For the Japanese maker of Subaru cars, the plunging yen has turned a problem—a shortage of production in the U.S.—into an unexpected boon.

That is because exporting cars from Japan has become a highly profitable proposition, and Subaru’s parent, Fuji Heavy Industries Ltd. , does it proportionally more than anyone. It still makes 80% of its vehicles in its home country compared with 21% for Honda Motor Co.

Fuji Heavy expects a record net profit of more than $2 billion in the year ending March 2015 thanks to its largest market, the U.S., where demand for Subaru’s Outback and Forester sport-utility vehicles is surging.

The company is turning into a model case of how currency swings can change corporate fortunes. It is good news for Fuji Heavy and potentially bad news in Detroit, which only recently halted a decades-long loss of U.,S. marketshare to Japanese auto makers.

As recently as two years ago, one dollar bought just 80 yen. Now, after Japan’s central bank further eased its monetary policy on Oct. 31, a dollar buys more than 115 yen. That is a plus for Japanese companies that pay workers and suppliers in less-valuable yen, while taking in dollars from customers overseas.

“We make a small number of limited types of cars and we can’t simply be following the footsteps of other Japanese companies going global,” said Yasuyuki Yoshinaga, Fuji Heavy’s chief executive, in an interview. “Our strategy is to have a high domestic production rate regardless of the currency rate, and to have special care for quality.”

Since mid-November 2012, when the yen started to decline against the dollar, Fuji Heavy shares have quintupled, giving the company a market capitalization of ¥3.2 trillion ($27.5 billion).

While the weaker yen gives Japanese exporters greater pricing power, some analysts say it is unlikely to trigger a price war given rising demand for new cars in the U.S. Adam Jonas, an analyst at Morgan Stanley , suggested in a recent report that Japanese car makers could offer buyers more car for the same amount of money.

“We don’t think that the Japanese will start a price war, but rather a product offensive,” Mr. Jonas said.

For Fuji Heavy, even the sales slowdown in Japan and China could help. It can ship more cars to the U.S., where it expects its seventh year of consecutive sales growth and where supply is constantly tight.

“The question is whether we will continue to see a shortage in the U.S. even if we ship the ones that could have been sold in Japan and China,” Mr. Yoshinaga said.

Despite the temporary windfall, Fuji Heavy is still moving to produce more cars in local markets, to reduce its exposure to currency swings. It plans to expand its sole plant in the U.S., in Indiana, by March 2017, with a goal of making 310,000 cars there annually, up from 200,000 currently.

In the long run, overall vehicle production in Japan is expected to keep shrinking. In 2007, Japanese auto makers made 11 million vehicles at home. That is expected to drop to 9.2 million vehicles this year, and decline further to 8 million vehicles by 2020, said Satomi Hamada, an analyst at IHS Automotive.

By this time, Fuji Heavy had hoped to have a plant in China too. But authorities there blocked the move because Fuji Heavy’s largest shareholder is Toyota Motor Corp. and Toyota already has plants in China.

The China effort meant Fuji Heavy, the smallest among Japan’s major auto makers, had to put a U.S. plant expansion on the back burner. Nonetheless, Subaru’s U.S. sales doubled over the last seven years, as the auto maker built bigger cars to suit American tastes. In 2014, Fuji Heavy expects to sell more than 500,000 vehicles in the U.S., up 18% from a year ago, and the U.S. accounts for more than half of its global vehicle sales.

In addition to reducing relative manufacturing costs in Japan, the weak yen lifts the value of Japanese companies’ earnings when converted into yen. For every one yen rise in the value of the dollar, Fuji Heavy’s full-year operating profit increases by ¥9.7 billion, the company says.

Toyota is a big beneficiary too, because it is more reliant on Japanese production than its peers. Fitch Ratings Inc., a credit-ratings firm, says Toyota profits stand to see a “pronounced” gain if the yen stays put or get weaker.