Let's be frank. $10,000 is quite a chunk of change. If you've accumulated $10,000, and are wondering where to invest it now, your first objective is probably making sure you don't lose $10,000 by making a bad bet. And yet, after seeing the stock market perform so well in 2020, you probably would like to make a bit of profit in 2021, too, right?

Lucky for you, you can have your cake and eat it, too.

How? First and foremost, limit the amount you can lose by investing in more than just one stock -- i.e., diversify. And second, buy stocks that are objectively cheap to limit your risk of overpaying, and maximize your chance that those stocks can grow. Three stocks that I think fit the bill on both counts are iRobot (IRBT -0.14%), LGI Homes (LGIH -0.05%), and Southwest Airlines (LUV 1.10%).

Stack of $100 bills wrapped in a $10,000 wrapper

Image source: Getty Images.

iRobot

No doubt about it, iRobot had a great year in 2020. In all three quarters reported so far, the company beat Wall Street's earnings estimates -- including in the June quarter, when earnings of $1.06 per share more than tripled analyst expectations.

This was partly a function of the pandemic. With cleaning services banned from most peoples' homes, and quarantined families making more mess at home than usual, Roomba robotic vacuums and Braava robotic floor mops "resonated" with consumers, according to management. But really, with sales up only 12.5% year-over-year through Q3, 2020's performance was pretty consistent with the 11% sales growth seen in all of 2019.

For this reason, analyst predictions that iRobot will suffer a slowdown in sales growth this year (7%) and next (9%) might be overly cautious. Management noted last quarter that "even as the competition intensifies," iRobot remains the "undisputed global category leader" in robotic floor-cleaning products. So rather than interpret 2020's sales success as "pulling forward" into 2020 sales that would otherwise have happened in 2021 (thus sapping sales strength this year), I suspect customers newly introduced to the company's products during the pandemic may actually turn into repeat customers in years to come, upgrading Roomba and Braava models from one year to the next.

And how much will you have to pay for these growth prospects, you ask? Valued at just $2.3 billion in market capitalization, iRobot stock sells for less than 15 times trailing earnings, and barely 10x its $235 million in trailing free cash flow. In other words -- it's a bargain.

LGI Homes

Entry-level homes-builder LGI Homes is another bargain. Despite a stock price that rose 49% in 2020, LGI shares still sell for a low 10.7 times trailing earnings. True, when valued on free cash flow, they're a bit pricier -- 15.4x FCF -- but with analysts forecasting 15.5% earnings growth over the next five years, LGI Homes stock is clearly in "bargain" territory.

The big question is whether LGI Homes can live up to the growth expectations. So can it?

Well, in 2019 sales at LGI grew 22%, and 2020's pandemic hardly dented growth at all. Through the first three reported quarters of the year, LGI grew sales 19% -- and profits grew 65%. Heading into the new year, furthermore, sales should continue to grow. After management noted in its last earnings report that orders grew 80% year-over-year in Q3, my fellow Fool Tyler Crowe called LGI "one of the fastest growing home builders in America," adding further that the company's 25% gross profit margin is "blowing [competing homebuilder margins] out of the water."

With a bargain-basement valuation and tremendous growth ahead of it, LGI Homes stock looks like a great place to sock away part of that $10,000.

Southwest Airlines

Last but not least, I'm going to suggest taking a bit of a flier (if you'll pardon the pun) on a pandemic rebound play: Southwest Airlines.

Now, I won't try to sugarcoat this: The pandemic has been horrible for airline stocks, devastating demand for travel, and at least initially forcing those airplanes that were still flying to do so with limited passenger loads. (Southwest Airlines is no longer limiting capacity on its flights, although it is warning passengers when flights are expected to be more than 65% full so that they can reschedule if they want to.) 

Unsurprisingly, this has done Southwest's revenues and profits no favors. Sales through the end of Q3 2020 declined 58% year-over-year, and instead of the $1.8 billion in profits Southwest had earned by this time last year, it's now looking at a $2.2 billion loss (which will probably get worse by the time Q4 results arrive).

All that being said, analysts expect Southwest's business to turn "green" again in 2021, as vaccines roll out and travelers resume traveling. Profits should return to 2019 levels within the next two to three years, and if you can be patient that long -- well, at just under $30 billion in market cap, Southwest shares currently sell for just 13 times 2019 earnings, and only about 10x 2019 free cash flow.

Southwest already looks like one of the strongest-positioned airlines in the industry, with a balance sheet that is net-cash positive and a cash flow statement that shows operating cash flow is also positive -- the exact opposite of how things look at rivals Delta Air Lines, United Airlines, and American Airlines. As the American economy emerges from its pandemic hangover, I expect Southwest to be the strongest performer in the airline industry by far.