Donaldson Co. announced a share repurchase program last year as part of its strategy to ­support “our strategic growth plan while also returning cash to our shareholders through dividends and share repurchase.”

What Donaldson didn’t add, and no other company seems to volunteer either, is that it’s also buying back shares in the market to keep the stock that executives receive from bloating the share count and penalizing earnings-per-share.

For all of fiscal 2015, Donaldson spent about $256 ­million to buy back 6.7 million shares, but the last two annual report filings with the Securities and Exchange Commission show that the share count didn’t decline by that much. So the share count would have grown without the buyback.

The story is the same at Polaris Industries, which bought back 2.2 million shares last year while the total share count didn’t decline by that much.

Of course, these companies are only doing what most big companies do, offsetting the dilution of stock they use as pay with share buybacks in the market. What’s different this year is that the practice is getting attention, partly because the New York Times highlighted an otherwise low-profile investment firm’s study criticizing it.

To that firm, New Jersey-based Wintergreen Advisers, a buyback helps create a hidden “look through” expense to shareholders. That is, the company’s owners bear an additional economic pain that will not hit the company’s financial statements.

A stock option or right to receive stock clearly has value, even with uncertainly over what it will be worth when cashing in, so financial statements capture an expense. The point here is that the dilution, and then the use of cash to buy stock in the market at higher prices to offset the stock awards, easily swamps the reported expense.

Even though a fashionable stock compensation plan now might feature performance share units, or PSUs, the effect on shareholders is the same as the board issuing a bunch of stock options. Wintergreen said executive compensation relentlessly increases the share count, on average about 2.5 percent per year for the companies in the S&P 500.

The problem with having more shares outstanding, of course, is that it means splitting the profits into more and smaller pieces. With a share’s value rising and falling on reported or expected earnings-per-share, having more shares outstanding cuts earnings per share (EPS) even if the business made just as much money as it did the last quarter.

One way for directors to fix this problem is to tell the executives they will no longer get any stock awards. But then they’d watch the executives disappear forever down the elevator after the board meeting. Their other choice is to approve buying back stock.

This isn’t the only reason to repurchase shares, of course. But checking into a half-dozen companies whose executives are on the top third of the Star Tribune’s compensation list, there wasn’t a one that didn’t have a share repurchase plan currently in place. All of them extensively used some form of stock-based compensation, too.

Paying executives in shares and buying stock back seem to go hand in hand, according to a study from earlier this year that broke apart the compensation practices in the S&P 500. This study is just the latest to suggest that share buybacks are a way of rewarding executives for short-term thinking.

While it might seem obvious that directors shouldn’t reward a CEO for reaching an earnings-per-share target in a disappointing year just because the share count was reduced, that’s actually happened.

In an example highlighted last year by Reuters, the big health insurer Humana reported worse than expected quarterly results in late 2014, easing the pain for shareholders by promptly announcing an additional $500 million share repurchase. This took out enough shares to allow Humana’s CEO to beat his EPS target by a penny — and collect a $1.7 million bonus.

Maybe this got the attention of some other boards; IBM actually made news this year by adopting the common-sense practice of not paying its CEO for meeting an EPS target if he or she got there only through an unplanned stock repurchase.

Even if companies figure out how to avoid paying for a fake EPS ­success, linking stock-based pay to total shareholder return can also turn the CEO into a vocal proponent of buying back stock.

That’s because one way to quickly boost the stock price is to take the cash in the bank, or even borrow money, and buy back a lot of shares.

You can almost hear the objections of experienced corporate directors, harangued for years to make sure they richly paid their executives only if shareholders did equally well. If using total return to shareholders to measure success is off the table, what exactly do you want us to use? Well, just make sure the plan rewards the creation of real business value.

Bloomington-based Donaldson happens to have a plan that does that, rewarding executives for both sales gains and return on investment, clearly concluding that if sales grow and the capital invested in the business yields enough return then the stock price should take care of itself. It’s no surprise that Donaldson’s shareholders, last time they were asked, overwhelmingly supported its stock compensation plan.

Target needed more than 30 pages in its latest proxy to explain what it is paying executives. And one of the measures in its long-term incentive plan is the compound annual growth rate of EPS compared to that of a group of similar companies.

It’s worth noting that Target is also an aggressive buyer of stock, acquiring 11.4 million shares at a cost of roughly $900 million in the most recent reported quarter. It was part of a program that, you guessed it, reinforces the Minneapolis retailer’s “long history of thoughtfully returning cash to shareholders through dividends and share repurchase,” as the ­company put it.

At the end of the last fiscal year, Target also disclosed that nearly 19 million shares could be issued as some form of pay, at an average exercise price of $53.47 per share. Meanwhile, the shares bought back in its most recent reported quarter cost an average of $78.37.

Just the difference in prices here, applied to those nearly 19 million shares, comes close to a half-billion dollars. Even for a company as big as Target, that seems like a lot of money.