The Big Six Canadian banks are some of the best investments Canadians can make. They have long histories of operation going back at least as early as 1869.

These banks pay solid dividends and have even maintained them through the last recession in 2008 and 2009. Further, they are priced at discounts of up to 21%.

Cheap shares benefit shareholders because the cheaper the shares, the higher the yields, and the more income shareholders receive from dividends.

After reviewing the Big Six banks, three look particularly attractive based on valuations.

Bank of Nova Scotia (TSX:BNS)(NYSE:BNS) is the most international Canadian bank. It has leading positions in North America, Latin America, the Caribbean and Central America, and parts of Asia.

Most importantly, Bank of Nova Scotia is the best-valued bank today. At $56 per share, the bank is trading at a multiple of 9.8. This is a discount of 21% compared with its historical normal multiple of 12.4. In other words, the fair value estimate of Bank of Nova Scotia is $71.

Because of the pullback, the shares are also yielding a historically high yield of 5%. In summary, investors can buy the bank’s shares today for a potential capital gain of 26%, while getting a 5% growing income to wait.

If you buy 100 shares today, an investment of $5,600, you’ll receive a projected $280 of dividends per year without accounting for potential dividend hikes.

National Bank of Canada (TSX:NA) is the sixth-largest bank in Canada, and the leading bank in Quebec. However, it also serves clients in the United States, Europe, and other parts of the world through a network of representative offices, subsidiaries, and partnerships.

National Bank of Canada is the second-best-valued bank today. At $40.40 per share, the bank is trading at a multiple of 8.6. This is a discount of 19% compared with its historically normal multiple of 10.7. In other words, the fair value estimate of National Bank of Canada is $50.

Because of the pullback, the shares are also yielding a historically high yield of 5.4%. In summary, investors can buy the bank’s shares today for a potential capital gain of 24%, while getting a 5.4% growing income to wait.

If you buy 100 shares today, an investment of $4,040, you’ll receive a projected $218 of dividends per year without accounting for potential dividend hikes.

Canadian Imperial Bank of Commerce (TSX:CM)(NYSE:CM) is the fifth-largest bank in Canada. With its full range of financial products, it serves 11 million clients in Canada and across the globe.

Canadian Imperial Bank of Commerce is the third-best-valued bank today. At $92 per share, the bank is trading at a multiple of 9.7. This is a discount of 16% compared with its historically normal multiple of 11.6. In other words, the fair value estimate of Canadian Imperial Bank of Commerce is $109.

Because of the pullback, the shares are also yielding a historically high yield of 5%. In summary, investors can buy the bank’s shares today for a potential capital gain of 18.5%, while getting a 5% growing income to wait.

If you buy 100 shares today, an investment of $9,200, you’ll receive a projected $460 of dividends per year without accounting for potential dividend hikes.

Conclusion

The Canadian economy looks gloomy because of fallen commodity prices. These three banks are selling at cheaper valuations because of that.

So, now is a good time to look for deals in quality companies like the big Canadian banks. They are great long-term investments as well as great investments as a part of a diversified portfolio for income. When their prices fall, it’s time to average in.

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Fool contributor Kay Ng owns shares of Bank of Nova Scotia (USA).