We all know that big American companies are having their profits hurt because of the dollar’s value rising relative to the world’s other major currencies.

But what you probably don’t know is that the dollar’s strength is making the profitability of some major American companies look better than it otherwise would.

Hello? Does this make any sense? Not in the real world. But in the accounting world, it adds up beautifully across and down, as I learned from Jack Ciesielski, publisher of the Analyst’s Accounting Observer.

Because of the dollar’s rise, a U.S. company’s assets denominated in foreign currencies are worth fewer dollars. This “currency translation” decline reduces a company’s stated net worth, which accounting and securities-analyst types call “equity.”

Return on equity — a company’s profit divided by its equity — is a key profitability metric. In fact, it is probably the key profitability metric when it comes to comparing financial performances of companies in the same industry. And, in many cases, return on equity is a key statistic when it comes to the formulas for executive bonuses.

Although the decline in the value of the dollar produces a loss of value to shareholders by reducing the company’s net worth, the decline directly reduces stockholders’ equity without showing up in the company’s reported profit. (Don’t ask why this is, because it will make your head explode. Just accept it as a fact.)

So the currency translation loss is great if all you care about is a company’s return on equity. Its profit stays the same, but its equity shrinks. This makes the return on equity — profits divided by equity — look better.

We’re talking serious money here. In the first quarter of this year, according to Ciesielski, the dollar’s rise knocked $72 billion — 1.5 percent — off the combined equity of the 289 members of the Standard & Poor’s 500-stock index that have fiscal years ending Dec. 31.

About a quarter of that currency-translation loss is from the decline in the dollar value of the cash the firms hold outside the United States, Ciesielski says. The rest of it is from the decline in the dollar value of other assets of companies’ offshore subsidiaries that keep their books in non-dollar currencies.

The biggest paper losers: Philip Morris International, whose equity shrank by $376 million because of the foreign currency effect; Corning, $319 million; Illinois Tool Works, $305 million; and eBay, $297 million.

“It’s not too bad yet,” Ciesielski told me, but “it’s like having a beachfront house with the waves getting a little closer.”

Given the chaos afflicting the euro these days, the dollar’s value relative to other foreign currencies’ seems likely to rise, at least for the short term. This means that currency-translation losses are likely to keep mounting. There’s no way to tell what they might total this year, but you can see where the figure could total $500 billion (my estimate, not Ciesielski’s) for the S&P 500 companies this year.

Ciesielski suggests that with stock prices at near-record highs and the dollar deterioration on equity starting to become more serious, this might be a better time for many companies to be selling new shares to bolster their equity than to buy back shares and deplete their equity. First-quarter buybacks totaled $102 billion. “I always thought that managements were supposed to be concerned about the capital structure for the long term,” he says. Yeah, right.

Ciesielski also suggests that in some cases, it could be worth a company’s while to pay whatever U.S. income tax it takes to bring its non-dollar offshore cash holding into the United States and convert it to dollars to avoid having it lose even more value. I don’t expect to see a whole lot of that, either.

This is, after all, the most glorious week of the year for those of us who take pride in our country. Hey, you never know: Some big American corporations might surprise us by caring enough about their balance sheets to do the right long-term thing for their shareholders and for our country. And on that note: a happy Fourth to you and yours.