FRA Lease Question beginning, copyright, calculator, 2010

kseniaru

Hey Guys

Could somebody help me with this question please? Note I have changed the question around to avoid copyright violations:

"At the beginning of 2010 ABC Ltd enters a finance lease requiring five annual payments of $10,000 each beginning on the first day of the lease. Assuming the lease interest rate is 8%, the amount of interest expense recognised by ABC in 2010 is closest to."
a) $2650
b) $3194
c) $3450

I originally chose $3450 after putting my calculator into BGN mode and then typing in the variables into my calculator and getting the PV of the lease than multiplying it by the interest rate (8%) = 3450

However the answer is A. I have no idea why this is so. This is the following answer for the question

"At the inception of the lease, the PV of the lease payments is $43121 (BGN mode: N=5, I=8, PMT=10,000, FV=0, solve for PV). After the first payment is made, the balance of the lease liability is $43,121 - $10,000 principal payment = $33121. Interest expense for the first year is $33,121 x 8% = $2650"

My question is, why are we subtracting the principal payment from the PV first then taking the 8% of that amount. Shouldn't we be multiplying the PV about by the interest rate to get the Interest cost for the year. Also shouldn't the question actually specify that the annual payment is only the principal component? Very confusing.

Thanks

Daniel1985

You give 10000 back to the lease company just the same day the lease agreement is signed. So there is no accrued interest for that amount. And you count interests only on the amount you actualy owe for year 2010 (43000-10000).
Another way to solve this problem is compute PV with end mode using N = 4. Because this is a number of end period payments until the lease is fully paid off.

And annual payment is not only principal payment, but principal plus interests.