At Wednesday’s Republican presidential debate, Carly Fiorina defended her record as C.E.O. of Hewlett-Packard. She was fired in 2005, and Donald Trump, among others, has criticized her performance.

The early 2000s were a tough time for the tech industry, she said, and yet, “despite those difficult times, we doubled the size of the company, we quadrupled its topline growth rate, we quadrupled its cash flow, we tripled its rate of innovation.”

The key undermining word in that statement is “topline.”

A company’s top line is its revenue — how much money it takes in, before expenses. What shareholders really care about is the bottom line, or profit. As Mr. Trump correctly pointed out on Wednesday, Mrs. Fiorina’s strategy to quickly grow H.P.’s top line was to buy another large company, Compaq Computer. That deal was widely criticized at the time because it got H.P. a big increase in sales but little profit. Revenue from personal computers barely exceeded the company’s cost to make and sell them.

H.P.’s best-known division, and by far its largest before the 2002 Compaq acquisition, is its printer business. H.P. had both the largest piece of the printer market and the most respected printer brand. This business made huge profits, especially off ink and toner. But printers were a mature business in the early 2000s and are even more so now as people print less: You can still make a profit on printer sales, but it’s hard to get the total size of the printer market to grow. If H.P. wanted to get bigger, it was going to have to grow in other areas.

Before the merger, H.P. was also in the business of manufacturing personal computers. This business wasn’t profitable like the printer business; Windows P.C.s were essentially commodity products. It was hard to convince consumers to pay more for a computer from H.P. than one from I.B.M. or Toshiba. Vicious competition on price drove profit margins down almost to zero.

At the time, H.P. struggled to compete with Dell, which had an advantage because it could sell computers directly to consumers instead of through stores and because it had lower manufacturing and distribution costs. (Dell’s fortunes have waned in the years since Fiorina’s tenure.)

The idea behind H.P.’s purchase of Compaq was that, by getting a bigger slice of the P.C. market, the company could find economies of scale, get better prices on parts and raise its profit margins. Mrs. Fiorina pushed the acquisition through over objections from much of H.P.’s board and, most notably, the family foundations of the founders that held a large chunk of the shares.

But the merger did not produce the expected improvements in profits. In 2004, the combined company had $24.6 billion in revenue from selling computers, slightly more than the $24.2 billion it took in from printers. But it made just $200 million in profit from its computer business, a profit margin of less than 1 percent, compared with $3.8 billion in profits from printers.

As Carol Loomis wrote for Fortune Magazine in 2005, the Compaq merger brought a lot of growth to H.P. but not the sort that H.P.’s board or its shareholders found attractive. Hewlett-Packard’s profits in 2005 were $2.4 billion, a billion less than in the year Mrs. Fiorina started as C.E.O. That is a key reason she was fired.

That said, profits rebounded under the next C.E.O.