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Attractive Financing or Cash Back when buying a car
Note: You can use any financial calculator to do this problem, but if you want the BEST, you can
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THE SCENARIO
It's nearly Halloween, and you know what that means: the Christmas buying season is already in full swing. Did that sound crotchety-old-man enough?
Anyway, every Christmas season, the 'December to Remember' and other similar car commercials are ubiquitous, and tout various deals and options for buying a new car, in an effort to get you to plop a big red bow on a new machine in the driveway, courtesy of Lexus or BMW or Chrysler or whatever.
When they present purchasing offers they are generally structured like this:
Buy at a 'reasonable, low' X percent financing for 5 years (or 3, or 7)
-or-
Get Y dollars cash back when you purchase with cash
If you're considering buying a car during the next couple of months (or, really, anytime, as these deals are available pretty much any time you want, even if they're not featured in radio and TV ads), it helps to know how to evaluate these kinds of offers. So let's do an example.
In this one, you can get a car for $40,000, financed for 5 years at 1.9%. Alternatively, you can get $3,500 'bonus cash' (i.e. a rebate or discount) when you buy it with cash. Let's assume that the financing option is zero down, and the $40,000 is the all-in cost, after taxes, fees, extraneous add-ons, and the like.
The question is: If you pay cash rather than taking the financing option, what's your ROI on that cash?
THE SOLUTION
This one has three parts.
First, you need to find out what your payment would be if you took the financing option.
Second, you need to figure out how much cash you'd have to pay if you bought the car with cash.
Third, you need to figure out your ROI for that amount of cash, if it saves you the financing option's payments.
Let's get started.
Step 1
First things first, make sure the calculator is using 12 Payments per Year.
N: 60 (The car loan lasts for 60 months)
I/YR: 1.9 (1.9% financing)
PV: 40,000 (This is a zero-down option, so you start out owing the whole $40,000)
PMT: (this is what I'm trying to find)
FV: 0 (The car is totally paid off at the end)
If you take the financing option, you'll be paying
$699.36 per month for the next 5 years.
Step 2
The car costs $40,000, but you get $3,500 off if you pay with cash. So you'll have to come up with
$36,500 in cash to buy the car.
Step 3
N: 60 (If you buy with cash, you save yourself 60 payments)
I/YR: (this is what I'm trying to find)
PV: -36,500 (With the cash option, you'll be paying $36,500 up-front for the car)
PMT: 699.36 (By paying with cash, you save yourself $699.36 per month in car payment)
FV: 0 (At the end of 5 years, the car would have been paid off, so your savings ends)
If you pay cash, you'll make 5.63% on that cash over the course of the 5 years.
The particulars of the various deals on-offer vary, and generally any part of any of them can be negotiated with a motivated salesperson (they want to buy gifts for their families, too, so they could use the commission). However, the general structure of the ads is the same, and if you plug the right numbers into the structure above, you should be able to figure out what the benefits of the various options might be.
What do you think? Would you buy a car like this with cash? On credit? Skip the fancy car and keep your money or buy 3 or more cheaper, used cars? Let us know in the comments!
