Lesson 8 of 25 · 6 min

Down payment and first-month loan to value

The ratio on day one is loan over cash price; a week later the denominator is already a different number.

Loan to value, LTV, is the loan divided by the asset. Track 1 lesson 6 computes it on a pledged portfolio. This lesson uses that ratio on the $33,890 car from lesson 7. It does not re-teach the ratio. It shows that the denominator on a car starts moving in the first week.

LTV = loan ÷ asset

loan: The financed amount outstanding.
asset: The mark used as the denominator — cash price on day one, a later mark thereafter.
LTV: The claim as a share of the collateral. Above 100 percent, the loan exceeds the mark.

Same book: cash price $33,890, $5,000 down, financed $28,890. Day-one LTV is $28,890 ÷ $33,890 = 85.2 percent. The down payment is the 14.8 percent that is not borrowed. A week later the car is marked at 92 percent of cash price, $33,890 × 0.92 = $31,178.80. The loan has barely moved. LTV is now $28,890 ÷ $31,178.80 = 92.7 percent.

Seven days produced a 7.5-point rise in LTV with no extra drawing. The numerator is still $28,890. The denominator fell because the mark fell. Track 1 lesson 6 already showed that the same loan reads two different LTVs if the denominator changes. On a car the denominator change is not a lender haircut. It is the car's own mark, moving, in the first week, without asking.

Day-one LTV is loan over cash price. First-month LTV is loan over a mark that is already a different number. Both are the same ratio. Only one of them is printed at the desk.

Key terms

Day-one LTV: Financed amount divided by cash price. The ratio at the moment the loan is written.
First-month LTV: The same loan divided by a later mark. The denominator has already moved.
Mark: The value used as the asset in the LTV ratio. On day one it is cash price. After that it is a later print.

Worked example

The same $28,890, two denominators

Marlow Street Garage. Cash price $33,890, $5,000 down, financed $28,890. A week later the car is marked at 92 percent of cash price.

Day-one LTV: 85.2%
Mark a week later: $31,178.80
Loan a week later: $28,890
LTV a week later: 92.7%
Rise in LTV: 7.5 points

A 14.8 percent down payment produced an 85.2 percent day-one LTV, and a week of mark movement produced 92.7 percent. The haircut was cash. The rise was the denominator.

Check yourself

Cash price $27,420, $4,000 down, so $23,420 is financed. Day-one LTV? A week later the car is marked at 91 percent of cash price. What is LTV then?

First-month loan to value on a car is the same ratio Track 1 lesson 6 computes on a pledged portfolio. 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.