"3.9% or $1500 off" is periodic interest PLUS prepaid
$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.
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.
from the government
and I'm here to help you.
Federal Trade Commission is responsible for enforcing Truth-in-Lending:
FTC, Bureau of Consumer Protection
600 Pennsylvania Ave, NW
Washington, D.C. 20580
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
Determine the true interest rate for dealer financing, then
shop for alternative financing. Only true rates are
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.
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.
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).
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.
- 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)
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
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.
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)