Finance Lease - beginning of year payments/interest calculat beginning, interest, liability

MonkeyBusiness

I’m confused on Schweser vs. CFAI calcuations for interest pamyments for beginning of year payments on finance leases.
If you open the Schwesr Notes, vol. 2, p.65/66, the solution for problem 7 says that for Year 1, the interest payment is 2734.  This makes sense I suppose, since your lease liability is reduced right away as you pay on Jan. 1., then get charged interest on that balance. However, if you now open the CFAI books, vol. 2, to page 81, they also list a table for a finance lease payment schedule, also strucured as beginning of year payments.
Where I’m confused it that the CFAI has ZERO for Year 1 interest, while Schweser has an interest payment for Year 1. What am I missing here as to why these seemingly two identically structured lease payments have different interest methods for Year 1?

Londonrocks

Hi Var_99,
I don’t have access to the current Schweser notes but I can see the Curriculum example which you are referring to. If it is any consolation, you are perfectly right to be confused by the way things have been presented here
However, do read the table on page 81 together with the one at the top of page 82, where the example is further analysed. I hope you will find the following explanation helpful:
At the inception of the lease, the initial liability balance is €100,000. As the lease payments are made upfront, this balance is immediately reduced by the first lease payment and becomes €71,321 (€100,000 - €28,679). What the table on page 81 is stating (in column c) is that this first installment does not pay off any interest. That’s because interest only accrues with the passage of time. Seeing as no time has elapsed yet, interest has not had a chance to accrue, and the first payment should be fully attributed to the reduction of principal.
This however does not imply, that the company incurs no interest expense for the year. Using the TVM worksheet on your calculator (assuming you have the TI) you can work out that the interest rate implicit in the lease is 10% (FV = 0; N = 3; PV = 71,321; PMT = -28,679; COMPUTE I/Y). Using this rate, the company accrues interest on the lease liability outstanding at the beginning of the year (10% x €71,321 = €7,132). The interest is charged to the Year 1 income statement, as shown in the table on pg. 82.
At the end of the first year, the finance lease liability (without the accured interest) is still €71,321. What the table on pg. 81 is not showing (and this I find potentially confusing) is that there must also be an interest liability on the balance sheet for €7,132 to correspond with the interest which was accrued over the course of the year and which remains outstanding at 31 December Year 1.
The payment on 1 January Year 2 pays off the interest which is sitting on the balance sheet from Year 1 (€7,132) and also reduces the finance lease liability by whatever amount remains after the interest is considered (€28,679 - €7,132 = €21,547). The lease liability becomes €49,774 (€71,132 - €21,547). Once again, the company accrues interest for the year on this balance which effectively remains outstanding for the duration of the year (10% x €49,774 = €4,977).
This interest is paid of with the payment made on 1 January of the following year … and so on.
all the best with your preparation!

Analti_Calte

HI again VaR_99,
the two methods are actually NOT DIFFERENT. What is different is the presentation in both books. If your numbers were used in the CFA material, you would see:
1. The same beg. lease value (Jan 1): €10,000
2. The same lease payment (Jan 1): 2,000.
The CFA book is not implying that there is zero interest charged in the first year. What is being said on page 81 is that this first payment is not paying off any interest, as interest has not had time to accrue yet! Please go back to pg 81 of the book and see that in the bullet points below the table, column (c) is described as ’Interest portion of January 1 payment’ NOT INTEREST EXPENSE for Year 1.
3. The same balance (on Jan 1): 8,000
4. The same interest (for the year): 800 charged at 10% on the balance above BUT the CFA Curriculum shows that interest accrual in a different table (at the top oof page 82), where you can see it impacting in the income statement in Year 1.
5. End of year balance (Dec 31): 8,800 BUT once again the CFA Curriculum shows only the 8,000 on page 81 (without the interest accrual) leaving you having to guess that there must also be an interest liability sitting on the balance sheet separately from the lease liability. If we combine the two, we get 8,000 + 800 = 8,000.
To reiterate, in the CFA Curriculum example, interest is charged to the income statement on the balance from point 3 (in any given year). That includes the final year, in which the last payment occuring on 1 January pays off the entire liability, so there is no outstanding balance for interest to be charged on. Please see that in the table on page 82 of the Curriculum, interest expense for the final year of the lease is zero, just as in Schweser.
The critical difference is that interest charged (as an expense to the Income Statement) DOES NOT EQUAL accrued interest which is paid off in any single year.
Hope this makes it clear!

karoliukas

bdgrdk, with finance leases, it makes a difference if the payments happen in arrears (at the end of the period) or in advance (at the beginning). The scenario on pg 77 is an example of in arrears payments (at the end of the year).
So you basically need to analyse what happens to the lease chronologically:
opening balance: 1,000
interest expense: 1,000 x 10% = 100 (interest accrues on the opening balance, which remains upaid for the duration of the year)
lease payment: 264
closing balance: 1,000 + 100 - 264 = 836
If we were told that payments are made at the beginning of each year (in advance), we would have:
opening balance: 1,000
lease payment: 264
interest expense: (1,000 - 264) x 10% = 73.6 (interest accrues on the opening balance adjusted for the payment which happens at the very start of the year)
closing balance: 1,000 - 264 + 73.6 = 809.6

busterbluth

Thank you very much. Now everything is clear. Very helpful. Very much appreciated!