The Money Mustache Community
Learning, Sharing, and Teaching => Ask a Mustachian => Topic started by: sockfight on January 09, 2020, 09:56:58 PM

While looking into cars, I came across the following GM offer "0% financing for 72 months and $5,000 cash allowance", and I thought to myself...how good is an interest free loan. I ran some numbers but would like a sanity check and discussion :)
Assumptions:
Let's say you have $20,000. You're considering buying a used car for $10K in cash or a new car for $20K, where you could pay cash but instead opt for the interest free loan mentioned above. Let's say $10K and $20K are your outthedoor prices after tax, allowances, discounts, fees, etc. Let's assume the cost of ownership for these two cars is equivalent (perhaps the older car has more maintenance but insuring the new car is more expensive). Let's imagine that after five years, if you were to sell either car, you could do so at 50% of what you paid for it. And, let's assume that any money not sunk into the car is in the stock market and say the average annual return is 7%.
I realize that's a lot of assumptions, and if any of them seem particularly unreasonable, please call them out!
I ran some calculations to try and figure out how much money you have after five years.
For the used car, this seemed straightforward: Your car's value is $5,000 and you put $10K in the market for five years (10,000x1.07^5), adding up to $19,026
For the new car, the car's value is $10,000. I used this savings withdrawal calculator at https://www.bankrate.com/calculators/savings/savingswithdrawalcalculatortool.aspx to figure out what happened to your money. I put in $20K where $277 (which is $20K/72 months) is withdrawn monthly for five years, and the 'interest' rate is 7%. The calculator said the resulting cash value would be $8,218. For a total of $18,218.
I was quite surprised at how close those two values were, and depending on how you alter the assumptions I made above, the better choice can easily flip around. And if you kept the car more than five years, things change as well.
Is this analysis sound? What do you think?

Addendum: I know it would be unwise to literally use the stock market as a savings account. If you imagine instead that you leave whatever you don't use to pay for the car in the market and then, every month, have $277 of income that you either use to pay the loan or add to your investment, you still arrive at the two scenarios being very close in value.

I think you need to use 20K divided by 60 months, which would be 5 years. Therefore drawing down $333 monthly instead of $277.
In your example you used a 6 year term. Your car wouldn't be paid off yet , you'd still owe $3324 [ $277 x 12 months] before they gave you the title...so you either wouldn't be able to sell it after 5 years, or you need to pull another $3300 out of your figures to reflect the actual amount of $$ spend on the car.

Wow. I can't believe I goofed on how many years 72 months is *facepalm*. $20K / 72 months is $277 but the drawdown period is six years, not five, leaving $5,345 behind.
OK, so, recalculating, and assuming for the sake of convenience that each car is worth 50% after SIX years:
Used 10K car scenario: $5,000 + $10,000x1.07^6 = $20,007
New 20K car scenario: $10,000 + $5,345 = $15,345
Or, envisioning this the way I stated in my addendum, i.e. whether you use an income stream to pay the loan or add to an in investment...
Used 10K car scenario: $10,000x1.07^6 (initial money in the market) + $5,000 (car value) + $2,467 ($277 p/m for six years, compounded at 7%) = $44,667
New 20K car scenario: $20,000x1.07^6 (initial money in the market) + $10,000 (car value) = $40,014
Either way, roughly $4,600 difference in wealth between the two scenarios if all my assumptions were true.