Yahoo Inc., on its third-quarter earnings call, disclosed that it was writing down the value of its assets by $42 million because of investments in original video content. One culprit: “Community,” the cult-favorite sitcom that the Internet company resuscitated after the show had been canceled by NBC.

Yahoo’s chief financial officer Ken Goldman said that the company “couldn’t see a way to make money over time” on such a series.

A closer look at the economics Yahoo agreed to when it took over the series reveals why that was the case.

The company hasn’t disclosed the show’s financials. But according to people familiar with the matter, Yahoo paid Sony Pictures Television, the studio that produces “Community,” roughly $2.7 million per episode for the show’s 13-episode sixth season.

NBC had paid Sony only about $1 million per episode to air the previous season, the people said. Why the big price difference? Yahoo’s rate covered the full production costs of the show. Plus, Yahoo agreed to pay Sony a guarantee for syndication fees, the people said.

Typically, studios recoup only part of their production costs when they license a show to a broadcast network like NBC. If a show like “Community” cost roughly $2.2 million per episode to produce and a broadcaster pays around $1 million an episode to license it, then the studios expect to cover the rest of their costs and generate a profit by selling reruns to other channels on the dial, to international TV networks and to streaming video services like Netflix.

There’s no guarantee that the economic equation will work out, however. Some shows have more rerun demand than others. And lately, the U.S. syndication market has been weak, because viewers aren’t watching reruns on cable as much as they once did and networks therefore aren’t willing to pay as much to acquire those reruns.

Sony also may have been weighing whether there would be a robust market for the show from on-demand streaming services after it had been streamed for free on Yahoo.

In this case, Yahoo covered the risk for Sony—and that proved costly. Comedy Central, the cable network that had cut a deal to air reruns of earlier seasons of “Community,” never expressed interest in the Yahoo season of the show, according to people familiar with the matter. That triggered the guarantee provision of the deal, which meant Yahoo was on the hook to pay Sony $2.7 million per episode.

Based on that per-episode fee, Yahoo wound up paying about $35 million for one season of “Community.” That’s the cost side of the equation for Yahoo.

But the revenue dynamics were also challenging. TV networks generally have dual revenue streams: they sell advertising, and they get a slice of the money consumers pay each month for cable TV service.

A scene from the "Community" pilot on Hulu Photo: Hulu

In this case, Yahoo was relying on advertising alone. And while it wouldn’t be impossible for Yahoo to break even, the numbers show it would be very difficult.

For starters, Yahoo signed a unique product placement deal with Honda; not only were Honda vehicles featured in the show, but one episode centered on a Honda CR-V. The company hasn’t disclosed how much it was worth, but several ad buyers familiar with similar product integration deals estimated Honda paid in the range of $2 million on the low end and around $10 million on the high-end. It would be possible to earn more than that, they said, but it is rare. Honda declined to comment.

As for the advertising that ran during episodes of the show, several buyers said Yahoo was seeking a rate of around $40 per thousand viewers, on the high side for online video, though they believed it was more likely the company didn’t reach that level in its deals.

One top media buyer said that it was rare these days for Web video ads to sell for as high as $30 per thousand viewers and that prices for premium Web video typically hover in the $20 range.

So let’s assume the relatively rosy scenario where Yahoo secured $10 million for the Honda deal and sold 16 ads per episode at its desired $40 ad price. Yahoo would still need around three million viewers per episode to at least break even. Those are a lot of assumptions, of course, but it gives an indication of the audience “Community” would need to draw to prevent Yahoo from losing money.

Three million viewers would be an ambitious target, media and ad executives say. While Nielsen data show that “Community” averaged 3.7 million viewers an episode in its fifth season on NBC, attracting that kind of audience would seemingly be challenging for a Web company jumping into TV-caliber video content for the first time without an existing base of TV viewership. To put it in perspective, Yahoo’s live stream of a National Football League game last month averaged 1.64 million viewers in the U.S.

If the assumptions were less generous—say, Yahoo could only fetch $20 ad prices instead—then the show would have needed to draw six million viewers per episode to just cover its costs.

Yahoo has not reported how many people watched “Community.”

It’s possible that Yahoo never expected to make money on “Community,” but instead saw the show as a loss leader that would drive more viewers to Yahoo Screen and its other content. But this past March, when the sixth season of “Community” premiered on Yahoo Screen, traffic to the site actually dipped by 2 million unique desktop visitors compared with the previous month, landing at just under 9 million, according to comScore.

That channel’s traffic had peaked in May at nearly 16.5 million unique users, but it slipped to less than 8 million visitors this past September. Of course, it’s possible that Yahoo Screen’s audience has grown on mobile devices and connected TVs, which comScore does not currently track.

Adam Kasper, chief media officer at Havas Media, said that Yahoo is learning a lesson that companies like Microsoft have already learned -- original content is a very tough business.

“Yahoo has so many priorities from a technology perspective, and is doing well with live video and current events video content,” he said. “I think they could not pay this particular effort the attention it needed.”

As of now, it is unclear whether a seventh season of “Community” will be produced. In August, star Joel McHale said on Twitter that the show hasn’t been canceled. Meanwhile, Yahoo continues to signal that the company is pulling back on acquiring original scripted series.

Write to Mike Shields at mike.shields@wsj.com