A while back, I heard a strategy when buying a car. Instead of paying cash, try to get a loan with a low interest rate. If you are able to get a low enough rate, it can be profitable to take the loan and invest the cash you have saved up. At the end of the loan period, you will have made more interest on the cash you had saved than you paid on the loan.

Sounds like a good, sophisticated, "I understand opportunity cost", economic approach. Professor James Kearl (of BYU's infamous Econ 110 class) would be proud.

Then I took a closer look at the numbers, and discovered a flaw in the argument:

Assumptions:

Car costs $20,000

The load period is 5 years

The loan interest rate is 5%

The investment interest rate is guaranteed at 6% (after taxes, etc.)

So the blind calculations are (after 5 years):

Total cost of loan (principle + interest): $22,645.48

Total value of investment (principle + interest): $26,977.00

So theoretically we make ~$4,300 by being smart. "Self, Great Day!"

PROBLEM: The argument forgot about the monthly payment. It needs to come from somewhere. Here's the breakdown:

Assuming no other income, we must make the monthly payment from our investment. The payment is $377.42/month.

The total cost of the loan is the same, but the total value of the investment takes a hit, as the principle decreases (and with it the interest amount earned) each month.

If we do the math, after making the final payment, we are left with $512.74 in our account.

Not too bad still. We make 500 bucks. "Self, Not-too-shabby day!"

I decided to explore the case where we have a monthly income. Let's say we have a monthly income surplus of exactly $377.42/month, allowing us to make the monthly payment without affecting our investment. Sounds great! We pay a total of $22,645.48 and have $26,977.00 in our investment. We make ~$4,300!

ALTERNATIVE: What if we paid cash, and decided to invest that $377.42/month instead. So we would empty our investment by paying cash, and instead of paying a monthly payment to the bank, we would use it to replenish our investment. So at the end of 5 years:

Total paid for car: $20,000.00

Total in investment: $26,464.27

Total gain: $6,464.27 "Self, Great day!!!!!!!!!"

So in conclusion, taking the loan and investing the cash appears to not be such a great deal after all. It only seems to make sense if you are (1) expecting no additional income during the loan and (2) guaranteed a high enough interest rate on your investment. Even then it's only a difference of $500. Not sure if that's enough to offset the risk of something going wrong. If you expect to have enough income to make the monthly payments from your surplus, then it is much better to pay in cash upfront and invest the monthly payment amount. It requires diligence, but clearly pays off.

Did I miss anything? The assumptions I made may not be very realistic, but I think they are generous enough to show a favorable, yet possible scenario. If things were more generous (like an interest rate of 10% on the investment) then perhaps the numbers would change.

Thoughts?

I think you are dead on. Unfortunately though in today's financial climate the numbers are not quite as optimistic as in your hypothetical example. Here's my scenario, purchasing a Prius tomorrow and paying $27,000 cash:

ReplyDeleteI could take out a loan for 6o months from my credit union at 2.74% and pay $482.04 a month, after 5 years I will have spent $28,922.40. I could invest the $27,000 cash in a 60 month CD at 2.71% and end up with $30,913.23 for a net gain of $1,990.83.

OR

I could pay $27,000 cash for the car and put the monthly payments of $482.04 into a savings account at 0.50% interest, after 5 years I will have saved $29,282.64 leaving me with a net gain of $2,282.64.

So, it is *slightly* better to pay cash using these interest rates that are current as of 3/27/11 from www.teachersfcu.org.

as of 4/24/11 the interest rates are

ReplyDeleteauto loan: 1.99%

60 month cd: 2.71%

savings account: 0.50%

with those rates,

auto payments: $28387.80 ( @473.13 per month)

cd : $30,913.23

cash down + savings account : $28,739.56

so there is a (pre-tax) gain of $2525.43 with auto loan vs $351.76 with cash down.

of course, the amount in savings account can be periodically converted to cd to increase the interest rates.

Yes. There are numbers in which things can sway in any direction. The right set of circumstances (such as a global economic downturn) can create all sorts of weird scenarios.

ReplyDeleteThe main point of my post is to highlight the fact that the third option (cash down + savings account) is often overlooked in these discussions. There are many scenarios in which it is the more effective solution. Other times it is not.