4-Bedroom Rent Calculation for Richmond County, NC

The 4-Bedroom FMR is computed from a 2000 Census Base 4-Bedroom Rent and updated using the same update factors derived for the 2-Bedroom FMR. The 4-Bedroom FMR may be separately rebenchmarked from the 2-Bedroom FMR by a special RDD of 4-Bedroom rental units.

The actual 2000 Census 4-Bedroom Base Rent and Revised Final 2005 4-Bedroom FMR for Richmond County, NC are: $528 and $591. All FMRs are 40th percentile rents. The update factors used to derive the Revised Final 2005 4-Bedroom FMR are summarized in the table below. The sources of the update factors are the same as the sources for the 2-Bedroom FMR update factors.

4-Bedroom FMR Update Process 
 for Richmond County, NC 
Data Year  Amount  Change from Previous* 
2000 Census Base  $528 -
2001   $540  2.2% 
2002   $559  3.6% 
2003   $558  -0.2% 
2004   $574  2.8% 
FY 2005 Final   $591  3.0% 
FY 2005 Revised Final   $591  No Change 
*Change factors may not precisely match those on the summary
page due to rounding of FMRs to the nearest dollar.

The remainder of this page demonstrates how the 2000 Census 4-Bedroom Base Rent is computed.


4-Bedroom FMR Computational Techniques

FMR estimates are calculated for 2-bedroom units, the most common size of rental units, and therefore the most reliable to survey and analyze. After each decennial Census, rent relationships between 2-bedroom units and other unit sizes are calculated and used to set FMRs for other units. This is done because it is much easier to update 2-bedroom estimates and to use pre-established cost relationships with other bedroom sizes than it is to develop independent FMR estimates for each bedroom size.

Adjustments are made to the Census results for areas with local bedroom-size intervals above or below what are considered to be reasonable ranges or where sample sizes are inadequate to accurately measure bedroom rent differentials. Experience has shown that highly unusual bedroom ratios typically reflect inadequate sample sizes or peculiar local circumstances that HUD would not want to utilize in setting FMRs (e.g., luxury efficiency apartments in New York City that rent for more than typical one-bedroom units). Bedroom interval ranges were established based on an analysis of the range of such intervals for all areas with large enough samples to permit accurate bedroom ratio determinations. The final range for 4-bedroom units is between 1.14 and 1.63 of the 2-bedroom unit FMR. In Richmond County, NC, the 4-bedroom unit base FMR is restricted to be between $465 and $665 before application of the large unit adjustment described below.

The rents for three-bedroom and larger units continue to reflect HUDís policy to set higher rents for these units than would result from using normal market rents. This adjustment is intended to increase the likelihood that the largest families, who have the most difficulty in leasing units, will be successful in finding eligible program units. The adjustment adds bonuses of 8.7 percent to the unadjusted three-bedroom FMR estimates and adds 7.7 percent to the unadjusted four-bedroom FMR estimates.

Bedroom rents for a given FMR area are further adjusted if the differentials between bedroom-size FMRs were inconsistent with normally observed patterns.


User Note

In computing 2000 Census RentBedroom Rents, HUD actually uses data on 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 FMR AREA. THAT IS, THE LARGER THE AREA, THE CLOSER THE CALCULATION BASED ON THE ROUNDED DATA IS LIKELY TO BE TO THE CENSUS BASE FMR COMPUTED FROM THE PROTECTED DATA.


Recent Mover and Standard Quality Rents

HUD uses rents for recent movers in standard quality units to set the Census 2000 Base Rent. "Standard Quality" units and rents are determined by limiting the full Census sample by including only responses meeting the following criteria:

a. Occupied rental units paying cash rent
b. Specified renter Ė on 10 acres or less
c. with full plumbing
d. with full kitchen
e. built before 1999
f. meals not included in rent

"Recent Mover" rents are determined by further limiting the "Standard Quality" sample with the following additional criterion:

g. moved in within the last two years

The 2000 Census did not include 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 Census questions). The "public housing" rent cut-off for 4-bedroom units in Richmond County, NC is $290.


40th Percentile Recent Mover Rent for 4-Bedroom Units

The following table and calculations demonstrate how the 40th percentile Census 2000 4-Bedroom Base Rent is determined for Richmond County, NC using the public distribution of recent mover rents for 4-bedroom units in the FMR area.

Portion of Recent Mover Rent Distribution Gross Rent Dollar Range Number of Units Percent of Eligible Distribution Cumulative Percent
Units below interval containing
public housing rent level of $290
$1 to $274 10 Not in Distribution Not in Distribution
Units in interval containing
public houising rent level of $290
$275 to $289 0.00 Not in Distribution Not in Distribution
$290 to $299 0.00 0.0% 0.0%
Units below interval containing
40th percentile recent mover rent of $429
$300 to $424 14 33.3% 33.3%
Units in interval containing
40th percentile recent mover rent of $429
$425 to $449 20 47.6% 81.0%
Units above interval containing
40th percentile recent mover rent of $429
$450 or more 8 19.0% 100.0%
Total units Above Public Housing Rent in Recent Mover Rent Distribution   42.00    

There were no recent mover 4-bedroom units in the rent interval containing the Public Housing Rent level of $290.

The 40th percentile recent mover rent for Richmond County, NC is computed by linear interpolation over the 20 units in the rent range $425 to $449. Linear interpolation uses the assupmtion that the 20 units' rents are uniformly distributed in the rent range around the 40th percentile. Under this assumption, the proportion of the rent interval ($25) 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 = 0.4 x 42.00 = 16.80

Units below the 40th percentile rent interval = 14.00 + 0.00 = 14.00

Units in 40th percentile rent interval needed to reach 40 percent of units = 16.80 - 14.00 = 2.80

Additional Units as Proportion of Interval = 2.80 / 20.00 = 0.14

Dollars Added to Lower Limit of Interval to reach 40th percentile rent = 0.14 x $25 = $4

40th percentile recent mover rent = $425 + $4 = $429


40th Percentile Standard Quality Rents for 4-Bedroom Units

Before using the Census 2000 recent mover rent as the base FMR, HUD checks the standard quality rent for the area to ensure that the recent mover rent is high enough to reach as the 40th percentile standard quality units. The recent mover rent may be below the standard quality rent in areas where rental housing markets are particularly stressed such that recent mover rents will not cover the expenses of operating standard quality units.

The following table and calculations demonstrate how the 40th percentile Census 2000 standard quality is determined for Richmond County, NC using the public distribution of standard quality rents for the FMR area.

Portion of Standard Quality Rent Distribution Gross Rent Dollar Range Number of Units Percent of Eligible Distribution Cumulative Percent
Units below interval containing
public housing rent level of $290
$1 to $274 20 Not in Distribution Not in Distribution
Units in interval containing
public houising rent level of $290
$275 to $289 0.00 Not in Distribution Not in Distribution
$290 to $299 0.00 0.0% 0.0%
Units below interval containing
40th percentile standard quality rent of $446
$300 to $424 40 23.3% 23.3%
Units in interval containing
40th percentile standard quality rent of $446
$425 to $449 35 20.3% 43.6%
Units above interval containing
40th percentile standard quality rent of $446
$450 or more 97 56.4% 100.0%
Total Units Above Public Housing Rent in Standard Quality Rent Distribution   172.00    

There were no standard quality 4-bedroom units in the rent interval containing the Public Housing Rent level of $290.

The 40th percentile standard quality rent for Richmond County, NC is computed by linear interpolation over the 35 units in the rent range $425 to $449. Linear interpolation uses the assupmtion that the 35 units' rents are uniformly distributed in the rent range around the 40th percentile. Under this assumption, the proportion of the rent interval ($25) 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 = 0.4 x 172.00 = 68.80

Units below the 40th percentile rent interval = 40 + 0.00 = 40.00

Units in 40th percentile rent interval needed to reach 40 percent of units = 68.80 - 40.00 = 28.80

Additional Units as Proportion of Interval = 28.80 / 35 = 0.8229

Dollars Added to Lower Limit of Interval to reach 40th percentile rent = 0.8229 x $25 = $21

40th percentile standard quality rent = $425 + $21 = $446

Since the standard quality rent of $446 is higher than the recent mover rent of $429, the standard quality rent of $446 is the unadjusted 2000 Census Base Rent for 4-Bedroom Units in Richmond County, NC.


Adjustments to 2000 Census Results

The unadjusted 2000 Census 4-Bedroom Base Rent of $446 is outside of the reasonable range of $465 to $665. It is therefore increased to $465.

To reflect HUDís policy to set higher rents for 4-bedroom units than would result from using normal market rents, the results obtained above are adjusted upward by 7.7 percent to $501 to increase the likelihood that the largest families, who have the most difficulty in leasing units, will be successful in finding eligible program units.

To ensure that the differentials between bedroom-size FMRs were inconsistent with normally observed patterns, the 4-Bedroom Base Rent is adjusted upward from $501 to $528.

The difference between the actual 2000 Census 4-Bedroom Base Rentof $528 and the demonstration 2000 Census 4-Bedroom Base Rent of $528 computed here is due to the effects of rounding on the public distribution as described above.


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