The National Low Income Housing Coalition (NLIHC) released its annual report about housing affordability last week. The headline is that housing is unaffordable to minimum-wage earners in every state in the country.

NLIHC defines affordability as being able to pay the rent of the fortieth percentile rental unit with 30 percent of the minimum wage. So, if the minimum wage is $7.25 (as it is federally), then the annual wage for a minimum wage earner is $15,080, and the monthly wage is $1,256.67. Thirty percent of $1,256.67 is $377. Thus, for housing to be affordable in an area under this measure, the fortieth percentile unit would need to rent for $377 or fewer dollars.

The peculiarities of this measurement always raise a few eyebrows from those who pay close attention. This year, Jodi Beggs was among those calling foul. Why does the NLIHC use 30 percent of the minimum wage as the barometer of affordability? Why does it use the fortieth percentile rental unit when you would expect a minimum-wage earner to live in, say, the tenth percentile unit?

These objections have understandable answers. The Department of Housing and Urban Development (HUD) considers families that spend more than 30 percent of their income on rent to be “cost burdened” and considers the fortieth percentile rent in an area to be the “fair market rent.” Also, HUD only publishes the fortieth percentile rents, meaning that is the figure the report authors have to work with.

But these answers still leave open a lot of interesting questions. Even if their measure of affordability is defensible, it would nonetheless be interesting to know: what does the tenth percentile rental unit charge? How affordable are units up and down the rental spectrum?

Hoping to answer some of these questions myself, I dug into the American Community Survey to produce the following figures. Note that, for these figures, I use the federal minimum wage and the rental distribution of the whole country. You could do this for individual states as well, but that would take more time than I want to devote to this.

Here is the rent level at each percentile. I cut it off at the eightieth percentile because units above the eightieth percentile rapidly escalate in price and throw the scale of the graph off (and are also somewhat irrelevant to the task at hand).

As you can see, the median one-bedroom unit rents for $830 while the median two-bedroom unit rents for $950. The fortieth percentile unit rents at $740 and $865 respectively. The tenth percentile unit rents at $330 and $540, respectively.

Here is the same graph, but the vertical axis is now expressed in terms of percentage of the federal minimum wage.

The fortieth percentile rent requires 58.9 percent of the minimum wage for a one-bedroom unit and 68.8 percent of the minimum wage for a two-bedroom unit. At the tenth percentile, the rents are 26.3 percent of the minimum wage and 43 percent of the minimum wage, respectively.

Finally, here is the same graph, but the vertical axis shows the hourly wage necessary to afford the rent without being “cost burdened,” i.e. to be able to afford the rent using only 30 percent of your labor income.

The fortieth percentile unit requires a wage of $14.23 for a one-bedroom and $16.63 for a two-bedroom. At the tength percentile, it’s $6.35 and $10.38.

Doing the same kind of calculations with the entire rent distribution basically confirms the headline argument of the NLIHC. It really does appear to be difficult to afford rent at the minimum wage, even at quite low percentiles of the rent distribution and even when looking at the entire country. Once you get past the weird rental values at the very bottom of the distribution (for example, the $4 rent at the zero percentile), you quickly run into units whose rents are so high that it would be hard to pay for them and still have enough money left over for your other consumption needs.

As I noted in my Huffington Post interview on this report, governments can take three steps to ensure low-wage workers can afford to rent housing: (1) build out an adequate supply of social housing, (2) increase wage floors, and (3) increase welfare incomes.