BART’s tentative new labor pact will guarantee “no strikes” for the next five years, but how the aging and budget-strapped system will pay for 10.8 percent in raises and other goodies remains to be seen.

According to a staff report presented at Thursday’s board meeting, the new union deals will cost about $77 million over the life of the new contract.

At same time, it was announced that BART faces a $400 million deficit over the next 10 years unless voters in San Francisco, Alameda and Contra Costa Counties approve a $3.5 billion fix-up bond.

But even if voters approve the bond, it won’t cover the labor deals — leaving BART to come up with the extra millions at time when ridership has maxed out and sales tax revenues that help fund day-to-day operations are slowing, the same report concluded.

Still, in announcing the new deals, BART General Manager Grace Crunican√ said they would not result in any new fare hikes outside those pegged to inflation.

So where will the money come from?

“That’s what we are waiting to find out,” said BART director Joel Keller, who represents eastern Contra Costa County.

San Francisco Chronicle columnists Phillip Matier and Andrew Ross appear Sundays, Mondays and Wednesdays. Matier can be seen on the KPIX TV morning and evening news. He can also be heard on KCBS radio Monday through Friday at 7:50 a.m. and 5:50 p.m. Got a tip? Call (415) 777-8815, or e-mail matierandross@sfchronicle.com. Twitter: @matierandross