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Copyright 2001, 2002, Joel Anderson

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

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"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 misrepresent 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
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

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 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 rigid.
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, would save on interest paid.

Calculating the interest rate on alternative financing

Cost vs Value

Financing costs the total of whatever it takes to get it. This includes immediate costs (e.g: the higher price incurred by foregoing a cash discount), and later incremental costs (monthly payments). But the value of the financing is only the value of the cash it replaces.

Determine the true interest rate for dealer financing, then shop for alternative financing. Only true rates are comparable.

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 true rates.

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


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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).
  1. The vehicle can be purchased for cash, for $19,500
  2. The vehicle can be financed, at $21,000 (higher price)
  3. The term offered is 3 years (36 months)
  4. The downpayment is $3000 (20% down +/-)
  5. 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
             - Downpayment =  -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 need to know the
               nominal rate for comparison purposes. But
               APY is the real cost of money.

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

  Spreadsheet: If you're extending the payments, included all pmts
               in @IRR's range or suffer a wrong result.

               APR      APY
    Calc>     9.77    10.22  <-Interest rates, dlr fin
      0  -16500.00 Cash value of loan (dlr fin's worth)
      1     530.63 Payment (on dlr-fin loan amount)
      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