Warren Buffett has described the cash pile held by his company, Berkshire Hathaway, as an "elephant gun." And while guessing what Buffett may use his elephant gun on for his next purchase may be an exercise in futility, it can serve as a screener of sorts when looking for new stock ideas.

Massive brands, wide moats, recession-proof operations, or a Benjamin Graham-worthy valuation -- there are many possible hallmarks of what may qualify a company as a "Buffett stock."

Three Fool.com contributors believe The Home Depot (HD 0.94%)Old Dominion Freight Line (ODFL -7.24%), and AutoZone (AZO 0.03%) would make great additions to Buffett's portfolio for the long haul.

Too late to reconsider the one that got away?

Josh Kohn-Lindquist (The Home Depot): Trading with a market capitalization of around $300 billion, home improvement behemoth Home Depot is on a shrinking list of companies that Buffett couldn't buy outright with his growing cash hoard.

Ranking No. 25 on the Kantar BrandZ Top 100 Valuable Brands List for 2022, it may not be shocking to see Home Depot's total return above 500% over the last decade.

This is the exact type of brand power that Buffett traditionally likes to find with his investments -- look no further than his $160 billion stake in Apple, Kantar's No. 1 brand. 

So should Buffett consider Home Depot for his next investment? He already did, in 2005 -- but it's one of the few picks that seemingly got away from him.

After initially snapping up shares of Home Depot in 2005, Buffett closed his position in full by 2010 as the Great Recession ended. While that's understandable considering the events of the time, Home Depot's share price would rise by over 700% since it was sold -- and its dividend increased consistently along the way.

However, with its share price having dropped around 27% year to date and trading with an attractive price-to-earnings ratio of only 18, Home Depot is worth a second look.

HD PE Ratio Chart

HD PE Ratio data by YCharts

Recording 7% sales growth year over year for the second quarter of 2022, Home Depot continued to prove that it is striking a beautiful balance between its Pro and do-it-yourself businesses. This balance is of particular importance to investors as it provides stability of sales, whether its customers are building new houses or remodeling old ones. This keeps Home Depot's operations surprisingly steady despite the volatility of the housing market.

Perhaps most impressively in the company's Q2 earnings call was its positive same-store comparables in each of its 19 United States geographical regions -- while Mexico and Canada grew even faster.

Consistently lowering its share count over time while steadily boosting its dividend along the way, Home Depot has been masterful at returning cash to shareholders.

HD Shares Outstanding Chart

HD Shares Outstanding data by YCharts

Despite all of these dividend increases, the company still only has a payout ratio of 45% -- meaning that there is plenty of room for further dividend growth.

Home Depot is trading at its lowest P/E of the last decade (outside of a brief moment in March 2020). Its brand power, steady operations, and consistent cash returns to shareholders make it an alluring pick for the Oracle of Omaha to consider buying again.

A transportation stock Buffett would love

Jeff Santoro (Old Dominion Freight Line): One of the most well-known investments made by Buffett is his stake in railroads. Burlington Northern Santa Fe (BNSF) is one of the largest railroad operators in North America, owning over 23,500 miles of track in 28 states and three Canadian provinces.

In 2009, Buffett was quoted as saying that a bet on the railroads was a bet on America. In that vein, I think there's another company that Buffett should consider adding to his portfolio: Old Dominion Freight Line.

For starters, Old Dominion has been a massive winner, outpacing the gain of the S&P 500 by over 1,100%. To put it another way, $10,000 invested in Old Dominion 10 years ago would be worth $146,000 today, while the same investment in an S&P 500 index fund would be worth $36,000.

A look at the most recent quarter gives some insight into what makes Old Dominion such a great investment. The second quarter of fiscal 2022 was record-setting for Old Dominion. Revenue was $1.7 billion, up 26% year over year and 11% sequentially. Net income reached $376 million, an increase of 40% compared to the year-ago quarter and 25% over the first quarter.

The company also reached an all-time low on operating ratio, which was 69.5% for the quarter. This means that Old Dominion's operating expenses account for only 69.5% of revenue, and it's the first time this ratio has ever been below 70%. Considering the inflationary pressures and high gas prices the company is facing, this is a very impressive result.

One competitive advantage Old Dominion has over its competition is its purposeful decision to operate with excess capacity. Essentially, Old Dominion aims to have the ability to ship 20% to 25% more goods even when that demand doesn't exist. 

While this can be a drag on the business during slow times, it's a massive advantage when demand surges. Old Dominion's ability to take on the additional demand ends up winning it customers and helping the business gain market share.

Lastly, the company prioritizes profitability and growth equally. On the Q2 earnings call, management stated, "Any dollar that we invest needs to have an appropriate return with it." The company has a stated goal of keeping its operating ratio below 70% and doesn't "want to just grow for growth's sake." As a shareholder, that is music to my ears.

Beat inflation by getting in "the Zone"

Bradley Guichard (AutoZone): Buffett is one of the most successful investors ever because he doesn't follow trends or jump from stock to stock with every headline. Berkshire Hathaway's holdings are a who's who of solid profit-making companies.

AutoZone is a terrific fit because the company has a tremendous buyback program, inflation protection, and a fair valuation. 

Apple makes up more than 40% of Berkshire's portfolio, and its prolific stock buyback program is a tremendous draw. However, AutoZone's buyback program is much larger as a percentage of the company's market cap. AutoZone has spent over $30 billion on buybacks since the program's inception in 1998 -- more than 70% of the current market cap. More than $4 billion, or 10% of the current market cap, was delivered in the last 12 months. You would be hard-pressed to find a company that can match this program pound for pound.

Vehicle prices are through the roof right now, and many folks feel priced out of the new and used vehicle markets. Prices have risen so fast that the damage is already done even when inflation ebbs. Automotive parts suppliers like AutoZone could be huge inflation winners as people hold on to their current vehicles. The anticipated demand for parts is a big reason AutoZone's stock is only down 1% this year, while the S&P 500 has tumbled 17%.

AutoZone stock is reasonably priced with a price-to-earnings (P/E) ratio under 19. This is lower than its chief competitor, O'Reilly Auto Parts, at 22. 

AutoZone isn't going to make investors rich tomorrow; however, long-term shareholders could have turned a $10,000 investment into $40,000 in the last five years. Buybacks, tailwinds, valuation, and history indicate that AutoZone is an excellent addition to a diversified long-term portfolio.