Auto loan ''3.9% or $1500 off'' gimmick - Low_Pct.WK1

''3.9% or $1500 off'' is periodic interest PLUS prepaid interest

Ways to skin a cat Auto companies and dealers know the value of money, they borrow it. They know that the average consumer lacks the sophistication to figure out how financing works. They attempt to recover what they've lost on price with gimmick financing. The easiest way to do this is to use a term of art; low-percent, below market, or zero-percent financing; to hide the cost of money. I'm from the government and I'm here to help you. The Federal Trade Commission is responsible for enforcing Truth-in-Lending: FTC, Bureau of Consumer Protection CRC-240 600 Pennsylvania Ave, NW Washington, D.C. 20580

$1500 in interest is disguised by including it in the higher price. By law, Truth-in-Lending, and logic, the difference between the cash price and the financed price is interest.

Calculating the composite interest rate on dealer-offered financing

Q:   How do I compare the dealer's low-rate financing at a higher price, with the taking the discount and getting the financing somewhere else?

A:  A discounted cash flow calculation will reveal the composite interest rate on the dealer financing. It will account for the periodic interest, and the prepaid interest included in the higher price.

The dealer's composite rate (based on the periodic rate PLUS the prepaid interest included in the higher price) should be compared to the lower, cash price (after taking the cash discount), and the true rate on financing the cash price from an alternative source.

With the dealer's composite rate in hand, shop for alternative financing by comparing true rates.

Adding a downpayment raises the rate.

The larger the downpayment, the higher the rate.

The cost of financing is higher with a large downpayment because the interest, included in the higher price you paid to receive the financing, is spread over a smaller loan. The larger the cash down, or the more valuable the trade-in, the smaller the loan and the higher the rate.

Shortening the term raises the rate

Rigid Financing Terms When interest paid is a combination of below-market rate PLUS prepaid interest included in the higher price, lengthening the term lowers the rate. This is why the term of below-market financing is rigidly limited, fixed in length.

Early payoff (you win the lottery):

Shortening the term means that the prepaid interest, the interest included in the higher price, is amortized over fewer months. Since the prepaid interest is fixed, shortening the term means having the use of the loaned money for less time, raising the rate.

The perverse effect of an early payoff raising the rate is another reason to use alternative financing, financing that doesn't include prepaid interest - even if the rate on the alternative financing is the same. An early payoff, a shorter term, that would save on interest paid.

$Value vs $Cost The value of financing is limited to the value of the cash it replaces. The cost of financing is whatever it takes to get it. Money costs money. Financing costs the total of whatever it takes to get it. This includes immediate costs, the higher price incurred by foregoing a cash discount, and later incremental costs (monthly payments).

Calculating the interest rate on alternative financing

Determine the true interest rate for dealer financing, then shop for alternative financing. Only true rates (APY) are directly comparable, comparing APRs is a compromise.

A discounted cash flow analysis of dealer financing can deliver an APR (a nominal rate) and a true rate (APY). But alternative loans are quoted in APR. To compare loan rates from alternative sources, do a discounted cash flow analysis of each of the alternative loan's flows to find their true rate (APY). Then compare rates.

If this seems complicated, try to remember that the banks wrote the rules to prevent easy comparisons.

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Spreadsheet

Download spreadsheet  

Increasing the downpayment or shortening the term raises the rate

In this example, "3.9% financing or $1500 off" is really 9.77% (APR), true rate 10.22% (APY).

Given:

The vehicle can be purchased for cash, for $19,500

The vehicle can be financed, at $21,000 (higher price)

The term offered is 3 years (36 months)

The downpayment is $3000 (20% down +/-)

The interest rate is 3.9% (a below-market rate)

The difference between the cash price and financed price is interest.

Since the nominal rate of interest is not zero, calculate the payments (using @pmt) and enter the payments into the monthly flows, and the prepaid interest (from the higher price), into the time-zero-initial-flow of the Discounted Cash Flow (DCF) calculation. Prepaid interest occurs at time zero, loan initialization.


1. Calculate the amount of the loan, dealer financing:

Vehicle price, dlr fin = 21000

- Down payment =   -3000

Loan Amount, dlr fin = 18000

2. Calculate the payment, dealer financing:

Rate APR (decimal) = 0.039

Term (mos) =      36

@PMT(prin,int,term) = 530.63

3. Calculate the equivalent cash value loan:

Vehicle price, dlr fin = 21000

- Downpayment = -3000

- Cash discount = -1500

Cash value of dlr fin = 16500

4. Use discounted cash flow [DCF] to determine the nominal (APR) and true (APY) rates on the dealer-offered financing.

RATES: Lenders quote rates in APR, a nominal rate (a rate in name only). You only need to know the nominal rate for comparison purposes. APY is the real cost of money.

DCF: the first value in a DCF calc is always negative.

Spreadsheet: If you're extending the number of payments, included all payments in @IRR's range.

Calculate	APR	APY
	9.77	10.22	Rate(s) Dealer Fin.
Months	Flows
0	-16500.00		Cash value of dlr's loan
1	530.63		Payment, $18000 dlr loan
2	530.63
3	530.63
4	530.63
5	530.63
6	530.63
7	530.63
8	530.63
9	530.63
10	530.63
11	530.63
12	530.63
13	530.63
14	530.63
15	530.63
16	530.63
17	530.63
18	530.63
19	530.63
20	530.63
21	530.63
22	530.63
23	530.63
24	530.63
25	530.63
26	530.63
27	530.63
28	530.63
29	530.63
30	530.63
31	530.63
32	530.63
33	530.63
34	530.63
35	530.63
36	530.63