A Papa John's location in Denver Hyoung Chang | Denver Post | Getty Images

It's not getting any easier for embattled pizza chain Papa John's. The company is widely expected to deliver terrible earnings Tuesday night that show a continued slide in pizza sales, a steep drop in profit and trouble with its franchise owners during the third quarter — making finding a potential buyer all the more difficult. Further clouding its future to survive on its own, Papa John's lenders cut its credit lines and raised its borrowing rates last month. Analysts are projecting revenue to fall by about 9 percent, from $431.7 million during the same quarter last year to an estimated $393.7 million, according to estimates compiled by Refinitiv. Earnings are expected to take an even harder hit, from 60 cents a share a year ago to 22 cents a share during the third quarter. Those results will further complicate its efforts to find a buyer without having solved the thorny question of what to do with its cantankerous founder, John Schnatter, people briefed on the process say. A public battle with the former chairman and CEO has pummeled the company's shares, which have fallen 7 percent so far this year and about 40 percent from their all-time high of $90.49 in Dec. 2016. Papa John's ousted Schnatter as its chairman in July after a conference call leaked in which he used a racially charged slur. Since then, the company has been embroiled in a public relations nightmare that's included a war of words and two lawsuits. That drama came as the company was already struggling to compete against more innovative competitors like Domino's.

Terrible quarter

The company's second-quarter earnings missed nearly every key estimate tracked by Wall Street. But this quarter will be the first to fully reflect the impact of its feud with Schnatter. "This quarter is going to be terrible," Mark Kalinowski, CEO of Kalinowski Equity Research, told CNBC. Sales at locations open at least a year, a key measure of performance, fell 10.5 percent in July, and analysts estimate that the decline for the quarter was even steeper, 10.9 percent from last year. Same-store-sales for the entire year are projected to fall by up to 8 percent from 2017, with continued declines through the second quarter of 2019, according to average estimates by analysts polled by Refinitiv. The restaurant has enlisted the help of Bank of America and Lazard to explore a sale that has attracted initial bids from both corporate and private equity buyers, people familiar with the process have told CNBC. Initial bids for a company do not always result in a sale, and potential buyers often have at least one more round of bids before a buyer is selected. In this case, the obstacles to securing a buyer remain immense, said people briefed on the process who asked not to be identified because the discussions are private. "I'm skeptical that any deal could be done," said Stifel analyst Chris O'Cull. "Because I can't think of a good candidate to buy them." Schnatter, through a spokesperson, declined to comment. Papa John's said it doesn't comment on market rumors or results prior to its earnings.

Severance plan

The company appears to be preparing for a potential sale, sweetening its severance plans for top executives in case of a "change of control," or a possible sale. The plan, which took effect Nov. 1, pays "parachute payments" if the company changes hands and the executives decide to leave within the first two years due to no fault of their own, the company said in a regulatory filing Friday. It would pay current CEO Steve Ritchie three years of his base salary as well as a "retention equity grants" equal to three times his base salary, or more than $4.9 million based on his 2017 base salary of $820,377 — plus other incentives. Chief Financial Officer Joseph Smith and Chief Operating and Growth Officer Michael Nettles would both qualify for cash bonuses and equity grants that are each equal to two years of their base salaries, which haven't been disclosed yet. The change of control provisions are generally designed to give executives an incentive to stay on through a sale process, making it financially attractive enough so they don't jump ship before a sale closes and staying on long enough to ensure a smooth transition, compensation experts say. If Papa John's doesn't find a savior to buy the company, it may need to shutter number of restaurants to make up for declining sales and higher borrowing costs. The company was able to buy it some more time by renegotiating its lending agreements, but it came at a steep price. CFO Smith warned investors in August that the company was at risk of breaching its debt covenants at the time because its leverage ratio was getting too high. Papa John's lenders agreed Oct. 9 to increase its leverage limits in exchange for cutting its revolving credit line from $600 million to $400 million and increasing its borrowing costs, according to a regulatory filing. The company also has a $400 million term loan and has drawn about $585 million between the two as of last month, the company said.

Restaurant closures