Lease Question first, liability, recognized, interest, beginning

EastCoastJ

At the beginning of 2006, Corp enters a finance lease requiring 5 annual payments of 10,000, each beginning on the first day of the lease. Assume interest rate is 8%, the amount of interest expense recognized bu 2006 is....

So I've calculated the liability value of the lease to be 43121
Their solution says to take 43121-10,000 and then x 0.08 = 2649
Whereas I thought it was 43121 x 0.08 = 3450

Can someone please shed some light for me



Edited 1 time(s). Last edit at Wednesday, April 6, 2011 at 02:54PM by bluejazzy.

dontknow1987

Just work through the whole life cycle of the lease to understand it. Your firm signs a lease today (January 1, 2006) for a 5 year term with payments due the first of each year for $10,000 a payment. Interest rate is 8%.

You write the check today for $10,000. That's done, book it, forget about it. Now what about the next 4 years? Find the present value of those payments: FV = 0, Int = 8%, PMT = 10,000, N = 4, calculate PV = $33,121.27. That's your lease liability. But we can also see that $40,000 total payments - $33,121.27 PV = $6,878.73 in interest for the whole lease.

January 1, 2007 rolls around. You owe $10,000. Write the check for the full amount, send it out. Part of that was for interest. 8% of $33,121.27 is $2,649.70 (interest expense). The payment to the lease liability is $7,350.30. That reduces the lease liability to $25,770.97. Total interest paid so far is $2,649.70.

January 1, 2008 rolls around. You owe $10,000. Write the check for the full amount, send it out. Part of that was for interest. 8% of $25,770.97 is $2,061.68 (interest expense). The payment to the lease liability is $7,938.32. That reduces the lease liability to $17,832.65. Total interest paid so far is $4,711.38.

January 1, 2009 rolls around. You owe $10,000. Write the check for the full amount, send it out. Part of that was for interest. 8% of $17,832.65 is $1,426.61 (interest expense). The payment to the lease liability is $8,573.39. That reduces the lease liability to $9,259.26. Total interest paid so far is $6,137.99.

January 1, 2010 rolls around. The last payment date. You owe the last $10,000. Write that check for the full amount. Part of it is interest. 8% of $9,259.26 is $740.74 (interest expense). The payment to the lease liability is $9,259.26, which matches our lease liability bringing it to $0. The total interest paid is $6,878.73, which matches what we said way up in the first paragraph.

pacmandefense

Where's this from?

ramzes

present value of the lease = 43121 given N=5, Pmt = 10,000 and I=8%

PV of lease on the first day of lease = 43121 and you pay 10,000 on the the first day of the lease
So, you owe 43121-10000 = 33121 on the first day of the lease. So, in first year you would recognize interest expense on 33121 i.e. 33121*.08 = 2649

Hope this is helpful

sdada

cpk123 Wrote:
-------------------------------------------------------
> small correction to this:
> On this principal, you accrue 8% interest in the
> whole 2006 year and you pay it on 1st Jan 2007 as
> part of the next $10,000 payment.
>
> On this principal, you accrue 8% interest in the
> whole 2006 year and you pay it on 1st Jan 2007 IN
> ADDITION TO THE NEXT $10,000 payment.

I am not sure about this. On Jan 1 2007, you pay $10,000 which includes interest accrued in 2006 and a part of the principal. You don't pay anything additionally, I think.
Am I missing something here?

Wasteoftime

bluejazzy Wrote:
-------------------------------------------------------
> i dont understand why its -10,000 though. I would
> think its 43121 x 0.08 to find the interest
> expense, and then take 10000 subtract that to find
> the liability repayment

You start the lease on 1st Jan 2006.

When you calculate interest for the year, it has to be calculated on the principal remaining because that is 'what you have to pay back, what you have borrowed'

Since you pay 10,000 immediately on 1st of Jan 2006 itself, for the year 2006, you have principal remaining of only 43121 - 10,000 = 33121

On this principal, you accrue 8% interest in the whole 2006 year and you pay it on 1st Jan 2007 as part of the next $10,000 payment.

Bluetick1010

Hi there,

were's that question or can you post complete question other forum members can follow and understand context of question?

Daniel1985

key word is FIRST DAY. So it's an "annuity due". So they take the 10,000 out and then calc 8% int exp. Just pay attention to those words...it could have just given you the date like "June 1" instead of "June 31" or something. Does that help?

FVPV

i dont understand why its -10,000 though. I would think its 43121 x 0.08 to find the interest expense, and then take 10000 subtract that to find the liability repayment