Appendix A — Deal & Payment Math Reference

This is the calculator behind the whole book. Every formula a deal uses, worked once, in one place, so you can find it fast at the desk. Each formula is stated, then plugged with real numbers, then read back in plain English — the same convention the chapters use.

Two reminders before you start:

• The illustrative numbers here are teaching figures. The canonical Okafor and Devon Wallace deals use the exact figures established in the chapters (and the continuity bible); other examples are labeled illustrative. Rates, fees, taxes, and reserve conventions vary by state, by lender, and over time — for any live deal, the contract and your finance director are the authority.
• Always be ready to show the math. The whole thesis of this book is that daylight on the numbers closes more deals than hiding them. A figure you can't say out loud is a figure someone's hiding.

Cross-references point to the chapter that owns each concept: financing math is Chapter 22, lease math is Chapter 23, F&I product margins are Chapter 24, subprime ratios are Chapter 26, the front-end deal structure is Chapter 12, commission/gross is Chapter 5, and used-inventory metrics are Chapter 19.

A.1 The monthly loan payment formula (the one everything runs on)

Every amortizing car loan payment comes out of one formula. Most salespeople punch it into a tool and read the answer; you should understand it, because the person who can show a customer why the payment is what it is — and what moves it — is the one the customer trusts.

        P · r · (1 + r)^n
  M  =  ---------------------
          (1 + r)^n  −  1

An algebraically identical form you'll also see (handy on some calculators):

              P · r
  M  =  ─────────────────
         1 − (1 + r)^(−n)

Worked example: $30,000 financed, 6.9% APR, 72 months

This is the book's headline teaching deal — a clean prime loan (Chapter 22 §22.5).

Step 1 — find r (the monthly rate). APR is per year; divide by 12 and convert percent to decimal:

r = 6.9% ÷ 12 = 0.575% per month = 0.00575

Step 2 — identify n. A 72-month loan is 72 payments: n = 72.

Step 3 — compute (1 + r)^n (the only part that needs a calculator):

(1.00575)^72 = 1.511064

In plain English: a dollar growing 0.575% a month for 72 months becomes about $1.51. That growth factor is the engine of the formula.

Step 4 — plug it all in:

       30000 · 0.00575 · 1.511064        260.66
  M = ------------------------------  =  --------  =  $510.03
              1.511064 − 1                0.511064

Narrated, so it's not a black box: - Numerator: 30000 × 0.00575 = 172.50, then 172.50 × 1.511064 ≈ 260.66 - Denominator: 1.511064 − 1 = 0.511064 - Divide: 260.66 ÷ 0.511064 ≈ 510.03

The monthly payment is $510.03.

Step 5 — interpret it. Total paid = $510.03 × 72 = $36,722.22. Borrowed = $30,000. So **total interest = $6,722.22** — about $6,700 to use the bank's $30,000 for six years.

The three levers (what changes the payment)

A payment has exactly three levers. Master what each does and you can solve almost any "I need to be at $X/month" conversation honestly.

Lever 1 — term. Longer term → lower payment, more total interest, slower climb out of negative equity. Same $30,000 at 6.9%:

Going 48 → 84 months drops the payment ~$266/mo but **adds ~$3,500 in interest** and three extra years in the loan. Stretching the term is a legitimate tool — but show the cost; never hide it inside a comfortable payment.

Lever 2 — rate (APR). Higher rate → higher payment and more interest. Same $30,000 over 72 months (this is the credit-tier table from §A.7, read as a lever):

Lever 3 — amount financed (down payment & equity). Less principal → lower payment. Same 6.9% / 72 months:

On this loan, every $1,000 down (or $1,000 of positive trade equity) knocks roughly $17/month off and lowers total interest. This is the honest lever — it lowers what's truly borrowed, not just the months.

A.2 Payment per $1,000 financed (the quick mental-math table)

When you need a payment in your head — on the lot, on the phone — multiply the **payment factor per $1,000** by the number of thousands financed. The factor is just the formula in §A.1 run on P = $1,000.

Payment per $1,000 financed, by APR and term (illustrative — rounded to the cent):

How to use it. Financing $30,000 at 6.9% for 72 months: the factor is **$17.00 per $1,000, and $30,000 is 30 thousands, so `30 × $17.00 = $510.00/mo` — matching the worked answer in §A.1 (the cent of difference is rounding). The Okafor amount financed of $41,030** at 7.9% / 72 mo: `41.03 × $17.48 ≈ $717.21` (the precise formula gives **$717.39** — close enough for a floor estimate, exact when you run the real numbers).

🧮 Sanity check. This table is a quick estimate tool, not the contract. Always confirm the real payment with the formula or the desking tool before you state a number a customer will hold you to.

A.3 Amount financed (what's actually borrowed)

The payment formula's P is the amount financed — and where customers fear hidden charges live, so walk it line by line.

  AMOUNT FINANCED = selling price
                    − cash down payment
                    − net trade equity
                    + sales tax
                    + fees (doc, title, registration)

Worked example: the canonical Okafor deal

Adaeze and Chidi Okafor, buying a three-row SUV (a Pilot-class vehicle) from the import store. These are the canonical figures — use them exactly whenever this deal appears (Chapter 22 §22.6). Assumptions: $2,000 cash down, a state trade-in tax credit (tax charged on price minus allowance), 6% sales tax, doc fee $599**, **title/registration $401.

  Selling price ........................  $43,500.00
  − Cash down ..........................  − 2,000.00
  − Net trade equity ($18,000−$15,000) .  − 3,000.00
  + Sales tax (6% of [$43,500 − $18,000]
              = 6% of $25,500) .........  + 1,530.00
  + Fees (doc $599 + title/reg $401) ...  + 1,000.00
  --------------------------------------------------
  = AMOUNT FINANCED ....................  $41,030.00

The logic, line by line: - Start at the agreed price, $43,500 — nothing sneaky on top. - Subtract the $2,000 cash** and the **$3,000 of trade equity — that's $5,000 they don't have to borrow. Their trade and cash do real work. - Add sales tax, computed only on $25,500 because the trade-in tax credit taxes the price after the $18,000 allowance — a genuine benefit worth `6% × $18,000 = $1,080` in tax savings here. - Add the fees, and name them ("a $599 documentation fee and about $401 for title and plates"). An unexplained "$1,000 fees" line breeds suspicion; named fees relax the customer.

⚠️ The trade-in tax credit varies by state. Many states tax on price − allowance; some tax the full price; a few handle it differently. Never quote the tax method across state lines from memory — confirm it.

A.4 APR vs. interest rate

These are not the same number, and customers should compare the right one.

• Interest rate — the cost of borrowing the principal, as a yearly percentage.
• APR (Annual Percentage Rate) — the all-in yearly cost, folding in certain finance charges and fees. It's the truest apples-to-apples comparison number, and it's the figure the federal Truth in Lending Act (TILA) disclosures are built around.

The rule to teach customers: compare APR to APR, not payment to payment. A lower payment can hide a longer term and more total interest. Two offers on $30,000:

Offer B has the lower payment but costs $1,165 more in interest. Same rate, worse total — purely the term. The payment-focused customer who only hears "$510 vs. $593" picks the costlier deal unless you show them the APR and the total. (TILA and the disclosures: Chapter 25.)

A.5 Front-end and back-end gross

Two kinds of gross, and which one your commission applies to changes everything (Chapter 5 §5.2).

Front-end gross — profit on the vehicle itself: selling price minus the dealer's cost in the car, adjusted for any over-allowance on the trade.

  FRONT-END GROSS = selling price − dealer cost in vehicle − over-allowance on trade

Back-end gross — profit made in the F&I office after the car is agreed on. Two sources:

  BACK-END GROSS = dealer reserve (financing spread)  +  F&I product margin

Worked example: the Okafor front end

From Chapter 12 §12.7. Canonical figures: MSRP $45,000, selling price $43,500, dealer cost in the vehicle ≈ $41,800, trade allowance $18,000, trade ACV $16,500.

  Selling price                       $43,500
  Dealer cost in the vehicle         −$41,800
  ─────────────────────────────────────────
  Gross on the car (before trade)     $ 1,700

  Trade allowance (shown)             $18,000
  Trade ACV (real wholesale value)   −$16,500
  ─────────────────────────────────────────
  Over-allowance (a cost to the deal) $ 1,500

  Gross on the car                    $ 1,700
  Less over-allowance                −$ 1,500
  ─────────────────────────────────────────
  TRUE front-end gross on the deal    $   200   (a "mini" — plus ~$900 holdback)

The lesson in that math: the trade allowance and the selling price are the same dollars in different boxes. Give $1,500 more on the trade and it comes straight out of front-end gross. On this fair, customer-friendly deal the car itself made almost nothing — the store's profit comes from the back end (§A.6, §A.8), ethically and with full disclosure. This is the Chapter 1 threshold made real: the new-car sale is nearly a loss-leader; F&I carries the store.

The mini (the floor under commission)

A mini is the minimum commission a pay plan pays on a deal regardless of gross. If your rate × gross is below the mini, you earn the mini. At a $150 mini and 25% of front-end gross, the mini governs any deal under **$600** of front gross (because `25% × $600 = $150`).

  Deal A: front gross $1,600 → 25% = $400.  $400 > $150 → earn $400
  Deal B: front gross $  200 → 25% = $ 50.  $ 50 < $150 → earn the MINI, $150
  Deal C: front gross  −$300 → 25% = −$75.  negative   → earn the MINI, $150

The pack (what shrinks commissionable gross)

Some stores add a pack — a fixed amount added to the dealer's cost before commission is figured, which lowers the gross you're paid on. With a $700 pack on the §A.5 deal:

  "Real" front-end gross              $1,600
  Commissionable ("packed") gross     $1,600 − $700 = $900
  Commission @ 25%:  was $400 (on $1,600) → now $225 (on $900)

A pack is legitimate if disclosed and reasonable, a red flag if hidden or evasive. (This is the cost-pack on your commission — distinct from payment packing on the customer, which is hiding products in a payment; Chapter 24 §24.8.)

A.6 Dealer reserve (buy rate vs. sell rate)

The dealer is a broker, not the lender. The lender quotes a buy rate (its wholesale price for the money); the dealer may offer a higher sell rate (within a cap); the spread, turned into dollars, is dealer reserve — the financing half of back-end gross (Chapter 22 §22.2).

  RATE SPREAD = sell rate − buy rate

Worked example: the Okafor reserve (the canonical 1% markup)

The Okafors have prime credit. The import captive's buy rate is 6.9%; the store's consistent, disclosed policy adds 1 point → sell rate 7.9%, 72 months, on the $41,030 amount financed.

At the buy rate (6.9%), if passed straight through:

  P = $41,030, r = 0.069/12 = 0.00575, n = 72
  (1.00575)^72 = 1.511064
  M = [41030 × 0.00575 × 1.511064] / [1.511064 − 1] = 356.51 / 0.511064 = $697.55/mo

At the sell rate (7.9%), what the Okafors actually pay:

  P = $41,030, r = 0.079/12 = 0.0065833, n = 72
  (1.0065833)^72 = 1.602637
  M = [41030 × 0.0065833 × 1.602637] / [1.602637 − 1] = 432.86 / 0.602637 = $717.39/mo

What the 1-point markup means, both sides of the desk:

  ----------------------------------------------------------
  Okafor payment at BUY rate (6.9%) ......... $697.55 / mo
  Okafor payment at SELL rate (7.9%) ........ $717.39 / mo
  ----------------------------------------------------------
  Difference (cost of the 1% markup) ........  $19.83 / mo
  Over 72 months ($19.83 × 72) .............. $1,428.11 total
  ----------------------------------------------------------

The ~$1,428 of extra interest, present-valued and paid to the dealer by the lender, becomes roughly ~$1,000 of dealer reserve on this deal (the exact figure depends on the lender's reserve schedule — treat ~$1,000 as the order of magnitude). With only ~$200 of front-end gross, this is where the honest deal makes its money.

Rate-markup caps. Lenders cap markup — a common cap is 2 points (200 basis points), often stepping down to 1 point on 60+ month terms, lower on large loans. Subprime caps are often tighter (1 point or a flat fee), precisely to limit predation. Maxing the markup on every customer ("packing the rate") is the disparate-impact pattern regulators built rules around — the professional question is "what's our consistent, disclosed policy for this tier?", not "what's the most I'm allowed?"

A.7 Credit tiers and what a tier costs

A credit score (commonly 300–850 on FICO/VantageScore scales) sorts customers into tiers that drive which lenders bid and at what buy rate. The bands are illustrative and vary by lender (Chapter 22 §22.3):

The cost of a tier compounds. Same $30,000 over 72 months, across the tiers (these are the real outputs of the §A.1 formula):

The deep-subprime customer pays over $15,000 more in interest than the super-prime customer for the exact same car. That's not the dealer's markup — it's the lender pricing real, tier-wide default risk. Which is why the most valuable thing you can do for a rough-credit customer is structure a loan they can actually pay, so on-time payments move them up a tier and a refinance becomes possible (§A.9).

A.8 F&I product margins (the Okafor numbers)

The other half of back-end gross is product margin — the dealer buys a protection product from a third-party administrator at dealer cost and sells it at retail; the spread is the gross (Chapter 24).

  PRODUCT GROSS = retail price − dealer cost

The canonical Okafor F&I products

  Extended Service Contract (ESC) on the Okafor Pilot
    Retail price (customer pays):   $2,200
    Dealer cost (Summit pays):        $800
    Dealer gross profit:            $1,400     (~64% gross on a $2,200 sale)

  GAP on the Okafor deal
    Retail price (customer pays):     $900
    Dealer cost (Summit pays):        $300
    Dealer gross profit:              $600

The margins are real and they fund the store — and the ethical posture isn't to hide them: the price is fair for genuine risk protection (a transmission replacement can run $4,000–$7,000; GAP can prevent an $8,500 catastrophe), it's negotiable, and the customer can often buy comparable coverage from a credit union for less. Saying all of that out loud is what makes you trustworthy.

Total back-end gross on the Okafor deal

  Dealer reserve (financing spread, ~1 pt)  ≈ $1,000
  ESC product gross                          $1,400
  GAP product gross                          $  600
  ─────────────────────────────────────────────────
  TOTAL BACK-END GROSS                       ≈ $3,000

  ...against ~$200 of front-end gross + ~$900 holdback.

That contrast — ~$200 front, ~$3,000 back — is the modern dealership's economics in one deal. Ethically done, every line visible.

A.9 Lease math

A lease pays for the depreciation you use, not the whole car (Chapter 23). Four numbers build every lease.

The two-part payment

A lease payment is two parts added together:

  MONTHLY PAYMENT (pre-tax) = depreciation charge + rent (finance) charge

  Depreciation charge = (adjusted cap cost − residual) ÷ term
  Rent (finance) charge = (adjusted cap cost + residual) × money factor   ← note the PLUS

The plus in the rent charge is right: you pay the money factor on the average of cap cost and residual (which is also why ×2400 carries a factor of 2).

Worked lease: Greg's compact SUV (every line shown)

From Chapter 23 §23.4 (illustrative figures, chosen to add up).

  Step 1 — cap cost:
    Gross cap = $31,500 + $695 = $32,195
    Adjusted cap = $32,195 − $0 = $32,195

  Step 2 — residual in dollars:
    0.58 × $34,000 = $19,720

  Step 3 — depreciation charge:
    ($32,195 − $19,720) ÷ 36 = $12,475 ÷ 36 = $346.53/mo

  Step 4 — rent charge:
    ($32,195 + $19,720) × 0.00125 = $51,915 × 0.00125 = $64.89/mo

  Step 5 — pre-tax payment:
    $346.53 + $64.89 = $411.42/mo

  Step 6 — tax (6% on payment, method varies by state):
    $411.42 × 0.06 = $24.69
    TOTAL MONTHLY PAYMENT = $436.11/mo

⚠️ Lease tax varies a lot by state — some tax the monthly payment (shown), some the full cap cost up front, some the cap cost reduction, a few the sum of payments. Never quote lease tax across state lines from memory.

Money-factor markup (reserve in lease clothing)

The dealer gets a buy money factor and may mark it up to a sell money factor, keeping the spread — the lease analog of dealer reserve. If Greg's buy money factor was 0.00100 and he was quoted 0.00125:

  Markup = 0.00125 − 0.00100 = 0.00025   (≈ 0.6% of APR)
  Extra rent/mo = (cap + residual) × 0.00025 = $51,915 × 0.00025 = $12.98/mo
  Over 36 months ≈ $467 of dealer reserve baked into the lease

Same ethics as a rate markup: a reasonable, disclosed spread is fair pay; a maxed, hidden one on a customer who'd qualify for the buy money factor is how you lose them.

Lease-end equity

  LEASE-END EQUITY = market value − residual

If the car is worth more than the residual, that gap is the customer's money (buy at the residual and sell/keep, or trade it toward the next car). If it's worth less, hand it back — the lender set the residual and eats the shortfall. A lease caps the customer's downside; that's part of what the rent charge buys.

A.10 Trade equity (positive and negative)

  EQUITY = trade value (or allowance) − payoff

The payoff is the exact dollars to clear the existing loan today (call the lender; it's not the same as last month's statement balance, and not the monthly payment). Positive equity reduces the amount financed; negative equity, if rolled in, increases it (Chapter 11 §11.7).

Positive equity — the Okafors

  Trade allowance     $18,000
  Trade payoff       −$15,000
  ─────────────────────────
  Positive equity     $ 3,000   (theirs — comes off the new purchase)

Even measured against the raw ACV: $16,500 − $15,000 = $1,500 — still above water either way.

Negative equity ("upside down" / "underwater")

  Trade ACV           $16,500
  Trade payoff       −$21,000
  ─────────────────────────
  Equity             −$ 4,500   (they owe $4,500 more than it's worth)

The $4,500 doesn't disappear. Three honest options: pay it in cash, keep the car, or roll it into the new loan with full disclosure. Rolling $4,500 into a $35,000 car means financing ~$39,500 (plus tax/fees) on a $35,000 car — the customer starts the new loan already upside down. State it plainly: "We're adding the $4,500 you still owe to the new loan, so you'll finance about thirty-nine-five on a thirty-five-thousand-dollar car and start out a bit upside down — I want you to see that." Never hide rolled negative equity.

Allowance vs. ACV (the over-allowance seesaw)

• ACV (actual cash value) = real wholesale value (Okafor: $16,500) — the dealer's real cost basis.
• Allowance = the number shown on the worksheet (Okafor: $18,000).
• Over-allowance = allowance − ACV ($1,500) — comes out of front-end gross (§A.5).

The allowance and the new-car price are a seesaw: push one up, the other comes down; the customer's net barely moves. Over-allowance is a legitimate, transparent tool to give the customer the trade win they crave at the same total — a scam only when the seesaw is hidden (a fake "$5,000 minimum trade!" offset by a jacked-up price, or burying negative equity). Always be willing to show the net: price − net trade equity = what they actually pay.

A.11 Commission (flat, % of gross, tiered)

Three ways commission gets paid; real plans bolt several together (Chapter 5).

Flat per unit

A fixed dollar amount per car, regardless of gross. Common at high-volume and one-price stores.

  $250/car × 20 cars = $5,000

Percentage of gross

A cut of gross profit — commonly 20–30%, often 25%. Find out: front-end only, or front + back, and at what rates.

  Front-end gross $1,600 × 25% = $400
  + Back-end gross $1,600 × 5%  = $80
  Total commission              = $480

Tiered volume bonus (where the real money hides)

Escalating bonus per car at unit thresholds — often retroactive (re-rates all the month's cars, not just those above the line). Illustrative tiers:

The cliff effect. On a retroactive plan, crossing a tier re-rates every earlier car. Going 14 → 15 units isn't "one more commission" — it's one more commission plus re-rating 14 cars from $100 to $200 each (a ~$1,400 swing). The marginal car at a tier boundary is the highest-paid car of the month.

Worked month: Carmen vs. Rick (the whole point)

Both on the sample Summit plan (25% front + 5% back, $150 mini, retroactive tiers above, $500 CSI bonus). Same store, same month — only how they sell differs.

RICK — 14 units (the grinder)
  Front: 14 × $900 × 25% = 14 × $225 = $3,150
  Back:  14 × $300 × 5%  = 14 × $15  =   $210
  Volume bonus (10–14 tier, $100/car): 14 × $100 = $1,400
  CSI (below target):                              $0
  ─────────────────────────────────────────────────────
  RICK'S TOTAL                                  = $4,760

CARMEN — 25 units (the consultant)
  Front: 25 × $450 × 25% = $112.50/car → BELOW $150 mini → 25 × $150 = $3,750
  Back:  25 × $1,000 × 5% = 25 × $50  = $1,250
  Volume bonus (25+ tier, $400/car):  25 × $400 = $10,000
  CSI (above target):                              $500
  ─────────────────────────────────────────────────────
  CARMEN'S TOTAL                                = $15,500

Carmen earned $15,500 to Rick's $4,760 — over 3× — with lower front-end gross per car ($450 vs. $900). Volume, back-end trust, retroactive tiers, and CSI all reward the help-don't-sell model. The grind optimizes the smallest number on the page and sabotages the three biggest.

Activity-to-income (run it backward)

  Cars/month needed = (annual income goal ÷ 12) ÷ all-in dollars per car
  Opportunities/month = cars needed ÷ closing ratio
  Opportunities/day = that ÷ working days

Goal $100,000, ~$550 all-in per car, 20% close, ~24 working days:

  $100,000 ÷ 12 = $8,333/mo
  $8,333 ÷ $550 ≈ 16 cars/mo
  16 ÷ 0.20 = 80 opportunities/mo
  80 ÷ 24 ≈ 3–4 real opportunities per day

Benchmark: 15 cars/mo × ($300 commission + $200 bonus) = $7,500/mo = $90,000/yr — a median full-time outcome. Top producers (25–30 units, high back-end, top tier) clear $150,000+.

A.12 Days' supply, inventory turn, and the cost of holding

Used-car retailing is a speed business (Chapter 19).

Inventory turn

  ANNUAL TURN = units sold in a year ÷ average units in inventory

Sell 600 cars/year carrying 100 on average → 600 ÷ 100 = 6 turns/year. Double the turn ≈ double the income on the same money: two dealers each with $2M of inventory and $1,800 gross/car —

Days' supply

  DAYS' SUPPLY = (current inventory ÷ units sold in a period) × days in that period

100 cars on the ground, 50 sold in the last 30 days → (100 ÷ 50) × 30 = 60 days' supply. Common sweet spot ~45–60 days (too low = thin selection, lost sales; too high = aging units). Check by segment, not just overall.

Price to market

  PRICE TO MARKET = (your price ÷ average market price) × 100

$20,500 priced against a $21,000 market average → 97.6% to market (in the visible cluster; shoppers sort by price). Price it at $23,000 → 109.5% — functionally invisible. Target band for a clean unit you want to move: ~95–99%, priced to market on day one, not day sixty.

Cost of holding (the melting ice cube)

A ~$20,000 used car costs roughly **$25/day** to hold:

By day 60, holding cost has eaten most of a $2,000 intended gross; by day 90 it's eaten all of it. The 60-day rule: a car still here at day 60 needs action (a price move, a wholesale-out, a spotlight), not hope.

Real gross on a used car (not the headline spread)

  REAL GROSS = retail selling price − wholesale cost − fees/transport − reconditioning − holding cost

Worked (Sofia's compact SUV, sold day 35):

The headline spread is $4,600 ($22,500 − $17,900); the *real* gross is $1,725. Reconditioning and holding quietly turn "great" grosses into "okay" ones — and you make the money on the buy (a disciplined buy plus an honest recon estimate, both worked backward from the market).

A.13 PVR (per-vehicle retailed)

PVR measures average gross per car, a core management number. There are several PVRs; know which one is being quoted.

  FRONT-END PVR = total front-end gross ÷ units retailed
  BACK-END (F&I) PVR = total F&I gross ÷ units retailed
  TOTAL PVR = (front + back gross) ÷ units retailed

Worked (illustrative month):

  Units retailed:            100
  Total front-end gross:  $140,000  → front PVR = $1,400
  Total F&I gross:        $130,000  → F&I PVR   = $1,300
  ───────────────────────────────────────────────────────
  Total PVR = ($140,000 + $130,000) ÷ 100 = $2,700

PVR lets a manager compare productivity across very different cars and salespeople on one number, and it shows the modern reality the Okafor deal illustrates: F&I PVR often rivals or beats front-end PVR — the back end carries the store.

A.14 PTI and LTV (the two subprime caps)

Two ratios decide whether a subprime deal can be structured at all (Chapter 26 §26.3).

Payment-to-income (PTI)

                monthly car payment
   PTI  =  ─────────────────────────────  × 100
              gross monthly income

Subprime lenders cap PTI commonly around 15–20%. The ethical pro also checks PTI including insurance, because the customer pays both.

Loan-to-value (LTV)

                 amount financed
   LTV  =  ──────────────────────────  × 100
            vehicle value (book)

Subprime lenders cap LTV commonly around 110–130% of book (the extra over 100% covers tax, fees, and sometimes a product). LTV protects the lender against lending more than the car is worth — and the customer against being buried.

Worked example: the canonical Devon Wallace deal

Devon Wallace, 23, ~580 credit, needs reliable transportation to keep a job. Devon's canonical numbers (Chapter 26 §26.6): gross income ~$2,600/month**; a clean late-model sedan priced **$13,995, booking (wholesale) about $11,500**; lender caps **PTI ~18%**, **LTV ~120%**; **$2,500 cash down.

The structure:

  Selling price ..............................  $13,995.00
  Sales tax (6% of price) ....................  +  $839.70
  Doc fee ....................................  +  $599.00
  Title / registration .......................  +  $401.00
                                                ───────────
  Subtotal ...................................   $15,834.70
  Down payment (cash) ........................  − $2,500.00
                                                ───────────
  AMOUNT FINANCED ............................   $13,334.70   ≈ $13,335

The rate: lender buy rate 17.9% + store's consistent, disclosed 1-point subprime markup = sell rate 18.9% APR, 60 months.

The payment (using the §A.1 formula):

  P = $13,334.70, r = 0.189/12 = 0.01575, n = 60
  Numerator: 13,334.70 × 0.01575 = 210.02
  (1.01575)^(−60) ≈ 0.39022, so 1 − 0.39022 = 0.60978
  M = 210.02 ÷ 0.60978 ≈ $344.43   →  ~$345/mo

The check against the caps:

The margin under both caps is what makes the deal fundable on the first submission and survivable for Devon — a deal that barely squeaks under both is one flat tire from default.

Why "no money down" hurts Devon, not just the lender. $0 down (~$15,835 financed) → LTV = $15,835 ÷ $11,500 = 138%. Likely won't fund at a 120% cap, and even if it did, Devon is 38% upside down on day one. The down payment isn't the dealer taking from Devon — at 116% it's the structure that keeps him from drowning.

The term trade-off (shown honestly)

Stretching to 72 months saves ~$34/month but costs **~$1,700 more in interest** and keeps Devon upside down longer — which matters because the goal is to refinance him in a year. Show the trade-off, recommend the option that serves the customer (the 60), let him decide.

The credit-repair payoff

On-time payments are the biggest credit-score factor. Devon pays on time; ~12–18 months later his score reaches near-prime; he refinances the ~$11,565 remaining balance at ~9.9% over 48 months → payment ~$293/mo** (about **$52/month less) for the same car. The affordable payment is what makes the credit repair possible; the credit repair is what makes the refinance possible; the refinance is the reward. A payment Devon couldn't carry destroys that chain at step one.

A.15 One-page formula sheet (the cheat card)

The canonical numbers, at a glance:

• Okafor (transparency deal): MSRP $45,000 · selling price $43,500 · trade allowance $18,000 (ACV $16,500, payoff $15,000 → $3,000 equity) · amount financed $41,030 · buy 6.9% / sell 7.9% (1-pt markup) / 72 mo → $697.55 buy-rate / **$717.39** sell-rate → ~$1,000 reserve · ESC $2,200 (cost $800) · GAP $900 (cost $300) · front-end gross ~$200, back-end ~$3,000.
• Devon Wallace (ethical subprime): sedan $13,995 (books $11,500) · $2,500 down · financed $13,335 · buy 17.9% + 1-pt = sell 18.9% / 60 mo → ~$345/mo · PTI 13.3% · LTV 116% → refinance ~mo 12–18 to ~9.9%/48 → ~$293/mo.
• Headline teaching loan: $30,000 @ 6.9% / 72 mo = **$510.03/mo**.

Keep this page where you can reach it. The salesperson who can show the math on the spot is the one the customer trusts — and trust is what closes the back end and earns the referral.