---
title: "The economics of a single deal"
url: https://lendriskanalytics.com/underwriter.html
publisher: LendRisk Analytics
kind: Page
description: "A method note on single-deal auto-loan economics: how probability of default, loss given default, expected loss, and lifetime ROA combine into a fund, counter, or decline read, with benchmark assumptions and a worked synthetic example."
html: https://lendriskanalytics.com/underwriter.html
---

# The economics of a single deal

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Methods · Note 09
Method note · 5 min read

Methods · Deal economics

# The economics of a single deal.

LendRisk Analytics · Method note · 2026

Every funded auto loan is a small standalone business: it earns interest on a shrinking balance, pays for its funding and servicing, and carries a probability-weighted loss. This note lays out the four-line arithmetic that turns a borrower, a vehicle, and a set of terms into a *fund, counter, or decline* read, and shows, on a synthetic example, when a counter-offer rescues a marginal deal and when nothing does.

12%

12-month base default rate, 600-649 score band

+25%

PD multiplier per 10 LTV points above 100

≈0.55×

Average balance on an amortizing loan, vs amount financed

50% / <0

Decline lines: lifetime PD, or expected ROA

## The question the method answers

Large lenders answer "should this loan be written?" with a scored model and a credit team. Small independent lenders and buy-here-pay-here operators answer it at a desk, in minutes, usually on instinct. The method here is the middle path: an explicit, checkable chain from deal inputs to an economic verdict. It does not predict any individual borrower's behavior. It asks a narrower question: **given typical loss behavior for this profile, does the deal's expected lifetime economics clear the lender's own hurdle?**

## Four lines of arithmetic

**Line 1, probability of default (PD).** Start with a 12-month base rate by credit-score band: roughly 1.5% at 800+, 4% at 700-749, 12% at 600-649, 20% at 550-599, 30% at 500-549, and 40% below 500. Then multiply by deal-shape adjustments: each 10 points of loan-to-value above 100 adds 25% to PD; debt-to-income above 45 adds 30-55%; each year of vehicle age past five adds 4%; and longer terms raise the per-period rate (about 0.85× at 36 months, rising ~0.12 per additional year). Finally, convert 12-month PD to lifetime PD with a term multiplier, about 1.8× at 36 months, 2.5× at 60, 2.85× at 84, capped at 85%.

**Line 2, loss given default (LGD).** Severity is driven by the collateral path, not the borrower. A base LGD by vehicle age (35% for near-new, 55% at four to six years, 75% past ten) is scaled by LTV at the time of default, approximated as origination LTV less about 15% of balance paydown, and bounded between 20% and 95%.

**Line 3, expected loss (EL).** PD × LGD × amount financed. This is the reserve-sized dollar figure the deal must earn back before it earns anything.

**Line 4, lifetime ROA.** Gross interest is the APR applied to the average amortizing balance (≈0.55× the amount financed) over the term. Subtract cost of funds on the same average balance, per-loan operating cost, and expected loss. Divide the remainder by the amount financed. The verdict follows mechanically: **decline** if lifetime PD is 50% or higher or expected ROA is negative; **fund** if ROA clears the lender's target; **counter** in between.

**Inference**Because the PD adjustments are multiplicative, risk factors compound rather than add. A 600-score borrower at 115 LTV on a 72-month note is not "three notches worse" than the base case, the multipliers stack to several times the base rate. In this framework, most decline verdicts are reached through the LTV multiplier, not the score band alone.

## Two lenders, two benchmark sets

The same arithmetic prices very different books depending on the lender's own economics. Two benchmark profiles anchor the method, an independent dealer or finance company writing mid-subprime paper, and a buy-here-pay-here operator self-financing older vehicles at deeper subprime scores.

| Benchmark assumption | Independent / finco | BHPH operator |
|---|---|---|
| Cost of capital | 7.5% | 9.5% |
| Operating cost per loan | $200 | $350 |
| Target lifetime ROA | 1.5% | 3.0% |
| Typical credit score | 615 | 540 |
| Typical APR | 18% | 22% |
| Amount financed | $15,500 | $10,500 |
| Vehicle wholesale value | $14,500 | $9,000 |
| Down payment | $1,500 | $1,500 |
| Term | 60 mo | 36 mo |
| Vehicle age | 5 yr | 9 yr |

Benchmark profiles used by the method. The BHPH set trades a shorter term and smaller advance against deeper scores, older collateral, and a higher hurdle, because the operator's own funding and servicing cost more per loan.

## A worked deal, walked to a verdict

A synthetic deal, deliberately marginal: a 615-score borrower at 38% DTI, a five-year-old vehicle worth $13,500 wholesale, $15,500 financed at 18% APR for 60 months, against the independent-lender economics above.

| Step | Value | Read |
|---|---|---|
| LTV at funding | 114.8% | Negative equity from day one |
| Lifetime PD | 49.3% | Just under the 50% decline line |
| LGD | ~54% | Mid-age collateral, near-100 LTV at default |
| Expected loss | $4,101 | 26% of the amount financed |
| Gross lifetime interest | $7,673 | 18% on the average balance, 5 years |
| Cost of funds | −$3,197 | 7.5% on the same average balance |
| Operating cost | −$200 | Per-loan servicing assumption |
| Net profit / lifetime ROA | $175 · 1.1% | Positive, but below the 1.5% target → COUNTER |

Synthetic example computed with the arithmetic above. Not a real borrower, vehicle, or lender.

Where the interest dollar goes · worked deal

Of $7,673 in expected lifetime interest, expected credit loss and funding cost consume almost all of it. The lender's margin is the sliver on the right.

**Cost of funds
**Operating cost
**Expected loss
**Net profit

Synthetic worked example. Values computed from the stated model assumptions, not observed data.

The read
Single-deal underwriting is a race between **interest margin and expected loss**, and on marginal subprime paper the two run nearly even. The verdict is rarely about whether the deal makes money in the good outcome, it is about whether the margin survives the probability-weighted bad one. **A deal that "pencils" at zero losses is not a priced deal.**

## When a counter rescues the deal, and when it can't

A counter verdict means the deal is under-priced for its risk, not unprofitable. The method searches for the single smallest change that clears the target, in order: a rate bump (half-point steps, capped at 29% APR), additional down payment ($250 steps), a shorter term (six-month steps, floor of 24), or a smaller advance. On the worked deal, the rescues are strikingly cheap. A **half-point APR increase to 18.5%** adds about $213 of lifetime interest on the average balance and lifts ROA from 1.1% to roughly 2.5%, clearing the target. So does **$250 of additional down payment**, which trims LTV, PD, and expected loss simultaneously.

The term lever, by contrast, fails on this deal at every step. Shortening from 60 to 48 or 36 months does cut lifetime PD meaningfully, but it cuts lifetime interest faster, and ROA never reaches the target. In this arithmetic, term reduction de-risks the deal and de-profits it at the same time; price and advance are the levers that actually move the verdict.

**Inference**The model treats a rate bump as pure margin: APR appears in the revenue line but not in the PD line. Real borrowers are not so obliging, a higher payment raises default risk, especially at stretched DTI. Treat rate-based counters as an upper bound on the rescue, and prefer the down-payment lever when the borrower can reach it: it is the only counter that improves both sides of the ledger.

## Limits

This is a decision-support heuristic, not a credit model. Its parameters are stylized calibrations to the shape of published industry default curves, not fitted coefficients, and a lender's own portfolio history should replace them wherever it exists. The score-band base rates step in cliffs, 599 versus 600 moves the base rate from 20% to 12%, where reality is smooth. The average-balance approximation (0.55×) and the fixed default-timing assumption (~15% paydown at default) are conveniences, not observations.

**Inference**The multiplicative stacking is calibrated to the independent-lender case and turns harsh at the deep-subprime end: the BHPH benchmark profile itself, 540 score, 117 LTV, nine-year-old collateral, stacks to a lifetime PD above the 50% decline line. BHPH economics survive in practice on levers this framework does not price: relationship collection, repossess-and-re-sell cycles, and down payments that exceed vehicle cost basis. For that segment, read the output as a stress reading, not a verdict.

Finally, lifetime ROA here is net profit over the amount financed across the whole term, not an annualized figure, comparable across deals of similar term, less so across a 36-month and a 72-month note. None of this changes the core discipline the arithmetic enforces: no deal is priced until expected loss has been subtracted.

**Sources & notes**
All model parameters in this note, score-band base rates, the LTV, DTI, term, and vehicle-age multipliers, LGD assumptions, the average-balance approximation, benchmark profiles, and decision thresholds, are the method's own stylized assumptions, calibrated to the general shape of published industry auto default curves rather than to any single dataset. All deals, borrowers, and lender profiles shown are **synthetic**. LendRisk Analytics is an independent research publication with no position in, and no affiliation with, any company mentioned. Not investment, legal, or accounting advice.

Have a question about the market, or a different view? [Send it through →](https://lendriskanalytics.com/contact.html).

LR

LendRisk Analytics

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