A new tweak in the state sales tax could allow King County and its cities to tap a big new source of funding for affordable housing — without raising new taxes.

On Wednesday, King County Council members will vote on whether to access a state sales-tax credit authorized by the Legislature this year. The new law, HB 1406, lets counties and cities to divert a portion of the state sales tax to affordable-housing projects, which in King County could be $99.6 million over the next 20 years, according to preliminary estimates from the King County budget office.

Earlier this month, Seattle passed similar legislation to claim its share of the tax credit, which the Seattle Mayor’s Office estimates could provide $4.5 million a year or bonded for about $50 million upfront.

King County officials are encouraging other cities to pass their own ordinances. Smaller cities can spend the tax credit on rental assistance, while cities with populations of more than 100,000 — including Bellevue, Kent and Renton — can create housing for people making 60% of the area median income (about $60,000 a year for a family of four) or less.

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Across the county, the money is badly needed. A regional housing task force estimates King County needs 244,000 more affordable homes by 2040 to meet demand from low-income families. The task force’s five-year action plan calls for the county to build or preserve 44,000 homes for people making 50% of the area median income or less by 2024.

“Frankly, our 44,000 goal is about preventing homelessness,” King County Councilmember Claudia Balducci said. “If you can keep people from being unstable in their housing, you can really make a big difference in terms of new people entering into homelessness.”

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But it’s unclear at this point how much money those 44,000 units will cost. Balducci’s own back-of-the-napkin math assuming $200,000 per unit suggests it could cost billions of dollars. The new state sales-tax money won’t be enough to fill the need.

“The magnitude of this crisis, the scale of what we need to produce, is going to require a wholesale change in thinking from commitments from the private sector, the public sector and all of us working together,” Marty Kooistra, executive director of the Housing Development Consortium of Seattle-King County, said.

At the same time, the new sales-tax credit could allow smaller King County cities to pool new resources. The sales-tax credit could allow South King Housing and Homelessness Partners, a new coalition of South King County cities working to address the local affordable-housing shortage, to tap into nearly $1 million a year, according to Auburn Mayor Nancy Backus.

“We’re really in our infancy, but HB 1406 is really a great opportunity for South County cities to be looking at this in a different light,” Backus said.

Fourteen other counties have taken steps to access the new revenue, according to the Washington Low Income Housing Alliance, from Grays Harbor in the west to Whitman County on the state’s most eastern border.