DTI, LTV & Qualification Math
~14 min read · Compute front/back DTI, LTV/CLTV, and qualifying income from paystubs to self-employment.
Three fractions run qualification: the front-end ratio (housing/income), the back-end DTI (all debt/income), and LTV (loan/value). The exam makes you compute all three — and know the benchmark limits each program tolerates.
The housing and debt ratios
Front-end ratio = monthly housing expense (PITI: principal, interest, taxes, insurance, plus HOA and MI) ÷ gross monthly income. Back-end DTI = (PITI + all recurring debt payments — cars, cards' minimums, student loans, support obligations) ÷ gross monthly income. Conventional folk-benchmarks: 28/36; FHA's published guides: 31/43; automated underwriting stretches back-ends into the high 40s (conventional to ~50) with compensating factors. The QM framework historically anchored on 43% before the price-based General QM replaced the hard cap — but 43% remains the exam's touchstone number.
- Front = PITI ÷ gross income; back = PITI + debts ÷ gross income
- Benchmarks: 28/36 conventional, 31/43 FHA
- Gross (pre-tax) income, always
- AUS approvals flex ratios with strong compensating factors
LTV and its cousins
LTV = loan amount ÷ the lesser of purchase price or appraised value. It prices risk (LLPAs), sets MI (PMI above 80% conventional), and caps programs. CLTV adds all subordinate liens' balances; HCLTV counts HELOC credit LIMITS rather than drawn balances — the trio governs refinances and piggybacks. 80% LTV is the no-PMI line; 95–97% marks conventional's high-LTV programs; FHA rides at 96.5%.
- LTV uses the LESSER of price or value
- CLTV: all liens' balances; HCLTV: HELOC limits
- 80% = PMI threshold; 96.5% = FHA's 3.5%-down complement
Working the numbers
Exam math discipline: monthly figures throughout (annual income ÷ 12), gross not net, minimum payments for revolving debt, and installment debts near payoff (under ~10 months) often excluded per guidelines. For maximum-payment questions, invert: max PITI = income × front-end limit; max total debt = income × back-end limit — the binding constraint is whichever produces the smaller housing payment.
Worked example
Gross income $8,000/month. Debts: $450 car, $150 card minimums, $250 student loan. Proposed PITI $2,300. Purchase $400,000, appraisal $390,000, loan $360,000. Compute front, back, and LTV — and pass/fail against 28/36 and the PMI line.
Front-end: 2,300 ÷ 8,000 = 28.75% — a hair over the 28 benchmark. Back-end: (2,300 + 450 + 150 + 250) = 3,150 ÷ 8,000 = 39.4% — over 36, inside FHA's 43 and typical AUS conventional tolerance. LTV: lesser of price/value is the $390,000 APPRAISAL → 360,000 ÷ 390,000 = 92.3% — above 80, so PMI attaches; above 90, so the appraisal shortfall matters doubly. Verdict: fails the classroom 28/36, plausibly approvable through AUS with compensating factors, carries PMI, and the low appraisal (not the price) set the LTV — the calculation the exam most wants you to get right.
Common exam pitfalls
Computing LTV from the purchase price when the appraisal is lower.
Always the LESSER of price or appraised value — a low appraisal raises LTV instantly.
Using net income or annual figures mid-formula.
Gross monthly income everywhere; convert annual salaries first.
Confusing CLTV with HCLTV.
CLTV sums lien BALANCES; HCLTV substitutes HELOC LIMITS — the difference decides refi eligibility.
28 the house, 36 the life, 43 the fed's old line, 80 the PMI door — and value means the lesser one.
Recap
- Front-end = PITI/gross; back-end adds all recurring debt
- Benchmarks: 28/36 conventional, 31/43 FHA, AUS flexes higher
- LTV = loan ÷ lesser of price or value
- CLTV = balances of all liens; HCLTV = HELOC limits
- 80% LTV: PMI boundary; 96.5%: FHA standard
- Monthly, gross, minimum-payment discipline in every calculation
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