I thought I would review the Time Value of Money after a friend of mine sent me a problem to solve.
Let's say you want to buy a new car valued at $25,000. Wait a minute! What are you doing? A new car loses almost a fifth of its value as soon as you drive it off the lot! Never buy a new car!
Okay...Let's say two guys with trench coats kidnap you at gunpoint and bring you to a new car dealership. They bring you to the smirking salesman and he says, "You have two deals: You can buy the $25,000 car for no interest and payments for 60 months or you can get a $4000 rebate today and pay 7% (yearly) interest on the balance for 48 months." Which is the better deal?
Your eyes dart across the street to the used car lot. You glance down at the "used car" section in the classifieds. Then you hear a "click" as the thug pulls back the hammer of his revolver. "Enough stalling! What's your decision!?"
First, let's figure out the payments. The first option (no interest 100% financing) would have a payment of $416.67 for 60 months. What's $416.67 x 60? $25,000.20.
The second option has payments of $502.87 for 48 months. That comes to $24,137.76. Seems a little cheaper, but remember that this includes a $4,000 rebate, so the number should be $21,000. The 3,137.76 is interest on the financing of the $21,000.
My friend suggested that I use the Present Value of money to solve the problem. Is this the correct approach? On the first option, the future value of his payments would be $25,000.20 after 60 months. The Present Value could be discounted at an alternative use of the money, say a CD at 5%. We can set up an algebra equation that looks like this:
PV(1st Option) = ($-416.67/0.004167)*[1 - 1/(1.004167)^60]
Notice how I've divided the 5% interest by 12 to get the monthly interest of 0.004167? This will give us a more accurate number.
If we solve for the first option's Present Value, we get $22,079.42.
PV(2nd Option) = ($-502.87/0.004167)*[1-1/(1.004167)^48]
PV(2nd Option) = $21,835.93
What does this tell us? Do we really care what an alternative investment would make? We want a car, darn it! Especially to appease these goons and their revolver pointed at your head. The answer is yes. This tells us that for 7%, 48 month financing option, plus rebate , if I invested $21,835.93 at 5%, I'd have the equivalent future value. If I invested $22,079.42 today at 5%, I'd have the future value of the 1st option.
So which one is better? The lower PV gets me the same car at "less"money. And since these guys are pointing a gun at your head, you should just take the 2nd option: the $4,000 rebate and 7% interest. You'll save $243.54.
There you have it. Easy peasy!
3 comments:
I'm glad you did the math - it wouldn't have been "easy peasy" for me.
But here's another idea. Take the rebate and the car, then pay it off with cash or within a much shorter period of time (12 months?)
Does this make it any more attractive to get a car with that nice "new car" perfume, no crud in hidden cracks and all the latest bells and whistles?
Wow, I never really realized that buying a car really takes tons of homework to do and meticulous calculations to make. I'm just about to buy our second car next month. My husband bought the first one, but he's in London right now so it's pretty much all up to me. I already had a handful of prospects from car dealerships in Indianapolis, Indiana.
Price and specs are two equal stuff I'm considering here for car dealerships. Indianapolis, inasmuch as it's a big city, is indeed a major city for buying cars.
Wow, cool post. I’d like to write like this too – taking time and real hard work to make a great article… but I put things off too much and never seem to get started. Thanks though. Milton Barbarosh
Post a Comment