Lesson 17 of 25 · 7 min
Front-end against back-end
A new car installment leaves the housing ratio still and moves the ratio the lender actually stacks.
Two ratios on the same income are two tests. Track 1 lesson 6 names the denominator trap: the same loan reads two LTVs if the base changes. Here the denominator is held still at $6,840 and the front-end numerator is held still at $2,140, so the housing ratio does not move. The back-end numerator grows. Capacity as the lender computes it moves. Housing as a share of income does not.
Same Cairn Street income of $6,840. Housing $2,140 is still 31.3 percent. Other debts were $1,115. Adding a $310 car installment, the monthly claim Track 22 computes on a financed car, takes the back-end to ($2,140 + $1,115 + $310) ÷ $6,840 = $3,565 ÷ $6,840 = 52.1 percent. The housing ratio did not move. The stacked ratio did, by 52.1 − 47.6 = 4.5 points.
The car did not change the house. It did not change the PITI. It changed the other-debts line that only the back-end reads. A reader watching the 31.3 percent sees no event. A process watching the 52.1 percent sees a different inequality. That is the trap: two bases, one of them looking unchanged, on a single income.
Loan-to-value can be restated against market value or against lending value and produce two figures for one balance. Debt-to-income can be restated against housing or against housing-plus and produce two figures for one income. The lesson is not which ratio is kinder. The lesson is that they are not interchangeable, so a still front-end is not a still test.
The housing ratio can sit still while capacity as stacked by the lender moves. The car installment is in one numerator and not the other.
Key terms
- Still front-end
- A housing ratio that does not move because neither housing nor income moved. It is not a still back-end.
- Stacked back-end
- Housing plus every other installment the file includes. On this book, 52.1 percent after the car line.
- Denominator trap (income version)
- Track 1 lesson 6's two-base problem, applied to one income and two numerators rather than to one loan and two asset figures.
Worked example
The car that the housing ratio cannot see
Cairn Street Lending. Monthly gross $6,840. Housing $2,140. Other debts $1,115, then plus a $310 car installment.
- Front-end, before and after
- 31.3%
- Back-end, before the car
- 47.6%
- Back-end, after the car
- 52.1%
- Move in the stacked ratio
- 4.5 points
$2,140 ÷ $6,840. Unchanged.
($2,140 + $1,115) ÷ $6,840.
($2,140 + $1,115 + $310) ÷ $6,840.
The housing ratio moved 0.
A $310 car installment was invisible to 31.3 percent and worth 4.5 points to 52.1 percent. Those are not two readings of one test.
Check yourself
Same $6,840 income, housing $2,140, other debts $1,115. A $425 car installment is added. What is the new back-end, and did the front-end move?
Two ratios on the same income are the everyday version of two LTV bases on the same loan, the denominator trap Track 1 lesson 6 names. Open Loan to value, and how to compute it →
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Educational only. Nothing in this lesson is investment, legal or tax advice, or a recommendation to enter into any transaction. Figures are illustrative and computed from the inputs stated in the lesson.