Lesson 9 of 25 · 7 min

Depreciation as a schedule, not a surprise

The car's mark falls on a timetable, so the collateral the lender is looking at is a declining series, not a shock.

Depreciation, the scheduled fall in the car's mark, is a timetable. It is not a shock that arrives unannounced. Lesson 8 showed one week taking the denominator from cash price to 92 percent of cash price. This lesson writes the next four years as a series, so the collateral side of LTV is a declining path rather than a single print.

Ashmere Motors sells a car for $32,840. Year 1 takes 18 percent: $32,840 × 0.82 = $26,928.80. Year 2 takes 14 percent of what remains: $26,928.80 × 0.86 = $23,158.77. Year 3 takes 11 percent: $23,158.77 × 0.89 = $20,611.30. Year 4 takes 9 percent: $20,611.30 × 0.91 = $18,756.29. Four-year decline is $32,840 − $18,756.29 = $14,083.71, which is 42.9 percent of the cash price.

Each year's percentage is applied to the remaining mark, not to the original cash price. That is why the dollar drop shrinks even as the percentage stays large: 18 percent of $32,840 is $5,911.20, and 9 percent of $20,611.30 is $1,855.02. The schedule is front-loaded. The first year does more of the damage than the fourth.

Track 1 lesson 19 is continuous repricing of pledged securities: the lender sees the mark and the borrower often does not. A car is slower and lumpier, but it is the same geometry. The collateral is being re-marked whether or not anyone looks. The loan's amortization, the next lesson, is a different schedule running at a different speed.

A falling mark is not a surprise if it is a schedule. The surprise is only that the loan's schedule and the car's schedule are not the same document.

Key terms

Depreciation: The scheduled fall in the car's mark. A timetable for the collateral, not a one-off shock.
Remaining mark: Last year's mark after that year's percentage is applied. Next year's percentage uses this figure, not the cash price.
Front-loaded decline: Larger percentage drops in the early years, so more of the four-year fall happens first.

Worked example

Four years of a declining denominator

Ashmere Motors. Cash price $32,840. Illustrative schedule: −18 percent, then −14 percent of remaining, then −11 percent, then −9 percent.

End of year 1: $26,928.80
End of year 2: $23,158.77
End of year 3: $20,611.30
End of year 4: $18,756.29
Four-year decline: $14,083.71

The collateral at year 4 is $18,756.29. Any loan still above that mark is already a ratio above 100 percent. The schedule did that in advance.

Check yourself

Cash price $24,680. Year 1 takes 16 percent, year 2 takes 12 percent of remaining, year 3 takes 10 percent, year 4 takes 8 percent. What is the mark at the end of year 4, and what share of cash price has gone?

Depreciation is the everyday version of a falling mark on collateral, the continuous repricing Track 1 lesson 19 says the lender sees and the borrower often does not. Open Why the lender sees your risk continuously and you do not →

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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.