Finance Lease - beginning of year payments/interest calculation

CFA Level II
#1

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?

#2

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 :slight_smile:

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!

#3

Hi Wojtek,

Thanks for the reply. It IS confusing! I get the methodology the CFAI example is using. To give you the example Schweser uses, I will make up some numbers since I don’t have book with me, but clearly rememeber the method they present:

So in Schweser, if you had lease with beginning period payments (lets say 2000 each), an implicit rate of 10%, and a PV of 10,000, YEAR 1 would look like this:

Year 1: (again, these are made up numbers, but same method)

1.Beg. Lease Value (Jan 1): 10,000

2.Lease Payment (Jan 1): 2000

  1. Balance (on Jan 1): 8000

  2. Interest: 800

  3. End year Balanece (Dec 31): 8800 (beg year bal + accrued interest of 800)

This is def. different than the way the CFA presents it; the CFA method would have charged interest off the balance in #1 of 10,000 in Year 1. Also in contrast, if this lease were, say, 5 years…the Year 5 interest charge in Schweser method would be zero, where as the CFAI method would have an interest charge of some amount.

#4

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 © is described as ’ Interest portion of January 1 payment’ NOT INTEREST EXPENSE for Year 1.

  1. The same balance (on Jan 1): 8,000

  2. 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.

  3. 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!

#5

Ha, ok this makes sense now (well in convoluted kind of way). It is definitely a little confusing how the CFAI text presents this, at least when you compare to Schweser. I see what you mean in bullet ‘c’ in the CFAI texts; there was no payable due on Jan. 1 becuase interest had yet to accrue - but come close of the period, interest had accured in year 1, so the income statement is hit with with 7132 in interest expense (which is what Schweser is showing).

Thanks for explaing this to me…it was very helpful!

#6

If it matters at all, Var_99, this is the same example from the CFA Level 1 books (FRA reading on non-current assets). The CFA material will make sense if you go back to the Level 1 readings and understand the basics of how the CFA tables were created.

If you look at the Level 2 material in isolation, it is confusing because (I think) the Institue assumes you know how the tables were created in Level 1. This has happened to me in a couple of places elsewhere, wherein the Institute (expectedly) jumps into the meat of things without warning.

Overall, the CFA material could be presented better, but I think the concepts will stick if you connect the dots by referencing the Level 1 material.

#7

Thank you all for the discussions above. I found it very helpful. I was also looking for some explanation on another example on CFA material regarding finance lease. Could anyone please look at the Example 10 on Page 77 (Reading 18) of the CFA curriculum book? For Question #2, the Solution shows that the interest expense for Year 1 is 100 for the finance lease alternative. I was wondering why it is not 73.6, that is, 10% of 736 (=1,000 - 264)…? Can anyone help? Thank you.

#8

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

#9

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

#10

Hello everyone,

One more confusing point for this example (i.e. Curriculum 2013 vol2 p.80 Example 11) - The income statement for solution 1 shows that the interest expense of $7132 is booked to year 1. - But the CF statement for solution 2 shows that the interest paid of $7132 is booked to year 2. Very Confused?! Or is it something wrong in this example in Curriculum??? Can someone please help to clarify. Larry.