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The amortised cost of a financial asset or financial liability is the amount

at which the financial asset or financial liability is measured at initial recognition
minus principal repayments,
plus or minus the cumulative amortisation using the effective interest method of any difference between that initial amount and the maturity amount, and
minus any reduction (directly or through the use of an allowance account) for impairment or un-collectability.

Amortisation based on estimated cash flows helps to smoothen the financial statement by incorporating the prepayment estimation into EIR calculation. With a proper prepayment model:

At portfolio level, estimated cash flows follow patterns similar to actual prepayments.
Amortisation already considers prepayment behaviour since prepayment is considered in EIR calculation

Hence, P&L volatility will be much smoother.

Amortised cost is derived using the EIR which is calculated by means of the cash flow plan:

FlexFinance_DE > Fortgeführte Anschaffungskosten > image2018-3-2_9-25-0.png

In view of the definition of the amortised cost, the following formula is used for its calculation:

Initially, the amortised cost of a deal equals the negative of its original costs:

At further payment dates, the amortised cost equals the amortised cost of the previous payment date, plus the difference of the current cumulative total amortisation TA(t_n) and the one from the previous payment date TA(t_n-1), plus possible principal repayments PR(t_n):

FlexFinance_DE > Fortgeführte Anschaffungskosten > image2018-3-9_16-13-58.png

The cumulative total amortisation TA(t_n) of payment date t_n is defined by

FlexFinance_DE > Fortgeführte Anschaffungskosten > image2018-3-9_10-37-53.png

The effective capital EC(t_n) of payment date t_n is defined as the negative of the sum of all future cash flows discounted by the effective interest rate:

FlexFinance_DE > Fortgeführte Anschaffungskosten > image2018-3-9_16-16-0.png
In order to check the calculation of the effective capital in Excel exports of the calculation analyser, the following equivalent recursive formula for the effective capital is useful:

The smoothing effective interest rate EIRs is calculated exaxctly like the EIR – only all cash flows of premiums/discounts/charges/transaction costs are ignored in the calculation.
Analogously, the smoothing effective capital ECs is calculated exactly like the EC – only the EIRs are used instead of the EIR.

The following annuity loan is considered:

Initially, there is also a charge of 5000 USD. Hence, the first cash flows for the deal are as follows:

FlexFinance_DE > Fortgeführte Anschaffungskosten > image2018-3-9_17-30-32.png

Applying the calculation method described, the calculation of the amortised cost of the deal starts as follows:

FlexFinance_DE > Fortgeführte Anschaffungskosten > image2018-3-12_11-29-37.png