Definition and concept of amortized cost
In practical terms, and adjusting the terminology according to whether it is assets or liabilities, amortized cost could be defined as follows:
- For a financial asset: it is the amount at which the asset was initially recognized less principal repayments already received plus or minus the accumulated amortization (calculated using the effective interest rate method) of any difference between that initial amount and the repayment value at maturity, less any impairment losses.
- For a financial liability: it is the amount at which the liability was initially recognized less principal repayments already made, plus or minus the accumulated amortization (calculated using the effective interest method) of any difference between that initial amount and the amount to be repaid at maturity.
Practical application of amortized cost
Since the above definition may be somewhat confusing or difficult to understand, there is nothing better than a couple of examples to clarify the meaning of “amortized cost.” Below are two calculation examples, one for a bond and one for a loan:
Bond
For this first example, consider a bond purchased by a Luxembourg company with the following characteristics:
| Nominal value (at maturity): | 100,000 euros |
| Purchase price: | 98,000 euros |
| Duration: | 3 years |
| Nominal interest rate of the bond: | 5% per annum, payable at the end of each year (coupon of 5,000 euros) |
The amortized cost would be calculated as follows:
- Step 1 - determination of cash flows and purchase price: In this case, the price paid today is 98,000 euros, and the expected future income is 5,000 euros at the end of years 1 and 2 and 105,000 euros (5,000 + 100,000) at the end of the third year.
- Step 2 - calculate the effective interest rate (IRR): The amortized cost method requires that each annual adjustment be made by applying the effective interest rate (IRR), which is the discount rate that equates what is paid today with the present value of expected future cash flows.
To find the IRR, the equation of the present value of future cash flows equaled to the purchase price is set up:
98,000 = 5,000 * (1 + IRR)^(-1) + 5,000 * (1 + IRR)^(-2) + 105,000 * (1 + IRR)^(-3)
Solving the equation, we find that the IRR is 0.057446876, or 5.7447%.
- Step 3 - Calculate the amortized cost for each year:The effective interest rate is now applied to the outstanding balance for each year to calculate the effective interest accrued (initial balance × IRR), the amortization (effective interest – coupon received), and the final balance, which is the amortized cost of the bond (initial balance + amortization).
This results in the following table with coupon collected as €5000 in each period:
| Period | Opening balance | Effective interest | Amortization | Closing balance (amortized cost) |
| 1 | 98000.00 | 5629.79 | 629.79 | 98629.79 |
| 2 | 98629.79 | 5665.97 | 665.97 | 99295.77 |
| 3 | 99295.77 | 5704.23 | 704.23 | 100000.00 |
Loan
For this example, a Luxembourg company obtains a loan from a financial institution with the following characteristics:
| Nominal value of the loan: | 200,000 euros |
| Application and origination fee: | 1% of the nominal value |
| Interest rate: | 6% |
| Term: | 4 years with constant annual payments due on December 31 of each year |
The amortized cost would be calculated as follows:
- Step 1 - determination of cash flows and future payments: In this case, the value received today is 198,000 euros (200,000 from the loan minus 1% application and origination fee), and the expected future payments must be calculated using the following formula:
200,000 = payment * (1 + 0.06)^(-1) + payment * (1 + 0.06)^(-2) + payment * (1 + 0.06)^(-3)
This gives annual payments of 57,718.30 euros.
- Step 2 - calculate the effective interest rate (IRR): The amortized cost method requires that each annual adjustment be made by applying the effective interest rate (IRR), which is the discount rate that equates what is paid today with the present value of expected future cash flows. To find the IRR, the equation of the present value of future cash flows equaled to the purchase price is set up:
198,000 = 57,718.30 * (1 + IRR)^(-1) + 57,718.30 * (1 + IRR)^(-2) + 57,718.30 * (1 + IRR)^(-3)
Solving the equation, we find that the IRR is 0.064402888, or 6.4403%. This IRR is higher than the nominal rate due to the effect of the origination fee.
- Step 3 - calculate the amortized cost for each year: The effective interest rate is now applied to the outstanding balance for each year to calculate the effective interest paid (initial balance × IRR), the amortization (payment made – effective interest), and the final balance, which is the amortized cost of the loan (initial balance + amortization).
This results in the following table with coupon collected as €57718.30 in each period:
| Period | Opening balance | Effective interest | Amortization | Closing balance (amortized cost) |
| 1 | 198000 | 12751.77 | 44966.53 | 153033.47 |
| 2 | 153033.47 | 9855.80 | 47862.50 | 105170.97 |
| 3 | 105170.97 | 6773.31 | 50944.98 | 54225.99 |
| 4 | 54225.99 | 3492.31 | 54225.99 | 0 |
Regulatory framework in Luxembourg
In Luxembourg, the accounting standards governing the valuation of financial assets and liabilities fall under two broad frameworks: Lux GAAP and IFRS.
- Lux GAAP (Luxembourg Generally Accepted Accounting Principles): this is the set of national accounting principles and rules that apply by default to the vast majority of companies incorporated in Luxembourg and is based on the Law of December 19, 2002, together with complementary regulations and circulars.
- IFRS (International Financial Reporting Standards): these are the International Financial Reporting Standards issued by the IASB and required for listed groups, public interest entities, and those companies that voluntarily choose to apply them, especially in international contexts.
Currently, both frameworks allow the calculation of amortized cost for the valuation of certain financial instruments, although with different degrees of mandatory application:
- Under Lux GAAP: amortized cost is permitted and recommended (especially since the 2016 reform that harmonizes Luxembourg with the European directive), but it is not mandatory in all cases. Traditionally, historical cost was applied, and the widespread use of amortized cost is recent, aimed primarily at instruments with significant discounts, premiums, or transaction costs. Small companies may continue to use alternative methods if there are no material impacts.
- Under IFRS: the use of amortized cost calculated using the effective interest method is mandatory for financial assets and liabilities managed under the hold-to-maturity model. There is also an obligation to systematically recognize expected impairment losses.
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Learn moreConclusion
Amortized cost is a fundamental pillar for the valuation of financial assets and liabilities in Luxembourg, allowing the actual book value of instruments such as loans and bonds to be reflected using the effective interest rate method. This article has explained what it consists of and how it is calculated using two examples. However, there may still be some doubts about the subject or it may not be fully understood, as there are technical aspects such as the calculation of the IRR that some readers may not grasp.
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