OTTAWA - The federal government is facing new questions about how much its plans for a rent-supplement program for low-income households will help them afford high rents, detailed in a new study and newly obtained government documents detailing the affordability crunch.

The new portable housing benefit is to roll out next year and will be tied to a person rather than a unit - meaning recipients can carry it with them through the housing market rather than losing the financial help when they move out of government-supported dwelling.

Its design is to be tailored to each province.

A study released Thursday by the Canadian Centre for Policy Alternative shone a critical light on the supplement as part of research that found a minimum-wage worker could afford to rent in just a few neighbourhoods in Canada.

Spending on the benefit is set at $4 billion over a decade - split among federal and provincial governments - which will require tough decisions about who gets it, how much they can receive, and when it gets taken away.

“You really have to ration it based on some simple criteria, otherwise you blow through your (spending) cap,” said David Macdonald, a senior economist with the CCPA who wrote Thursday's study.

“Second of all, it's likely not generous enough to substantially reduce the rent for renters, particularly at the lower end of the income spectrum and particularly in big cities like Vancouver, Toronto, Victoria, Calgary, Ottawa.”

A spokeswoman for Social Development Minister Jean-Yves Duclos, the minister in charge of the new rent supplement, called the Canada Housing Benefit, “a new tool fighting the challenge of housing affordability.”

Valerie Glazer said the benefit, when it rolls out, “will provide rapid and responsive relief from rising housing costs” for at least 300,000 households and “deliver unique local solutions to local housing needs and priorities.”

Thursday's report from the CCPA painted a grim picture for low-income renters.

The report said that someone earning minimum wage would only be able to afford a one-bedroom rental in nine per cent of 795 neighbourhoods in Canadian cities in the study. The figure dropped to three per cent of neighbourhoods when looking at the affordability of two-bedroom units.

The report defined “affordable” rent as 30 per cent or less of a renter's pre-tax income, the same cut-off used by federal officials.

Roughly one-third of households, or 4.7 million, are renters and they are often low-income earners, young adults, or newcomers to Canada.

The October briefing note to the top official at the Finance Department said that about 11 per cent of all renters lived in subsidized units in 2015. The vast majority earned about $17,000, less than half of the Canadian average of $48,000.

The Canadian Press obtained a copy of the document under the access-to-information law, but officials have blocked from release swaths of the briefing note containing advice to government.

Average rents, adjusted for inflation, have increased since the early 1990s as construction of traditional apartments declined in favour of homes and then condominiums, Macdonald said.

In the 1970s, he said, it wasn't uncommon to see 100,000 new, purpose-built rental units being constructed each year.

While there has been some uptick in rental construction over the last decade - mostly in the luxury rental market, Macdonald said - the Liberals hope to use billions in federal funding to help finance more than 100,000 new rental units to boost supply and drive down costs.

At the rate that money is being committed to projects, the study estimated most units won't come open until the late 2020s. Combining provincial and federal commitments, the study projected an average of 15,400 new rental units annually, well below the number the country saw decades ago when the population was smaller.

Macdonald said the benefit could provide some short-term help while the country awaits new rental units. But he said the benefit may not be enough for low-income renters to close the affordability gap.

“The Canada Housing Benefit is a good short-term solution as we wait 10 years for the rental housing market to build up and then hopefully increase vacancy rates and also stabilize rents,” Macdonald said.