IFRS16: How to make the financial mathematics work

As a treasurer, I have always found that financial mathematics underpins the way in which any treasury works. One of the first questions I always ask an interviewee is how they would accrue interest on a loan or deposit – if you can’t answer that, your treasury career is going to be short-lived. Financial mathematics range from the simple (accruing interest) through to the mind-blowing (valuations of exotic derivative products).

This is why the new lease accounting standard, IFRS16 is so fascinating. It sits somewhere at the lesser end of complexity using core treasury mathematics such as accruing interest, discounting cashflows and setting up loan (principal plus interest) repayment schedules. The great thing however is that all the calculations are interconnected.  I’m going to try to focus purely on the mathematics in this blog.  If you are looking for lots of technical references to accounting standards then this probably isn’t the blog for you.

IFRS16 comes into effect for lessee accounting for accounting periods beginning on 1 January 2019 or thereafter. Whilst some treasurers may believe that this is one for the accountants to sort out, I would disagree. For anyone with a substantial lessee position you are going to have to manage a significant increase in both assets and liabilities plus some large timing differences in the profit and loss account. For companies who are lessees, their treasury team will be instrumental in determining the incremental borrowing rate (where a borrowing rate is not immediately observable) to be used in the calculations.

Calculations

There are a lot of really good publications on IFRS16 which have been released by the major accounting firms. Many of them are worthy of a read (see end of the blog) however all of the examples contained within them are based on annual examples. These are great to conceptually demonstrate how the standard works, however in the real world there aren’t many leases where payment is only made once a year.

All of the annual examples work brilliantly.  However if you try to apply exactly the same mathematics to an example where there are more frequent cashflows you will find that it doesn’t work.  If you use the same incremental borrowing rate for discounting and accruing your principal and interest schedule it will not pay down to nil by the end of the lease.  If that doesn’t make sense now, it should later.

Remember that different auditors have different interpretations on the way in which the accounting standards should be implemented.  Before beginning any new methodology to implement IFRS16 it would be wise to check with your auditors first.

Example

  • Annual rent of CU1,000,000 payable in equal monthly installments
  • Payments are made 2 working days before month end
  • No bank or public holidays
  • 10 year lease term from 30 June 2017 to 30 June 2027
  • Expected life of the lease is exactly the same as its term
  • For this example transition to IFRS16 is on 1 July 2017
  • Calculated using a standard month end financial calendar
  • Annual discount rate = 8%
  • Basis = 365 days
  • No impairment of lease or prepayments
  • Transition method: modified retrospective
    • Lease was previously classified as an operating lease
    • Where the Right of Use (ROU) Asset is made equal to the Lease Liability

Each part calculation methodology is abbreviated in the interests of space.  On many of the tables below you can click on them to see the full calculation.

1. Calculate the present value of the lease liability and right of use asset

This is done by discounting all of the cashflows back to the commencement date of the lease.  In this example, although the lease started on 30 June 2017, this was before the transition date of 1 July 2017.  Therefore 1 July 2017 is the commencement date with the days calculation in the discount formula based on number of days from this date.

Discount_Factor_Formula

Basis usually depends on the standard for that currency.  Whether you use a 360 or a 365 day basis, as long as it is used consistently in all calculations the methodology will work.

Discount_Cashflow_10y_Abbreviated

Because we have elected to use the modified retrospective transition method where the ROU Asset equals the lease liability, the following accounting entries are generated on commencement date:

Accounting_10y_Discount_Cashflow

2. Calculate the depreciation schedule for the ROU asset

This is a fairly simple calculation to do.  The ROU asset is depreciated over the expected life of the lease according to the number of days in each accounting month.  This will depend on the accounting calendar which you are using.  Remember to adjust the first and last months by the number of days in the month where the lease was not in existance.

As the depreciation is straight line the same amount is expenses in the P&L through the life of the lease in the months which have identical day count.

The number of days which is used in this calculation (3,651) should be exactly the same as the number of days calculated in part 3 (interest expense).

This generates the following accounting entries in the first month

Accounting_10y_Amortisation_Schedule

3. Calculate the principal and interest schedule for the lease liability

This requires the setting up of a standard principal and interest schedule as if the lease was a loan from the lessor. In the modified retrospective option the starting lease liability is the same amount as the right of use asset which was calculated in part 1. The loan is then repaid by making a rental payment each month which reduces the principal amount of the loan.  This is one of the conceptual parts of IFRS16 which you need to get your head around – rental payments are no longer expensed through the P&L, they are an entry to the balance sheet.

Interest accrues on the loan on a daily basis. IFRS16 requires that the rate used for accruing interest is the same as the discount rate. There is one problem here. As we know from the principles of compound interest an annual interest rate is not the same as a monthly interest rate.

To get around this problem it is necessary to adjust the interest rate from an annual rate to a rate for each period depending on day count. This is done using the following formula.

Adjusted_Interest_Rate_Formula

So an 8% annual rate is adjusted to 7.719682% for a 29 day period. This rate is then used to calculate the interest accrual.

Interest_Accrued_Formula

The interest accrued is then capitalised back into the outstanding liability balance each time there is a cashflow or at the end of each accounting period.

Interest_Schedule_10y_Abbreviated

The important thing about this schedule is to ensure that the outstanding principal is paid off to nil by the end of the life of the lease. If you get this calculation right in the above schedule the carried forward amount on the last day of the calculation is nil. As you see above the balance is CU1. This is a result of rounding to 2 digits for cents in each line of the calculation.  Don’t worry if you are a few CUs out at the end, but it shouldn’t be more than a few.

Also note that the number of days interest accrued in total (3,651) should be the same as the depreciation schedule.

On 30 July 2017 the first rent payment is made, this has a negative cashflow and reduces the operating lease liability.  On the same day the accrued interest expense is capitalised into the liability balance.  On 31 July 2017 accrued interest expense is again capitalised because it is a month end,

Accounting_10y_Interest_Schedule

Notes

  • Interest Accruals

The day count is calculated based on the number of days, based on start date, which fall in the same month. This is the normal practice for calculating accruals in accounting. In the above example there are 31 days in which interest accrues in the month of July. Even though you see the interest end date in July 2018 as being in August.

Whilst this is the correct way to accrue if you accrue on the basis of end date rather than start date the differences are minimal.

  • Financial Calendars

Whilst many companies use a calendar month as their month end day, some companies use weekly cycles for month ends (eg a 4+5+4 week cycle where there are 364 days in a financial year which is caught up with a 53rd week periodically).

By using the method of capitalising the accrued interest at cashflow dates and month end dates the interest expense over the life of the lease will the same irrespective of the month end convention used.

  • Discount Rates

To make the calculations works perfectly it is best to use an annual discount rate. This may take a bit of conversion depending on the quoting convention of each element of the discount rate.

If a company has an equivalent traded debt instrument with tenor the same as the expected life of the lease then this is pretty easy: use the current all-up market yield on the debt instrument. Remember that if the debt instrument pays interest on a frequency other than annual it must be adjusted back to annual.  The same methodology for adjusting interest rates as per part 3 above can be used to convert to an annual interest rate.

However for a company which may not have a debt instrument of equivalent tenor to the expected life of the lease then some derivation of rate may be required. For example the base rate at which a company may borrow for 10 years at commencement date of the lease may be the fixed swap rate for that tenor. However these may be quoted on a monthly, quarterly or semi-annual basis and must be adjusted back to annual.  In addition a credit margin could also be quoted on a basis of other than annual.

Profit and Loss

This table shows the effect of IFRS16 relative to the current accounting standards in the profit and loss. Currently rent is expensed as incurred on cash basis, meaning that the profit and loss is consistent at CU1,000,000 per annum.

Under IFRS16 however the profit and loss is the sum of the depreciation expense plus the interest expense. This means that the profit and loss is significantly higher in the early years of the lease, but gets significantly less towards the end of the lease.  Over the life of the lease the overall profit and loss effect will be the sum of the rental cashflows (ie CU 10,000,000).  However there is now a timing difference in the way that the IFRS16 P&L is recognised compared to previous standards.

The aim here is to try to create a level playing field between buying and asset and leasing it. If a company buys a fixed asset then the fixed asset is depreciated and the company must fund it. Assuming that the company funds from debt then there would be an interest cost to doing so.

If a company enters into a lease agreement then the right of use asset is depreciated and IFRS16 deems that the lease is funded as if it was debt, hence the interest cost at the company’s incremental cost of borrowing.

Does it really create a level playing field? Sort of, but it’s not perfect. When buying a fixed asset the initial asset value is what was paid for it.  In leasing it is the present value of the future cashflows for the expected life of the lease at a derived discount rate. A fixed asset may be funded from operating cashflows, debt or equity and may not necessarily give rise to an interest cost. A lease liability, however, will always give rise to an interest cost.

If there are no changes to the structure of the lease (eg a change in the expected life of the lease) then all the accounting entries for that life are known on day one.  Depreciation expense is straight line so it is only increases in leap years.  Interest expense is higher in the early years are more of the rental payment goes to paying off interest rather than principal (this is exactly the same concept as how a home loan works).  Monthly figures can be seen by clicking on the table.

Profit_Loss_10y_Annual

The graph below shows these same values.  In the early years the overall profit and loss expense is about 20% higher than under current accounting standards.  However by the last year it is almost 30% less.

The interesting line is the cumulative effect which shows that by the middle of the lease the total expense under IFRS16 is CU5.6m compared to CU5.0m under the old standard (ie 56% of the expense is taken in the first half of the lease and 44% in the second half).  This effect does change slightly as discount rates and tenor varies, however the impact on total expense is less signficant than one might expect.

Profit_Loss_10y_Chart

Balance Sheet

Because the ROU asset reduces on a straight line basis but the lease liability reduces on a capital repayment schedule basis, the value of the liability will be greater than the asset over the entire life of the lease.

Balance_Sheet_10y_Chart

This differential peaks at CU0.6m in the middle of the life of the lease (which is the same as the cumulative difference in profit and loss expense).

Formula
Alternative Methodology: Continuous Compounding

This is largely a variation on the above, however this is the only way I can think of where the rate used to discount (step 1) is the same rate which is used to accrue (step 3).  However it gives exactly the same numeric result as the methodology above.

Continuous compounding is something which I learned in my ACT exams about 15 years ago and could never find an application for its use.  It uses a principle that interest accrues daily and is immediately capitalised into the principal.  This means that a continuously compounded rate is much lower than the equivalent annual discount rate.

Remember in the discussion around the interest that I explained that the discount rate needed to be an annual rate.  This same annual rate can be converted to a continuously compounded interest rate by using the formula.

Continual_Compounding_Formula

Where e is a constant = 2.7182818 (this can be found on your calculator)

Using the above example an 8% annual interest rate can be converted to a continuously compounded rate as follows:

Continual_Compounding_Proof

Part one of the above methodology is where r is the continuously compounded annual interest rate of

Discount_Factor_Compound_Formula

In part three of the above methodology the accrual

Interest_Accrued_Formula_Continuous_Compounding

Mathematically you get exactly the same result as the main methodology.  However you can at least say that you used the same rate for both discounting and calculating the interest (even if there is some mathematical slight of hand in saying this).

Is it possible to use the same interest rate for both Step 1 and Step 3?

Yes where the cashflow on the lease only occurs annually, however in practice this rarely happens.  However for anything other than annual flows this will never work.  This is result of the discounting using a compounding methodology whilst accruing interest is a linear methodology.

Further Reading

If you’ve made it this far then you might be the sort of person who enjoys further reading

About the Author

Alistair_McLean_Colour

Alistair McLean is a Non-executive Director of The Mac and Group Treasurer of Metcash Limited.   Alistair is a Fellow of the Association of Corporate Treasurers, a Fellow of the Finance and Treasury Association, a Chartered Management Accountant and a Graduate of the Australian Institute of Company Directors.

Between 2003 and 2005 Alistair designed Commonwealth Bank of Australia’s hedge accounting system to comply with IFRS39.  IFRS16 would appear to be a similar challenge which will require good systems to be able to handle the quantum of calculations involved.

The opinions expressed in this article are personal and do not necessarily reflect the views of either Metcash Limited or The Mac.

What is the reference to Zona Dorada: The US town with a ZIP Code of 91516 which links to the same 3 accounting standards which the financial community are currently implementing (IFRS9, IFRS15 and IFRS16)
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