# Best example Amortised cost and EIR calculations

## Amortised cost at subsequent periods: a numerical example Amortised cost and EIR calculations

### Example Amortised cost and EIR calculations

The following example illustrates the principles underlying the calculation of the amortised cost and the effective interest rate (EIR) for a fixed-rate financial asset:

• On 1 January 2019, entity A purchases a non-amortising, non-callable debt instrument with five years remaining to maturity for its fair value of €995 and incurs transaction costs of €5. The instrument has a nominal value of €1,250 and carries a contractual fixed interest of 4.7% payable annually at the end of each year (4.7% * €1,250 = €59). Its redemption amount is equal to its nominal value plus accrued interest.
• The instrument qualifies for a measurement at amortised cost. As explained in the preceding section, its initial carrying amount is the sum of the initial fair value plus transaction costs, i.e. €1,000.
• The Effective Interest Rate (EIR) is the rate that exactly discounts the expected cash flows of this financial asset, presented in the table below, to its initial gross carrying amount (i.e. €995 + €5 = €1,000 in this example). In practice, entities will need to establish a timetable of all the expected cash flows of the financial instrument (see the table below) and then use for example an Excel formula to determine this rate. The table below summarises the timing of the expected cash flows of the instrument:
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Figure 1

In the present case, using an Excel formula, the EIR amounts to 10%. The following table shows that the sum of the discounted cash flows amounts to zero:

Figure 2

The table below provides information about the amortised cost, interest income and cash flows of the debt instrument in each annual reporting period:

Figure 3 Example Amortised cost and EIR calculations

Even if effective interest rate calculation principles are straightforward the implementation for some complex instruments could be challenging. Below additional examples are provided on how to calculate the amortised cost for financial instruments.

### Example Fixed rate debt instrument with a prepayment option

Assume the same example (Example Amortised cost and EIR calculations) above except that the contract specifies that the borrower has an option to early repay the instrument without penalty.

At inception, entity A expects that the borrower will repay the instrument at the end of the third year and includes this assumption in the calculation of the effective interest rate. The following table summarises the timing of the expected cash flows of the instrument:

Figure 4 Example Amortised cost and EIR calculations

The effective interest rate in this case amounts to 13.2% (this rate exactly discounts the expected cash flows of the financial instrument, as presented in the table below, to its initial amortised cost).

Figure 5 Example Amortised cost and EIR calculations

The table below provides information about the amortised cost, interest income and cash flows of the debt instrument in each annual reporting period in the scenario where the cash flows are realised as expected (i.e. complete reimbursement occurs at the end of the third year):

Figure 6 Example Amortised cost and EIR calculations

### Example Revision of estimates

Assume the same fact pattern as in the above (Example Amortised cost and EIR calculations).

At 31 December 2020, entity A revises its estimates for the cash flows and expects now that the reimbursement will occur at the end of 2022 rather than at the end of 2021 as initially expected.

At 31 December 2020, entity A adjusts the carrying amount of the debt instrument to reflect the newly expected cash flows (reminder: the revised cash flows are discounted using the original effective interest rate). Any difference between the carrying amount just before the revision of cash flows and the carrying amount just after the revision of cash flows should be recognised in profit or loss (IFRS 9.B5.4.6).

In this example, the carrying amount of the debt instrument following the revision of cash flow estimates at 31 December 2020 amounts to €1,073.

Figure 7 Example Amortised cost and EIR calculations

Thus, at 31 December 2020, entity A recognises a catch up adjustment of €83 (€1,1562 2 amortised cost as of year-end 2020 just before the revision of estimates, see table in Example Amortised cost and EIR calculations above – €1,073) triggering a loss in profit or loss. This reflects the fact that the principal will be repaid later than expected initially, thus resulting in a partial reversal of the amortisation of the initial discount and transaction costs recognised in previous periods.

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The table below provides information about the amortised cost, interest income and cash flows of the debt instrument in each annual reporting period in the scenario where the remaining cash flows are realised as expected in 2021 and 2022:

Figure 8

### Example Floating rate instrument without a prepayment option

The following example illustrates how entities may account for a floating rate debt instrument (this is one possible approach, other approaches may also be envisaged):

• On 1 January 2019, entity A purchases a non-amortising, non-callable debt instrument with five years remaining to maturity for its fair value of €995 and incurs transaction costs of €5. The instrument has a nominal value of €1,250 and carries floating rate of interest indexed to 12-month Euribor (not floored) plus a 2% credit margin payable annually at the end of each year. The instrument’s redemption amount is equal to its nominal value plus accrued interest.
• The instrument qualifies for a measurement at amortised cost. As explained in section 4.5, its initial carrying amount / amortised cost is the sum of the initial fair value and of the transaction costs, i.e. €1,000.
• At the beginning of 2019, the entity establishes a new timetable of the expected cash flows based on (a) the then applicable 12-month Euribor rate for year-end 2019 (as the contract specifies that the 12-month Euribor is observed at the beginning of the interest period) and (b) on market derived forward rates for the subsequent periods, as displayed in the table below:

Figure 9

• Using an Excel formula, the entity determines that at initial recognition, the rate that exactly discounts the expected cash flows of this financial asset – as presented in the table below – to its initial gross carrying amount (i.e. the EIR) is 8.5%. The following table shows that the sum of the discounted cash flows amounts to zero:

Figure 10

• This EIR will be used by the entity to account for the debt instrument in the first year: the entity will recognise an interest revenue of €85 (€1,000*8.5%) in profit or loss and the amortised cost at the end of the first year will amount to €1,048.

Figure 11

• At the end of 2019, the entity establishes a new timetable of the expected cash flows based on (a) the then applicable 12-month Euribor rate for year-end 2020 (as the contract specifies that the 12-month Euribor is observed at the beginning of the interest period) and (b) on market derived forward rates for the subsequent periods, as displayed in the table below:

Figure 12

• The entity then determines, using an Excel formula, a new EIR that exactly discounts these expected cash flows to the amortised cost of the debt instrument as of 31 December 2019 – the EIR equals 9.4%. The following table shows that this EIR discounts the new expected cash flows to the amortised cost of the debt instrument at the end of 2019:

Figure 13

• In 2020, the entity will use this EIR of 9.4%, to account for revenue interest and determine the amortised cost of the instrument at the end of the period.

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Figure 14

• At the subsequent periods, the entity will duplicate the same process as the one described above, i.e.:

• determine the new EIR based on the newly expected cash flows (i.e. the EIR that discounts these cash flows to the amortised cost of the instrument at the end of the preceding period);

• use this EIR to recognise interest revenue and determine the amortised cost of the instrument at the end of the reporting period.

This floating EIR can be determined as being the then Euribor 12 Month interest curve that will be updated at each closing, plus a fixed margin determined initially. In practice entities may consider applying different types of shortcuts to simplify this mechanism provided that the actual outcome it not significantly different from the theoretical outcome.

### Example Fixed-rate debt instrument with interest step-up

The following example aims to illustrate how a constant effective interest rate should be calculated for a debt with a contractually specified interest rate step-up.

Assume that on 1 January 2019, entity A issues a debt (the entity did not incur any transaction costs) for a price of €1,250 which is also its principal amount. The debt is repayable in total on 31 December 2023 (i.e. this is a non-amortising financial liability).

The rate of interest is specified in the contract as follows: 6% in 2019 (€75), 8% in 2020 (€100), 10% in 2021 (€125), 12% in 2022 (€150) and 16.4% in 2023 (€205).

In this case, the EIR that exactly discounts the stream of the expected cash flows of the debt is 10%.

Thus, the entity will recognise interest expense based on the effective interest rate (10%) rather than the contractual interest rate with a step-up feature.

The table below provides information about the amortised cost, interest income and cash flows of the debt instrument in each annual reporting period:

Figure 15

# Example Amortised cost and EIR calculations

Example Amortised cost and EIR calculations Example Amortised cost and EIR calculations Example Amortised cost and EIR calculations

Example Amortised cost and EIR calculations Example Amortised cost and EIR calculations Example Amortised cost and EIR calculations

Amortised cost and Effective interest rate How is amortised costs calculated? What is Amortised costs using the effective interest method

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