Financial Lease Calculation wiz needed

September 8, 2008 10:30 AM

Finance wiz needed: Although interest rates do not exist in leases, customers constantly ask what is the interest rate for the lease. I have a question regrading how to calculate the implied interest rate in order to get the most favorable comparison.

For purposes of illustration I will use a $10,000 60 month $1 purchase option lease with 2 advance payments, a lease rate of .02345 which will yield a monthly payment of $234.50.
The traditional present value method will give an implied interest rate of 15.687% using Tvalue calculator available here http://tinyurl.com/6gewp4

Recently a friend showed me another method which according to him yields an interest rate of 8.24%.
He does the calculations as follows:
$234.50*60=$14,124.00 Total payment
$14,124.00-$10,000=$4,124.00 Total Interest Paid
$4,124.00/5=$824.80 Interest Paid per Year
$824.80/$10,000.00= 8.248% Interest Rate per Year

Something seems weird in this calculation and I was hoping for a finance wiz to clarify the error.

posted by thinktwice to work & money (9 comments total)

Your friend isn't compounding the interest, nor is he taking into account the decrease of the amount of the principal over the lifetime of the loan. I'm pretty sure your answer is right.
posted by Johnny Assay at 10:43 AM on September 8, 2008

Interest is paid on the remaining balance, not on the total principal like your friend calculated.
posted by caddis at 10:47 AM on September 8, 2008

You have the money factor, correct? Why don't you just multiply it by 2400? I believe anything else would be misleading at best. This is for automobile leasing, correct?
posted by geoff. at 12:19 PM on September 8, 2008

No this is not for automotive leasing, so the multiply by 2400 does not work. And again there is no principle or interest in a lease.
posted by thinktwice at 4:25 PM on September 11, 2008

And again there is no principle or interest in a lease.

Then why did you ask the question?

Look, if you want to calculate interest, whether it is implied or actual, you have to start with the amount to which it implies. We call that principal. I give you an auto worth $50,000 and you pay me in monthly payments. It works in effect like a loan. Talk to the contrary is just the line dealers give to sell to unsuspecting buyers. Selling based on monthly payments is a lot easier than selling based on total price. Anyway, to calculate an implied interest from this arrangement subtract from the value of the auto the down payment and the net present value of the value of the vehicle at the end of the lease. That is in essence what the customer is making lease/loan payments against; that is the principal of this implied loan. With a principal and payment schedule you can calculate the interest rate. To calculate the interest, put various interest rates into this formula until you can balance the equation:

PV * ( 1 + i )^N = PMT * [ ( 1 + i )^N - 1 ] / i

where

PV is the present value (value of vehicle minus money down and minus the value at the end of the lease) = 10,000-234.5*2-1=9,530

N is the number of payments = 60

i is the simple monthly interest and you could start with what you found 0.15687/12 =0.01307

I leave the tedious math to you, but your method sounds about right and your friend's method earns a big fat zero on the test.
posted by caddis at 7:07 AM on September 12, 2008

Let me clarify.
The question is whether the is a 'hole' in the way my friend is calculating the numbers. From my perspective the calculations make the most sense I have seen in order to try, and I underscore try, to get an APR approximation on a lease payment. Also keep in mind that we are not talking about vehicles. Vehicles leasing involves residual payments and is a whole different animal.

To reiterate, there is no interest in a lease. Only a lease rate. You are not borrowing money. You are in effect renting equipment. There is no principle.

This is an incredibly difficult concept to grasp for most people and that is why I have come her for help. I have run this by CPA's and while they agree on the calculation they don't feel very comfortable with it either.
posted by thinktwice at 10:36 AM on September 12, 2008

We are talking semantics here. Legally it is a lease. In reality rent to own is a high interest rate finance system often preying on the poor and uninformed.

But the industry contends it does not sell. It claims it only rents, because if a consumer wants to stop making payments, he or she can do so and return the goods without further payments. RTO stores generally refuse to comply with state usury ceilings or interest rate disclosure laws such as the Truth In Lending Act.

Muslim finance employs similar techniques to avoid the sin of charging interest. Far from predatory, this finance system is creative and tends to be very pro-consumer. I am not sure whether there has been a front page post on it, but it would make a fascinating post with some better links than wikipedia and some stories on the benefits it provides to communities.

My point is if it walks like a duck and quacks like a duck, it's a duck. You can say it's not a loan, it's only a lease and you can then belittle those who disagree by saying that the concept is hard to grasp. However, it functions like a loan and you can calculate an equivalent interest rate for the transaction.

The formula above will allow you to calculate simple interest. If you want to find the APR take that interest rate and plug it into this formula:

APR = (1+[i/12])^12-1.
posted by caddis at 12:10 PM on September 12, 2008

We are not talking semantics. We are talking definitive concepts. Loans and leasing are not the same. Take for example operating leases and how they are treated, FASB 13, etc... People are drawn to comparing to loans as a moth to flame. You would be comparing apples to oranges. And it is a hard concept to grasp, otherwise we would have already and a definitive answer here. I have run this by some pretty smart people and every one of them gets confounded by this.
I wish it were easy.
posted by thinktwice at 11:02 AM on September 18, 2008

I gave you a definitive answer. I just didn't do your math for you.
posted by caddis at 5:15 PM on September 18, 2008