Chapter 22 — Exercises: How Auto Financing Works

Work these with a calculator and the payment formula from §22.5 nearby. Calculation answers are in <details> blocks; conceptual and writing exercises are for your portfolio and discussion (selected answers live in Appendix I).

Difficulty legend: ⭐ basic · ⭐⭐ applied · ⭐⭐⭐ synthesis/judgment · ⭐⭐⭐⭐ research/extension

Part A — Conceptual Understanding ⭐

  1. In one sentence, explain what it means that "the dealer is a broker, not the lender."

  2. Define each term in plain English a customer could understand: buy rate, sell rate, dealer reserve.

  3. What is the difference between an interest rate and an APR? Which should a buyer use to compare two loan offers, and why?

  4. Name the three kinds of lenders an indirect auto loan is typically shopped to, and give the defining feature of each (who owns it / what it's best for).

  5. List the four inputs to the monthly payment formula and what each one represents.

  6. What does amount financed mean, and write out the formula for building it (the five components).

  7. True or false, and why: "The lowest advertised APR (e.g., 'from 1.9%') is available to any buyer who walks in."

  8. What is a captive finance company? Give two real-world examples and the one thing captives can offer that banks and credit unions usually cannot.

  9. Roughly order these credit tiers from lowest typical rate to highest: subprime, super-prime, near-prime, prime, deep subprime.

  10. Why does rate-shopping within a short window (e.g., two weeks) generally not hurt a buyer's credit score?

  11. What is dealer reserve also sometimes called? List two alternative names, and state what determines how big it is.

  12. Fill in the blank and explain: "The dealer is an _ lender, meaning the loan is funded by a third party and merely arranged by the dealer."

  13. A customer says, "I want the cash rebate and the 0% financing." Why is that usually not possible, and which type of lender is the 0% offer coming from? (Recall the rebate-vs-rate choice from Chapter 12.)

Part B — Applied Analysis ⭐⭐

  1. A lender returns a buy rate of 5.4% and allows a 2-point markup. The finance manager offers the customer 6.4%. (a) What is the dealer reserve in rate terms? (b) Is it within the cap? (c) If the store's policy is a flat 1-point markup, did the manager follow policy?

  2. A customer is financing $28,000 at 7.5% APR for 60 months. Walk the payment formula step by step (show r, n, (1+r)^n, and M). Then state the total of payments and total interest.

Answer r = 0.075/12 = 0.00625; n = 60; (1.00625)^60 ≈ 1.452957. M = [28000 × 0.00625 × 1.452957] / [1.452957 − 1] = 254.27 / 0.452957 ≈ **$561.34/month.** Total of payments = 561.34 × 60 = $33,680.40; total interest = $33,680.40 − $28,000 = **$5,680.40.**
  1. Same $28,000 loan at 7.5%. The customer wants a lower payment. Compute the payment at 72 months and at 84 months. How much does each extra year of term add to total interest versus the 60-month version?
Answer 72 mo: (1.00625)^72 ≈ 1.565681; M ≈ [28000 × 0.00625 × 1.565681]/[0.565681] ≈ **$484.39/mo;** total interest ≈ $34,876 − $28,000 = **$6,876** (~$1,196 more than 60 mo). 84 mo: (1.00625)^84 ≈ 1.687199; M ≈ [28000 × 0.00625 × 1.687199]/[0.687199] ≈ **$429.55/mo;** total interest ≈ $36,082 − $28,000 = **$8,082** (~$2,402 more than 60 mo).
  1. A customer's score is 610. Which tier is that (roughly), and what three things might a lender require to approve a subprime deal that it wouldn't require from a prime customer?
Answer A 610 is roughly **subprime** (near the subprime/near-prime line — banding varies by lender). Subprime approvals commonly require some combination of: **(1) a larger down payment** (to reduce the lender's exposure), **(2) a shorter or capped term** and/or limits on the vehicle's age/mileage/price (the collateral must hold value), **(3) proof of income/residence/insurance** (stipulations, or "stips") the lender insists on before funding, and sometimes a higher rate floor or a maximum advance over the vehicle's value. The point for you: with subprime, the *structure* (down, term, vehicle choice) is as important as the rate — which is the whole subject of [Chapter 26](../chapter-26-subprime-special-finance/index.md).

  1. A buyer brings a credit-union pre-approval at 6.2% APR. Your finance office's best approval comes back with a 6.0% buy rate. (a) Can the store beat the credit union and still earn reserve? (b) What sell rate would you offer to clearly beat 6.2% while staying ethical? (c) Why is this a good outcome for everyone?

  2. Explain to a payment-focused customer, in plain language, why "$450 a month" tells them almost nothing about whether a loan is a good deal. Reference at least two of the three levers.

  3. On the Okafor deal, the amount financed is **$41,030.** The captive's buy rate is **6.9%** and the store marks up **1 point** to **7.9%,** 72 months. Reproduce the two payments ($697.55 and $717.39) and state the per-month and total-life cost of the markup.

Answer At 6.9%: r=0.00575, (1.00575)^72≈1.511064, M ≈ $697.55. At 7.9%: r=0.0065833, (1.0065833)^72≈1.602637, M ≈ $717.39. Difference $19.83/mo × 72 ≈ **$1,428 over the life** of the loan — which becomes the store's dealer reserve (~$1,000 paid up front by the lender).
  1. A customer with negative equity of $4,000 on their trade is buying a $32,000 car and putting $0 down. Ignoring tax and fees, what's the amount financed, and what is the one sentence you must say to them before they sign? (Recall Chapter 11.)
Answer Amount financed ≈ $32,000 + $4,000 = **$36,000** (the $4,000 they still owe gets rolled into the new loan). The required sentence, in your own words: *"We're adding the $4,000 you still owe on your current car to this loan, so you'll be financing about $36,000 on a $32,000 car and you'll start out a bit upside down — I want you to see that clearly before you decide."* Hiding the roll is the violation, not the roll itself.

Part C — Skills & Practice ⭐⭐–⭐⭐⭐

  1. Write your word track. Draft your own version of the broker explanation — 2 to 3 sentences telling a nervous customer that the dealer is not the bank. Then read it aloud and time it: can you say it in under 20 seconds, warmly, without jargon?

  2. Write your word track. Draft the buy-rate-vs-sell-rate disclosure you'd actually say in the finance office. It must (a) name that the store earns a markup, (b) say it's consistent/capped, and (c) invite the customer to compare. No shame, no fog.

  3. Calculate this deal, start to finish. A customer buys a $26,500** used SUV, puts **$3,000 down, has a trade worth $9,000** with a **$6,500 payoff, in a state with a 7% sales tax and trade tax credit, a $500 doc fee,** and **$350 title/reg. (a) Find the net trade equity. (b) Build the amount financed. (c) At a 9.4% sell rate for 66 months, compute the monthly payment.

Answer (a) Net trade equity = $9,000 − $6,500 = **$2,500** (positive). (b) Taxable = $26,500 − $9,000 = $17,500; tax = 7% × $17,500 = $1,225. Amount financed = $26,500 − $3,000 down − $2,500 equity + $1,225 tax + $850 fees ($500+$350) = **$23,075.** (c) r = 0.094/12 ≈ 0.0078333; n=66; (1.0078333)^66 ≈ 1.674; M ≈ [23075 × 0.0078333 × 1.674]/[0.674] ≈ **$449/month** (about $448–$450 depending on rounding).

  1. Role-play this. Pair up. Partner A is a customer who says, suspiciously, "I heard dealers jack up the interest rate. What's your rate?" Partner B handles it using the broker explanation + the invitation to shop. Swap. Debrief: did B build trust or get defensive?

  2. Build the lever table. For a $35,000 loan at 6.5% APR, build a three-row table showing the monthly payment at 60, 72, and 84 months, plus the total interest for each. Then write the one sentence you'd say to a customer to explain the trade-off honestly.

Answer 60 mo: M ≈ $684.82, total interest ≈ $6,089. 72 mo: M ≈ $588.35, total interest ≈ $7,361. 84 mo: M ≈ $519.73, total interest ≈ $8,657. Sample sentence: *"I can get your payment down by stretching the term, but every year I add knocks roughly a hundred off the monthly and costs you over a thousand more in interest — let me show you so you can pick the trade-off you're comfortable with."*

  1. Diagnose what went wrong. A salesperson told a customer on the floor, "You've got great credit, you'll be around 4%." In the finance office the real approval came back at 8.4%. The customer exploded and walked. Identify the specific mistake and write the sentence the salesperson should have said on the floor instead.

  2. Calculate the cost of the markup. A near-prime customer is financing $33,500 for 75 months. The lender's buy rate is 8.9% and it allows a 2-point markup. Compute the monthly payment at (a) the buy rate, (b) a 1-point markup (10.9% — wait, that's 2 points; recompute carefully), and (c) a 2-point markup. State the per-month and total-life cost of going from a 1-point to a 2-point markup. (Be careful: 8.9% + 1 = 9.9%; 8.9% + 2 = 10.9%.)

Answer (a) Buy 8.9%, 75 mo: M ≈ **$583.97.** (b) +1 pt = 9.9%: M ≈ $600.84. (c) +2 pts = 10.9%: M ≈ $617.90. Going from 1-point (9.9%) to 2-point (10.9%) markup costs the customer about **$17.06/month** ($617.90 − $600.84), or roughly **$1,280 over the life** of the loan. Going all the way from the buy rate to the 2-point sell rate costs ~$33.94/month (~$2,545 life). This is exactly the kind of "won't notice" packing the §22.2 warning is about — and on a 75-month subprime-ish loan, it's real money.
  1. Show the math on the spot. A customer on the floor wants a ballpark before going to finance. They're looking at a $45,000 vehicle, putting nothing down, and a fair prime rate is 5.5%. Without a calculator app — using the formula and the fact that (1.00458)^72 ≈ 1.389 — estimate the 72-month payment, then check yourself. Then state how you'd frame this number honestly for a customer (what caveat must you attach?).
Answer r = 0.055/12 ≈ 0.004583; n = 72; (1.004583)^72 ≈ 1.389. M ≈ [45,000 × 0.004583 × 1.389]/[0.389] ≈ 286.45/0.389 ≈ **$736** (precise: ~$735.20). The required caveat: *"This is an estimate at a 5.5% rate — your actual rate depends on your credit and which lender approves you, and finance will shop several and show you the real number. I'm just showing you how the math moves."* Never present an estimate as a promise.

Part D — Synthesis & Critical Thinking ⭐⭐⭐

  1. The chapter argues that disclosing the buy/sell spread doesn't usually cost the dealer the reserve. Lay out the argument in your own words. Then steel-man the opposite view (when might disclosure cost a deal?), and say where you land.

  2. Regulators pushed much of the industry from discretionary dealer markup toward flat or capped, non-discretionary reserve. Explain the disparate-impact concern in plain English, and argue whether a flat-markup policy is better or worse for (a) customers, (b) the dealership, (c) you the salesperson. Is there a tension between the three?

  3. A finance manager could legally mark a customer's rate to the lender's full 2-point cap. The customer is unsophisticated and "didn't ask about the rate." Walk through the gut-check from the canon — "would I be comfortable if this customer could hear my thoughts?" — and decide what the markup should be and why.

  4. Is dealer reserve ethically different from front-end gross on the car? Both are a margin between a wholesale cost and a retail price. Make the case that they're morally equivalent; then make the case that financing markup deserves more scrutiny. Which argument is stronger?

  5. The "spot delivery" / yo-yo scenario in §22.7 weaponizes a customer's emotional attachment to a car they've already driven home. Why is emotional commitment such a powerful (and dangerous) lever in financing specifically? Connect it to a theme from the canon.

  6. A customer with rough credit (say, a 560 score) genuinely cannot get a low rate — the high rate reflects real risk the lender is pricing, not dealer greed. How do you have an honest conversation with this customer that neither lies to them ("I'll get you a great rate") nor crushes them ("your credit is terrible")? Draft the approach, then explain how a well-structured high-rate loan can actually help them (preview Chapter 26 and the Devon Wallace story).

  7. The chapter claims daylight on the reserve is more profitable over a career, not less. But on any single deal, hiding the spread clearly makes more money. Reconcile these. What assumption about the business does the "ethics is profitable" claim depend on, and when might that assumption break down (e.g., a one-time tourist sale, a store with no repeat market)? Does the ethical case survive?

Part M — Mixed / Interleaved Practice ⭐⭐–⭐⭐⭐

  1. (Ch 22 + Ch 11) A customer's trade has an ACV of $14,000,** a **payoff of $18,500, and you show a $15,000 allowance.** (a) What's their equity (use the allowance)? (b) Positive or negative? (c) If they buy a $30,000 car with $0 down and roll the negative equity, what's the amount financed (ignore tax/fees)? (d) Name the one sentence you owe them. (This combines Ch 11 equity with Ch 22 amount-financed.)
Answer (a) Equity = $15,000 allowance − $18,500 payoff = **−$3,500.** (b) **Negative** (underwater by $3,500). (c) Amount financed ≈ $30,000 + $3,500 = **$33,500.** (d) The negative-equity disclosure sentence from Ch 11/§22.8 — name the roll, the bigger amount financed, and that they start out upside down.
  1. (Ch 22 + Ch 5) Your pay plan (from Ch 5) pays 25% of front-end gross + 5% of back-end gross. A deal has $300 front gross** (mini is $150) and back-end gross of $1,000 reserve + $1,400 product margin.** What do you earn? Then explain what this implies about how you should treat the handoff to F&I.
Answer Front: 25% × $300 = $75, which is *below* the $150 mini, so you earn the **mini, $150.** Back: 5% × ($1,000 + $1,400) = 5% × $2,400 = **$120.** Total **$270.** Implication: most of your pay on this deal came from the *back end* — so a smooth, trusting handoff (not a ground-down customer) is literally how you get paid. Burn the customer out grinding price and you torch your own back-end commission.

  1. (Ch 22 + Ch 12) On the Okafor deal, the front end netted ~$200 of gross after the $1,500 over-allowance. The financing reserve added ~$1,000. (a) Roughly what did the deal make before any F&I products? (b) Why does this prove the Ch 1 threshold concept that "the new-car sale is often a loss-leader"?

  2. (Ch 22 + Ch 3) Recall the five customer types from Chapter 3. For the price buyer and the researcher, how would you tailor the financing conversation differently? Which type is most likely to bring a credit-union pre-approval, and how do you turn that into a trust win rather than a fight?

  3. (Ch 22 + Ch 13) A customer objects in the finance office: "Your rate is higher than my bank's." Using the objection-as-information-request framing from Chapter 13, what's the real request behind that objection, and what's your response?

  4. (Ch 22 + Ch 23 preview) Without reading ahead in detail: a lease pays for the car's depreciation, not the whole car. Predict — should a lease payment on the same car generally be higher or lower than a loan payment, and why? (We'll verify in Chapter 23.)

  5. (Ch 22 + Ch 1 + Ch 5) Put three ideas together. The Okafor deal made ~$200 front-end gross, ~$1,000 financing reserve, plus product margin to come in Ch 24. (a) From Chapter 1, which "profit center" carried this deal? (b) From Chapter 5, if your plan pays 25% front + 5% back, why does this structure mean the salesperson who protects the F&I relationship out-earns the one who grinds price? (c) State the single sentence that ties the threshold concepts of Ch 1 and Ch 22 together.

Answer (a) The **F&I profit center** carried it (the new-car sale was nearly a loss-leader — the Ch 1 threshold concept). (b) Grinding adds maybe $200 more front gross (×25% = $50 to you, often eaten by the mini) while torching the trust that lets F&I earn the ~$1,000+ back-end you also get a slice of (×5%) — so the grind costs more than it makes. (c) Something like: *"The dealer barely makes money selling the car and isn't even the one lending the money — it makes its living arranging the financing and the products, which means the honest, trusting handoff is the whole business."*

Part E — Research & Extension ⭐⭐⭐⭐

  1. Look up the Truth in Lending Act (TILA) and Regulation Z (start with the CFPB and FTC). What specific loan terms must be disclosed to a borrower, and in what form? Summarize the "TILA box" a customer signs and tie each line back to this chapter's vocabulary. (Note: this previews Chapter 25.)

  2. Find the current manufacturer-subsidized APR offers from any one automaker's captive finance company (their consumer website lists them). Identify which models, which terms, and the fine print on credit qualification and rebate-vs-rate choices. Then explain why those rates can exist when no bank would offer them.

  3. Research the history of the CFPB's 2013 guidance on dealer markup and the subsequent legal and regulatory developments. Without overstating any single rule's current status, summarize the enduring fair-lending principle a dealership should operate by today, and how flat/non-discretionary reserve policies address it.