Lesson 11 of 25 · 6 min

The months the car is worth less than the loan

Underwater is a ratio, not a feeling: the loan sits above the mark for a run of months you can count.

The months the car is worth less than the loan are the months LTV sits above 100 percent. Track 1 lesson 6 is that ratio. Lessons 9 and 10 are the two schedules that feed it: a falling mark, and a slowly falling balance. This lesson puts both schedules on the same dates and reads the gap.

Cinderwell Dealer finances a $31,460 car with $0 down at an illustrative 7.9 percent for 84 months. The installment is $488.78. Year-1 depreciation is 22 percent, applied as a constant monthly factor so month 12 prints 78 percent of cash price, then 13 percent a year after that. Three snapshots follow.

Month 1: balance $31,178.34, mark $31,460 × 0.78^(1/12) = $30,815.31, LTV $31,178.34 ÷ $30,815.31 = 101.2 percent, gap −$363.02. Month 12: balance $27,954.91, mark $31,460 × 0.78 = $24,538.80, gap −$3,416.11, LTV 113.9 percent. Month 48: balance $15,620.72, mark $24,538.80 × 0.87^3 = $16,158.87, gap +$538.15, LTV 96.7 percent. The loan is above the mark for a run of years, and back below it by month 48.

Nothing in those months requires a missed installment. Both schedules ran as written. The mark fell faster than the amortization table retired principal, so the ratio crossed 100 percent and stayed there until the two paths crossed again. Lesson 12 names that gap.

A gap of −$3,416.11 at month 12 is not a default. It is LTV of 113.9 percent, produced by two schedules that were both on time.

Key terms

Gap: Mark minus loan, or loan minus mark. Negative when the claim exceeds the collateral.
Underwater months: The run of dates on which LTV is above 100 percent. A property of two schedules, not of a missed payment.
Crossing: The later date on which the falling balance and the falling mark meet again, and LTV passes back through 100 percent.

Worked example

Three dates on one $31,460 loan

Cinderwell Dealer. Cash price $31,460, $0 down, illustrative 7.9 percent APR, 84 months. Year-1 depreciation 22 percent as a monthly factor, then 13 percent a year.

Installment: $488.78
Month 1: balance / mark / LTV: $31,178.34 / $30,815.31 / 101.2%
Month 12: balance / mark / LTV: $27,954.91 / $24,538.80 / 113.9%
Month 48: balance / mark / LTV: $15,620.72 / $16,158.87 / 96.7%

The ratio is above 100 percent at month 1, further above it at month 12, and back below it at month 48. The installments were current the whole way.

Check yourself

On the month-12 book, the loan is $27,954.91 and the mark is $24,538.80. What is LTV, and what is the gap?

Those months are loan to value above 100 percent, the same ratio Track 1 lesson 6 computes. 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.