<!-- [if gte mso 9]> -->FORTUNE -- When a Wal-Mart executive boasted at a Goldman Sachs investor conference in September that 475,000 of the company's U.S. store associates make more than $25,000 -- meaning that a large portion of its 1.4 million workers in the U.S. make less -- a long-simmering debate about the company’s wages boiled over. Last week, a large protest outside a California Wal-Mart store led to 50 arrests.
Fueling the anger, Payscale, a salary information site, estimates that Wal-Mart CEO Mike Duke's 2012 pay of $23.2 million was 1,034 times more than the company's average worker. Wal-Mart has called that figure inflated.
So how much should Wal-Mart (wmt) pay its employees? To tackle that tricky question, I crunched a bunch of numbers and concluded this: Wal-Mart’s workers should get a 50% raise.
And get this: The company wouldn’t even have to disappoint Wall Street to pull it off. I’ll explain the math in detail below.
There are a number of ways to answer the question of what Wal-Mart should pay its employees. One possibility is this: The lowest wage that Wal-Mart can get away with paying. That is probably the way many employers do it, but it's far from the best economic answer. Better-paid employees are likely to work harder and stick around longer. If employees made more, they would have more to spend at Wal-Mart.
Many critics argue that because Wal-Mart made $17 billion in profits last year, it can afford to pay more and even has an obligation to do so. That's silly, too. Public companies have to make enough money to satisfy shareholders, or else their stocks tank and executives end up getting canned.
I came up with what I feel is a better, more scientific way to determine the answer. Then I called a couple of really smart economists to get it "peer"-reviewed. Sendhil Mullainathan, who teaches at MIT and received a MacArthur genius grant for his work in behavioral economics a few years ago, said he basically came to a similar conclusion as mine a few years ago. He says companies have more discretion in setting wages then they let on. "Really the question is not whether this is possible but why some companies don't do it [this way]," says Mullainathan.
Wal-Mart didn’t respond to requests for comment.
So without further ado, here’s my methodology: Start with Wal-Mart's sales, and then subtract what it has to pay the suppliers that make all the stuff on its shelves. Last quarter that number was $28.7 billion.
What remains is Wal-Mart's gross profit. Wal-Mart, like all companies, has to split that between three groups -- bondholders, stockholders, and employees. How much should go to each? Bondholders are easy. They've agreed in advance to an interest rate. Last quarter, Wal-Mart's interest payments were $553 million. That leaves us with $28.2 billion, based on last quarter, or $112.8 billion a year.
How much to pay stockholders is a little bit trickier. But you can figure it out by looking at the market. Here's where my math comes in. Stock market valuations and return on equity (ROE) tend to go hand in hand. ROE is the measure of how much income a company makes compared to a company's net worth, which is also sometimes called shareholder's equity. Charles Lee, a finance professor at Stanford -- my second peer reviewer -- has done a lot of research that shows investors are willing to pay more for companies that can produce higher returns on shareholders' equity.
But you can also use Lee's research to figure out just what returns Wal-Mart's investors are looking for. The average ROE of retailers in the S&P 500 (spx) is 16.95%. Their shares trade at price-to-book ratio of 2.9. Wal-Mart's price-to-book ratio of 3.5 is 20% higher than the group, which means that investors, based on Wal-Mart's current $79 share price, are expecting it to produce a higher-than-average ROE. How much higher? Lee says the relationship is not linear, or one for one. Let’s call it 18%. That means, based on Wal-Mart's current stock price, investors are signaling that they are looking for a return of 20%.
Remember, that's not money that Wal-Mart actually pays out to investors. Most of that money is reinvested in its business. But it does pay out some in the form of dividends. And Wal-Mart has a higher dividend yield than the average retailer in the S&P 500 -- 2.4% vs. 1.3%. Adjust that for Wal-Mart's valuation vs. other retailers, and that means 4.6% of the return shareholders are looking for comes from the giant retailer's outsized dividend. That means the ROE it has to satisfy investors after dividends is 15.4%. Wal-Mart's actual current ROE is 21%. "What that suggests is that even Wal-Mart's investors think the company should pay its employees more, or at least expects it will," says Lee.
How much more? Wal-Mart has a book value of $76.7 billion. Take 15.4% of that, and that means investors are looking to get paid $11.8 billion a year. That leaves $101 billion to pay employees.
Wal-Mart paid its top executives and board members $66.7 million last year. The rest of the money has to be split among Wal-Mart's remaining roughly 2.2 million employees. Of those, about 1.4 million work in the U.S. Assume that Wal-Mart spends about 2/3 of that on the salaries of its U.S. employees, because salaries are generally higher here. That leaves $66.6 billion for the U.S. workers, or $47,593. The Bureau of Labor Statistics estimates that 30% of the average U.S. workers' total compensation is spent on benefits.
That means the average Wal-Mart employee's take home pay should be $33,315. Wal-Mart doesn't say what its actual average salary is. But Payscale estimated it to be just over $22,000 at the end of last year.
The conventional wisdom, of course, is that if Wal-Mart were to hand out raises, its stock would tank. That may not be true. When Google (goog) announced a 10% raise for its employees three years ago, the stock dropped a bit but mostly recovered within a year. And Google's stock is 60% higher now than it was before the raise.
As Lee points out, investors are basically giving Wal-Mart's executives a green light to raise wages. So why not?