A troubled pension fund for union workers at Lunds & Byerlys supermarkets is a key sticking point in a court battle to determine the value of the Lund family’s business.

Lunds plans to withdraw from the pension fund — pending approval by union employees on Sunday — and pay out $57 million to cover its liability. Attorneys for Kim Lund, one of the company’s four sibling owners, questioned the timing of the withdrawal, arguing that it improperly reduces the value of her stake in the company.

Kim Lund sued Lunds Inc. and her brother, CEO Russell “Tres” Lund III, to cash out her 25 percent stake in the company. A five-day trial ended Monday, and now Hennepin County Chief Judge Ivy Bernhardson — who has ruled already that Lunds Inc. must buy Kim Lund out — must figure out the value of Kim Lund’s equity.

Kim Lund’s financial experts say her stake is worth about $80 million; Lunds says the number is just over $21 million. Plus, there’s a quirk.

Lunds’ valuation of Kim’s stake was lowered from an original June 2016 number of $42 million due to a downward revision of its financial projections — and the cost of the pension withdrawal.

Lunds’ largest pension fund “is seriously endangered,” Fred Miller, Lunds’ vice president for finance, testified during the trial. “It is seriously underfunded.”

But the withdrawal wasn’t authorized by Lunds’ board until Dec. 16 — more than two months after the court-determined valuation date of Kim’s stake in the company.

“It is undisputed on the record before the court that as of the Oct. 2, 2016, valuation date, the hypothetical future possibility of Lunds’ withdrawal from the pension fund was not certain, known, probable or even reasonably probable,” say court documents filed by Kim Lund’s attorneys.

The pension payout isn’t just a complication for Kim Lund. The $57 million obligation — combined with the minimum of $21 million that Lunds must pay Kim — will saddle Lunds’ now pristine balance sheet with at least $78 million in new liabilities. That means the company will likely have less cash for expansion and store remodeling, just as grocery competition intensifies in the Twin Cities market.

The company has 26 Lunds & Byerlys stores in the Twin Cities, where it targets an upscale niche in the grocery market. The solidly profitable company, which has a local market share of up to 10 percent, is equally owned by four siblings whose grandfather was the company’s founder, Russell T. Lund Sr.

Kim Lund, 57, filed her lawsuit in late 2014 after years of trying to free up her share. A teacher for 30 years, she testified during the trial that she wants to use her inheritance for philanthropy.

The two other sibling owners, Shauna Lund McFeeley and Robert Lund, have sided with Tres and the Edina-based company, testifying that Kim’s buyout will hurt both Lunds’ and their own financial interests, including possibly reducing the dividends they receive. The four Lund siblings get an annual pretax distribution of $2.7 million.

In order to keep the company in family control, Lunds has rejected any independent buyout of Kim’s stake, instead saying it will borrow to pay Kim Lund out over at least 10 years. The higher Kim Lund’s buyout value, the more debt Lunds must load on in addition to its $57 million pension liability, which is due to be paid out over five years.

The United Food and Commercial Workers, particularly Brooklyn Center-based Local 653, represents the majority of Lunds & Byerlys’ 3,700 employees. A pension withdrawal agreement between Local 653 and Lunds & Byerlys is up for a ratification vote on Sunday.

Local 653’s multi-employer pension plan, whose largest member is Supervalu’s Cub Foods, has become increasingly troubled, according to testimony at the trial. The plan has been “seriously endangered” since May 2016, according to Lunds finance vice president Miller.

The 653 pension has experienced poor returns on its assets, Miller said. And, like many pensions nationally, it’s suffered from the erosion of union employment. As union membership decreases, fewer employees are paying into pension plans.

Local 653 saw its ranks decline by 39 percent to 9,617 members between 2000 and 2013, according to annual reports filed with the U.S. Department of Labor. Membership increased a bit in 2014, before falling to 9,265 in 2015. Records for 2016 aren’t yet available.

Unionized supermarkets have been hit with steep nonunion competition over the past two decades, as Target, Wal-Mart, Costco and more lately Hy-Vee have captured chunks of the Twin Cities market.

Miller testified that UFCW Local 653 agreed there was a problem with the pension, and that management and labor have long worked together to solve it, short of a withdrawal. Local 653’s president, Matthew Utecht, didn’t return calls for comment.

Miller testified that by August, after receiving a pension actuary report, “It just didn’t look like a sustainable situation to us” to remain in Local 653’s pension plan. A withdrawal was in order. The longer Lunds stayed in the deteriorating plan, the more its pension liability would grow — increasing its financial risk.

Lunds’ board decided in December to negotiate a withdrawal from the pension with Local 653 leadership. The two sides met in January and came to an agreement.

Under the plan, Lunds & Byerlys workers vested in the pension would get the benefits they accrued before the withdrawal. After the withdrawal, those workers as well as new workers would be eligible for a 401(k) plan, which Lunds & Byerlys would help fund as it did the pension.

Lunds’ 2016 fiscal year concluded Oct. 2, which is why the judge set that as the valuation date. Kim Lund argues that the company’s audited 2016 statements do not take into account the $57 million pension withdrawal, so the court should not either.

“If the pension withdrawal had been ‘either probable or reasonably possible’ as for the Oct. 2, 2016, valuation date, then the auditor would have been required to record that associated liability in the audited financial statements,” say court documents filed by Kim Lund.

The auditor, while it noted Lunds’ difficulty with the pension plan, didn’t record a withdrawal liability.