Accounting & Bookkeeping & Small Business Forum

[Danny9394]

Let's say I lease an auto and I will purchase it at the end

Auto value
$50,000

Total lease payments
$55,000

Term
24M

Car value after 12M / Purchase option price
$100

How should I determine the interest rate?
How should I record the interest expense?

:roll: :?:

[dp1903]

It would be easier if the monthly payment had been provided. The stated or nominal interest rate is approximately 9.3% compounded monthly with an effective yield of 10.97%. That rate yields $4,987.01 interest on $50,000 in 24 months with a monthly payment of $2,291.13. That makes total payments of $54,987.01 which is close to $55,000.

Using an HP 12-C calculator makes this a lot easier to solve.

I first solved for the Present Value of an Ordinary Annuity of 1 factor for n periods at i interest. That formula is (1-(1/((1+i)n)))/i . n is a superscript. I couldn't make it a supercript here because I don't know if this forum supports superscripts.

i = monthly interest rate
n = number of periods

9% divided by 12 = .75% which is the periodic or monthly interest rate I started with. 1+ the interest rate = 1.0075 to go into the formula above. n = 24. Solving with these variables, the Present Value of an Ordinary Annuity = 21.889146

Next to solve for the monthly payment I use the Present Value of an Ordinary Annuity formula [the formula I used above] times R for Rent. It is expressed as R(PVF-OAn,i) where both n and i are subscripts. n represents the number of periods, i represents the monthly interest rate and R represents the Rent or monthly payment.

Dividing the present value of $50,000 by 21.889146 [present value of an ordinary annuity of 1 factor for 24 periods at .75 interest] yields a Rent or monthly payment of $2,284.24.

Amortizing $50,000 for 24 months at .75 percent per month [9%/12] with a $2,284.24 monthly payment yields $4,821.68 in interest. Therefore, the interest rate is a little higher than 9% and I kept raising the rate by a tenth of a percent using the steps above until I found that 9.3% approximates the total interest paid of $5,000.

[dp1903]

What doesn't make sense is that after a year or 12 months you have an option to purchase the car for $100. At that time you will still owe $26,157.15 on the lease and the lessor will only have recovered $27,493.56 of their cost of the vehicle. If the market value of the vehicle is $50,000 when the lease starts, the lessor is losing money and you are making money if you purchase the vehicle at the end of 12 months.

If the lease is noncancelable then it is defined as a capital lease because it contains a bargain purchase option to acquire the asset at a price which is significantly below its fair market value at the time the option may be exercised. You would setup an asset and a liability for the lease just like you were purchasing it on credit.

Record the asset and liability at the lower of (1) the present value of the minimum lease payments (excluding executory costs) or (2) the fair market value of the leased asset at the inception of the lease. Use 9.3% as the interest rate. Set up an amortization schedule based upon this info for the liability and that will provide you with the monthly amounts to apply to principal and interest to write off the liability.

Finally, please forward $100 to me for my time to help you with your homework!!! :P

[Danny9394]

:D :D got it

Thanks~

[Ahshucks]

dp ... you described the booking for the GAAP books, but what is the effect for the tax books? The lease amount paid is fully deductible for the business use of the auto.

I guess it depends if the owner wants GAAP books or tax books.

[dp1903]

In the case of capital leases, IRS guidelines are pretty much the same as GAAP. The IRS calls the car lease in this situation a "conditional sales agreement". See Pub 535 - Business Expenses. In such cases the item is to be capitalized and depreciated rather than expensed as a normal rent agreement. The idea is the same as GAAP. The item is essentially being purchased on credit rather than being rented.

I tried to post a link to pub 535 at the irs website but the forum wouldn't let me, sorry.