The following information provides details on how the 2015 ACS 5-Year Adjusted Standard Quality 40th Percentile Rent of **$899** was developed for Madison, WI HUD Metro FMR Area using the publicly releasable distributions from the 2015 ACS.

The Standard Quality Gross Rents that HUD uses in generating FMRs are derived from rent distributions that are prohibited from public release under Title XIII to protect the confidentiality of respondents. The distributions used in this demonstration are rounded versions of the actual, protected data.

The rounding scheme is as follows:
0, count = 0

1 to 7, count = 4

all other counts are rounded to the nearest 5 (e.g., 10, 15, 20, 25, etc.)

Calculations using the rounded data may not produce the same result as calculations using the protected data. The difference between HUD's actual results and those demonstrated here is inversely related to the size of the area. That is, the larger the area, the closer the calculation based on the rounded data is likely to be to the census base rent computed from the protected data.

"Standard Quality" units and rents are determined by limiting the full ACS sample by including only responses meeting the following criteria:

- a. Occupied rental units paying cash rent
- b. Specified renter – on 10 acres or less
- c. With full plumbing
- d. With full kitchen
- e. Not constructed in the last 2 years from the survey date
- f. Meals not included in rent

The 2015 ACS did not included a question that could be used to filter public or assisted housing from the rental distributions, however HUD is required to ensure that FMRs exclude non-market rental housing in their computation. Therefore, HUD excludes all units falling below a specified rent level determined from public housing rents in HUD's program databases as likely to be either assisted housing or otherwise at a below-market rent (perhaps due to quality problems not otherwise captured by the survey questions).

The "public housing" rent cut-off for **Madison, WI HUD Metro FMR Area** in 2015 is $315.

The following table and calculations demonstrate how the 40th percentile 2015 ACS
Standard Quality Gross Rent is determined for **Madison, WI HUD Metro FMR Area**
using the public distribution of Standard Quality Gross Rents.

Portion of Standard Quality Gross Rent Distribution | Gross Rent Dollar Range | Number of Units | Percent of Eligible Distribution | Cumulative Percent |
---|---|---|---|---|

Units below interval containing public housing rent level of $315 |
$0 to $300 | 320 | Not in Distribution | Not in Distribution |

Units in interval containing public housing rent level of $315 |
$301 to $314 | 42.00 | Not in Distribution | Not in Distribution |

$315 to $349 | 98.00 | 0.3% | 0.3% | |

Units below interval containing 40th percentile Standard Quality Gross Rent of $899 |
$350 to $799 | 7,360 | 20.1% | 20.3% |

Units in interval containing 40th percentile Standard Quality Gross Rent of $899 |
$800 to $899 | 7,330 | 20.0% | 40.3% |

Units above interval containing 40th percentile Standard Quality Gross Rent of $899 |
$900 or more | 21,920 | 59.7% | 100.0% |

Total Units Above Public Housing Rent in Standard Quality Gross Rent Distribution | 36,708.00 |

The numbers of units with Standard Quality Gross Rents above and below the Public Housing Rent level of $315 for Madison, WI HUD Metro FMR Area is determined using linear interpolation over the 140 units in the rent range $301 to $349. Linear interpolation uses the assupmtion that the 140 units' rents are uniformly distributed in the rent range around the Public Housing Rent level. Under this assumption, the proportion of the rent interval ($49) that is below the Public Housing Rent level is the same as the proportion of units with rents in the interval (140) that have rents below the Public Housing Rent level.

Proportion of rent interval below the Public Housing Rent Level: ($315 - $301) / $49 = 0.2857

Units in the Public Housing Rent Level Interval below the Public Housing Rent Level: 0.2857 x 140 = 40.00

The 40th percentile Standard Quality Gross Rent for **Madison, WI HUD Metro FMR Area** is computed by linear
interpolation over the 7,330 units in the rent range
$800 to $899. Linear interpolation
uses the assupmtion that the 7,330 units' rents are uniformly distributed
in the rent range around the 40th percentile.
Under this assumption, the proportion of the rent interval ($100)
that needs to be added to the lower limit of the interval to reach the 40th percentile rent
is the same as the proportion of units in the interval that needs to be added to the units in lower rent intervals
to reach 40 percent of units in the distribution.

40 percent of units = .4 x 36,708.00 = 14,683.20

Units below the 40th percentile rent interval = 7,360.00 + 98.00 = 7,458.00

Units in 40th percentile rent interval needed to reach 40 percent of units = 14,683.20 - 7,458 = 7,225.20

Additional Units as Proportion of Interval = 7,225.20 / 7,330 = 0.9857

Dollars Added to Lower Limit of Interval to reach 40th percentile rent = 0.9857 x $100 = $99

**40th percentile Standard Quality Gross Rent = $800 + $99
= $899 **

Prepared by the Economic and Market Analysis Division, HUD. Technical Problems or questions? Contact Us.