Lesson 14 of 25 · 6 min

Day-one loan to value after a roll

Opening above one hundred percent means the maintenance test is already failed before the first installment is due.

Day-one LTV after a roll is the new principal divided by the new cash price. Lesson 13 produced $32,400 of principal on a $29,680 car. The ratio is $32,400 ÷ $29,680 = 109.2 percent. The loan already exceeds the asset before the first installment is due.

Headroom, the surplus of collateral over the claim, is negative on day one. Track 9 lesson 1 is a call as a failed inequality: balance larger than the permitted figure. A car loan does not always carry a maintenance test of that form. The geometry is still the same. Opening at 109.2 percent is opening already through 100 percent. The down payment of $1,500 never had a chance to print a ratio below 100, because $4,220 of old gap was sitting on top of it.

A clean book on the same car would have financed $28,180. Day-one LTV would have been $28,180 ÷ $29,680 = 94.9 percent. The roll moved the ratio 14.3 points, from a gap of +$1,500 to a gap of −$2,720. That −$2,720 is $32,400 − $29,680, which is $4,220 − $1,500: the rolled leftover minus the new cash at the start.

Lesson 8's first-month mark movement then operates on a ratio that is already above 100 percent. A week at 92 percent of cash price would mark the car at $29,680 × 0.92 = $27,305.60, and LTV would be $32,400 ÷ $27,305.60 = 118.7 percent. The failed inequality gets worse as the denominator falls, which is Track 9 lesson 1 with a shrinking right-hand side.

A roll can open a loan through 100 percent on day one. The first installment has not failed. The ratio has.

Key terms

Day-one LTV after a roll: New principal divided by new cash price. Can exceed 100 percent before any installment is due.
Negative headroom: Collateral already smaller than the claim. The surplus that would have sat below 100 percent LTV is gone.
Failed inequality: Balance larger than the figure the asset supports. Track 9 lesson 1's test, read here as LTV already above 100 percent.

Worked example

109.2 percent before the first month

Ashmere Motors. New car $29,680, financed $32,400 after the roll from lesson 13.

Day-one LTV: 109.2%
Day-one gap: −$2,720
Clean LTV on the same car: 94.9%
Points the roll added: 14.3
LTV after a 92% mark: 118.7%

The loan opened through 100 percent. A week of ordinary mark movement took it further through. The inequality failed on day one.

Check yourself

A new car costs $24,100. After a roll the financed amount is $26,880. What is day-one LTV, and is headroom positive?

Day-one loan to value above 100 percent is the everyday version of opening a line already through its maintenance test, the failed inequality Track 9 lesson 1 describes. Open A call is a test failing, not a decision being made →

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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.