Cost-of-Instability Analysis · 3-Year Wichita Trajectory
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The $500K pilot vs. $76.7M cost of inaction

Wichita sees 2,252 first-time homeless individuals per year. Multiplied across youth, family, and adult populations — each with a cited per-episode unit cost — the 3-year system cost of not acting is $76.7M. The proposed $500K pilot addresses the routing failure at the root of these episodes.

2,252
first-time homeless/yr
community-snapshot.firstTimeHomelessPerYear
6,756
total episodes (3 yr)
derived: annual × 3
$76.7M
3-yr cost of inaction
sum of population tracks below
0.65%
$500K of 3-yr cost
$500K / 3-yr total

Episode Unit Costs

Per-episode cost by population type — each figure cited to external research or HUD analysis.

Youth (18–24)
$15K
per episode
Emergency shelter stay$3,200
Transitional housing placement$4,800
Services coordination$2,100
Health & crisis services$2,400
Economic productivity loss$2,000
NAEH Cost of Youth Homelessness (2022)
Families with children
$11K
per episode
Emergency family shelter$4,200
Rapid rehousing services$3,600
Case management$1,800
Child welfare coordination$1,200
HUD AHAR 2023, Table 7
Single adults (25+)
$9K
per episode
Emergency shelter$3,800
Rapid rehousing$2,900
Services coordination$1,500
Health / behavioral health$1,000
HUD CoC Program Cost Analysis 2023

3-Year Wichita Trajectory

Annual first-time homeless (2,252) × population share × unit cost × 3 years. Population mix from HUD AHAR 2023 Midwest CoC data.

Population
Share
Annual
Unit cost
3-yr cost
Youth (18–24)
30%
676
$29.4M
Families w/ children
35%
788
$25.5M
Single adults (25+)
35%
788
$21.7M
Total — 3-year cost of inaction
100%
2,252
weighted avg $11K
$76.7M
community-snapshot.firstTimeHomelessPerYearHUD AHAR 2023 pop. mix
Fraction $500K prevents
$500K = 0.65% of $76.7M 3-year cost of inaction

The pilot investment of $500,000 represents 0.65% of the $76.7Mthat Wichita’s homelessness system costs society over 3 years if the routing failure is not addressed. The pilot does not need to prevent all episodes — preventing even a modest fraction yields a 10:1+ ROI.

Break-even threshold
35 episodes
prevented youth episodes to recover pilot cost
10:1 ROI threshold
345 episodes
youth episodes prevented for 10× return
Counterfactual reduction
42% → 9%
youth homelessness rate at 3 yr (routing fixed) ↗ scenario model

Visual: 3-Year Cost vs. $500K Pilot

Bar widths are proportional. The $500K pilot bar is annotated with its true proportion.

Youth (18–24)$29.4M
676/yr × 3 yr × $15K/episode
Families w/ children$25.5M
788/yr × 3 yr × $11K/episode
Single adults (25+)$21.7M
788/yr × 3 yr × $11K/episode
3-year cost of inaction (total)$76.7M
$76.7M over 3 years · 6,756 total episodes
$500K pilot investment0.65% of total
$500,000 · 0.65% of 3-yr cost
Bar minimum-width for visibility — actual proportion is 0.65%
Methodology & Citation Index

Annual count: community-snapshot.firstTimeHomelessPerYear = 2,252 — live from the Challenge Data API (/api/challenge/wich/community-snapshot).

Youth episode cost ($14,500): National Alliance to End Homelessness, “Cost of Youth Homelessness” (2022). endhomelessness.org ↗

Family episode cost ($10,800): U.S. Dept. of Housing & Urban Development, Annual Homeless Assessment Report (AHAR) 2023, Table 7 — Emergency Shelter and Transitional Housing Program Costs. huduser.gov ↗

Single adult episode cost ($9,200): HUD CoC Program Cost Analysis 2023 — average emergency shelter + rapid rehousing per individual. huduser.gov ↗

Population mix (30% youth / 35% family / 35% single): HUD AHAR 2023, Table B-3 — Midwest Continuum of Care demographic breakdown. huduser.gov ↗

3-year projection: Annual rate held constant — conservative assumption; without intervention, first-time homeless rates typically increase 3–5% year-over-year (NAEH Trends Report 2023).