Royal Bank of Canada (TSX:RY)(NYSE:RY), the second-largest bank in Canada in terms of total assets, announced third-quarter earnings results before the market opened on August 26, and its stock has reacted by rising about 1% in the trading sessions since. Let’s take a closer look at the results to determine if this could be the start of a sustained rally higher and if we should consider establishing positions today.

Breaking down the third-quarter results

Here’s a summary of RBC’s third-quarter earnings results compared with its results in the same period a year ago.

Metric Q3 2015 Q3 2014
Earnings Per Share $1.66 $1.59
Revenue $8.83 billion $8.99 billion

Source: Royal Bank of Canada

RBC’s earnings per share increased 4.4% and its revenue decreased 1.8% compared with the third quarter of fiscal 2014. The company’s strong earnings-per-share growth can be attributed to its net income increasing 4.1% to $2.48 billion, driven by 12.6% growth to a record $1.28 billion in its personal and commercial banking segment and 51.8% growth to $167 million in its investor and treasury services segment.

Its slight decline in revenue can be attributed to its non-interest income decreasing 5.6% to $5.05 billion, led lower by its insurance revenues decreasing 26.2% to $1.02 billion and its trading revenue in non-interest income decreasing 80.4% to $56 million, which was only partially offset by its net interest income increasing 3.7% to $3.78 billion.

Here’s a quick breakdown of six other notable statistics from the report compared with the year-ago period:

  1. Total assets increased 18.7% to $1.085 trillion
  2. Total deposits increased 15.4% to $694.24 billion
  3. Total loans, net of allowance for loan losses, increased 7.5% to $462.6 billion
  4. Total securities increased 18.3% to $235.52 billion
  5. Total assets under management increased 13.9% to $508.7 billion
  6. Book value per share increased 17.2% to $38.20

RBC also announced a 2.6% increase to its quarterly dividend to $0.79 per share, and the next payment will come on November 24 to shareholders of record at the close on business on October 26.

Will the stock head higher from here?

It was a solid quarter overall for RBC, so I think its stock has responded correctly by rising. I also think this could be the start of a sustained rally back towards its 52-week high, which it still sits more than 12% below, because the stock still trades at very inexpensive valuations and has a very high dividend yield.

First, RBC’s stock trades at just 11.1 times fiscal 2015’s estimated earnings per share of $6.63 and only 10.6 times fiscal 2016’s estimated earnings per share of $6.94, both of which are inexpensive compared with its five-year average price-to-earnings multiple of 13.6 and the industry average multiple of 12.8. It trades at a mere 1.92 times its book value per share of $38.20, which is a major discount compared with its market-to-book value of 2.47 at the conclusion of the year-ago period.

Second, RBC now pays an annual dividend of $3.16 per share, which gives its stock a 4.3% yield at today’s levels, and this is significantly higher than the industry average yield of 2.3%. The company has also increased its dividend for five consecutive years, and its consistent free cash flow generation and strong financial position could allow this streak to continue for decades.

With all of the information above in mind, I think Royal Bank of Canada represents one of the best long-term investment opportunities in the market today. All Foolish investors should take a closer look and strongly consider making it a core holding.

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Fool contributor Joseph Solitro has no position in any stocks mentioned.