Investing guru Benjamin Graham once quipped that in the short run, the market is a voting machine, but in the long run, it is a weighing machine. In other words, just because the market offers you a price for the shares you own, that doesn't mean they're trading at a fair value for what the underlying business is worth. Smart investors recognize that Graham's words mean every once in a while, the market offers a price for a company that is simply too good to pass up.

We asked three Motley Fool contributors to search the market for situations where it looked like the market was offering to sell investors shares of a company at a bargain price. They picked (CYOU), Caterpillar (CAT -0.39%), and Realogy (HOUS -0.30%). Read on to discover why, and determine for yourself whether one or more of them may be worth investing a bit of your hard-earned money.

A graph with a y cost axis and value x axis, with an arrow targeted on low cost and high value.

Image source: Getty Images.

This Chinese video game company offers multiple ways to win

Keith Noonan ( Ask most American video game fans and investors what they know about and the question might elicit blank looks -- but anyone seeking deeply discounted stock would do well to narrow in on the company. The Chinese video game developer and publisher was spun off from Sohu (SOHU 1.23%) in 2009 and is most known in its domestic market for its role-playing-game franchise TLBB. The game series may be past its heyday, but it's still putting up solid results and helping deliver regular profits after enabling the company to build up a sizable cash pile.

After paying out roughly $500 million in a special dividend distributed in June, Changyou still has roughly $170 million in cash and zero debt on the books. The company has a market capitalization of roughly $500 million and trades at just 4.5 times this year's expected earnings. Back out that cash position (along with real estate holdings and other assets) and the stock looks even cheaper.

Sohu remains Changyou's majority shareholder, and with the parent company needing cash to offset weakness for its core business and potentially looking to take both companies private, it's not unreasonable to expect that another special dividend could be paid within the next year. That would once again have the effect of moving cash back to Sohu, and then pave the way to take the gaming company private and funnel profits to the parent business without having to pay a premium on the offshoot's cash pile at the time of a buyout. It's usually not prudent to buy a stock and bank on an acquisition to power your returns, but there's a good chance investors can look forward to the beaten-down company fetching a premium in the event of a sale. And if Changyou isn't sold and remains public, investors can feel reasonably confident they're buying the stock at deep-value prices.

This stock is the Cat's meow

Rich Smith (Caterpillar): Last fall, shares of industrial giant Caterpillar were selling for nearly $160 apiece. Just nine months later, the stock costs less than $134 today -- cheaper by $25 and change. If you ask me, that's a nice price to pay for a stock of Caterpillar's caliber.

So why is Caterpillar so cheap?

In part, I suspect fears that the Trump trade war with China will depress sales abroad have been keeping investors away from Caterpillar stock. In another part, investors are worried that rising interest rates will put a damper on the housing industry's demand for construction equipment.

But the trade war's been going on for some time now -- yet Caterpillar grew its earnings 13% last quarter. And this week, The Wall Street Journal reported that the Fed is more likely to lower interest rates than to raise them, at least in the short term.

Despite these reasons for optimism, Caterpillar stock today sells for just 12.5 times earnings. (To put that in context, the lowest average P/E ratio Caterpillar stock has endured over the past five years was 12.9.) Analysts on average predict the company can grow earnings at 11% a year going forward -- and Caterpillar pays a 3.1% dividend yield, half again as much as the average S&P 500 stock.

At a depressed valuation and with business looking up, I think Caterpillar stock looks absurdly cheap right now.

Is the market "fighting the last war" when it comes to real estate?

Chuck Saletta (Realogy): Real estate was a large driver of the 2007-2008 financial collapse. Enabled by cheap money, crazily lax lending standards, and the insane belief that real estate prices could only go up, a bubble formed, then burst. That bursting bubble knocked out much of the lending market and took out some fairly substantial financial companies when it did. Investors scarred by that experience are proving to have fairly long memories, which may well be creating an opportunity in Realogy.

The parent company behind such real estate titans as Century 21, Coldwell Banker, and ERA, Realogy makes money whenever one of its companies is involved in a real estate transaction. That makes it very exposed to the ups and downs of the real estate market. As a result, when investors are worried about real estate, they're generally worried about Realogy as well.

Realogy recently traded hands at less than eight times its trailing and six times its projected earnings, levels you'd typically expect for businesses in terminal decline. Yet analysts are expecting its earnings to grow at a whopping 20% annualized rate over the next five years, which is completely inconsistent with where the market is pricing its shares. Either the market is overly pessimistic or analysts are wildly optimistic, but at least one set of prognostications looks to be substantially off base.

That's where the opportunity in Realogy's shares comes from. Even if you presume that the analysts are way off base, there's a massive gap between 20% annualized growth and terminal decline. As long as the company's business remains relatively stable or shows any growth at all over time, Realogy's shares look absurdly cheap today.