With 1,263 Pizza Hut restaurants in 28 states, privately held NPC International is the largest franchisee of the Yum! Brands (NYSE:YUM) chain and the largest franchisee of any restaurant concept in the U.S. It owns one-fifth of the entire domestic Pizza Hut restaurant system and 22% of Yum!'s whole Pizza Hut franchise system in terms of number of units. In short, as NPC goes, so goes Yum!'s pizza business.

And lately it ain't going well. Sales last quarter fell 4.5% to $266.4 million as sales at restaurants open more than a year tumbled over 5%, much worse than the 4% decline in the year-ago period. NPC's President and Chief Executive Officer Jim Schwartz admits Pizza Hut is "struggling to find a functionally relevant consumer proposition and emotional connection" with customers who are struggling to save money even as it feels the pressure of a hypercompetitive marketplace.

Recently, I noted that despite growing interest in so-called gourmet pizza causing the proliferation of fast-causal pizza shops like PizzaRev, Blaze Pizza, and Pie Five, all of whom want to be the next "Chipotle of pizza," pizza sales are going flat. Following a number of years of strong growth, pizza sales are expected to grow just 2% this year, down from the 2.3% expansion in 2013, which itself was down from the nearly 4% growth the year before that. Unlike its dough, pizza is not rising.

That's borne out by Yum!'s own declining record of sales, with comps dropping for six straight quarters.

Source: Yum! Brands SEC filings.

That lack of a "functionally relevant consumer proposition" is likely why NPC International has been going on a buying spree, not of pizza parlors but burger joints, namely Wendy's (NASDAQ:WEN) restaurants. Over the past year, the franchise operator has strung together three separate purchases of Wendy's units, and this past Friday announced it was buying 56 more, giving it a total of 146 restaurants.

In contrast to NPC's experience with Pizza Hut, its Wendy's business is starting off well, as it helped increase sales by $17 million, or 7%. As it only began investing in the burger business last July, setting up a separate division called NPC Quality Burgers to run the outfit, how their overall impact is felt will be seen after it laps its first investment next month. But if Wendy's corporate operations are any indication, it should lead to further purchases.

First-quarter revenues came in at $523.2 million, down 13% from the year-ago period, but that was largely the result of closing over 400 stores during the past year. Company-owned stores saw comps rise 1.6% while franchised operations saw a 0.6% increase. That disparity, though, was due to the company-owned restaurants being more heavily represented in its Image Activation program, which is heavily overhauling the company's logo, packaging, and design.

Source: Wendy's.

Wendy's issued very bullish guidance earlier this year for 2014 based on further rolling out the program, and NPC International is equally hopeful for the future in that it plans to be part of the makeover.

While the franchisee itself isn't selling any of its Pizza Hut restaurants at the moment, and because it had grown so large by building up with just one brand, the Wendy's investments can also be seen as a smart way to diversify its business. True, but considering it's chosen Wendy's and even Yum! Brands is having difficulties getting all its moving parts working together, an investor would be making a smart choice in betting on the burger business growing even as the pizza shop falls.