorite tools for value investing.

The PE10 compares the current share price with average earnings per share for the last ten years. This smoothes out any short-term volatility and lets you see whether a company looks cheap compared to its long-term earnings.

Today, I'm going to take a look at the PE10 for the U.K.'s third-largest bank, Barclays (BARC 0.17%) (BCS 0.58%).

Is Barclays a buy?
Barclays shares have risen by 79% over the last year. Are they now fully priced, or is there still more to come?

Let's take a look at the bank's current P/E and its PE10:

 Trailing
P/E
PE10
Barclays 9.8 6.9

Barclays' trailing P/E of 9.8 is higher than its PE10 of 6.9, suggesting that the bank could still be a buy, as its long-term average earnings are higher than its current earnings.

Discount to book value
There's a second reason I believe Barclays may be a strong buy. As I write, Barclays shares are changing hands for around 320 pence. This is 21% below the bank's net asset value per share of 405 pence, and 7% below its net tangible asset value per share of 344 pence.

Healthy banks normally trade slightly above book value, so these discounts indicate that the market is still pricing a lot of risk into Barclays -- risk I believe may be exaggerated.

Return to profits
Barclays' first-quarter results showed the bank returning to profit, and brokers' consensus forecasts suggest that full-year earnings could be around 35 pence, placing Barclays on a forward P/E of 9.2.

The firm's dividend is also expected to rise this year -- last year's payout of 6.5 pence is expected to rise by around 12% to 7.3 pence, providing a forward dividend yield of 2.3%.

Although this remains below the FTSE 100 average of 3%, there is scope for substantial long-term growth. In 2012, Barclays set aside 1.6 billion pounds for PPI compensation payments, and in the first quarter of 2013, the bank incurred 514 million pounds of costs as part of its Transform restructuring program.

These costs reduce the amount of spare cash Barclays can return to shareholders, but this situation won't last forever. I think Barclays is a buy.

Can you beat the market?
If you already own shares in Barclays, then I'd strongly recommend that you take a look at this special Motley Fool report. Newly updated for 2013, it contains details of top U.K. fund manager Neil Woodford's eight largest holdings.

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