What the effective interest rate is
Under FRS 102 Section 11, basic debt instruments such as bank loans, bonds, loan notes and intercompany loans are usually measured at amortised cost using the effective interest method. Paragraph 11.16 defines the effective interest rate (EIR) as the rate that exactly discounts the estimated future cash payments or receipts over the expected life of the instrument to its carrying amount at initial recognition. IFRS 9 uses the same idea for entities reporting under IFRS.
The EIR differs from the coupon rate whenever the amount first recognised differs from the amount the coupon is charged on. That happens when there are:
- Fees and transaction costs. Arrangement fees, legal costs and broker fees directly attributable to the loan;
- Discounts and premiums. A bond bought for less than its face value, or one redeemed at a premium;
- Stepped or unusual interest. Payment holidays, rising coupons or a final balloon payment.
Initial measurement
Paragraph 11.13 measures a basic financial instrument at its transaction price adjusted for transaction costs. For a lender, a loan is recognised at the cash advanced plus transaction costs. For a borrower, a bank loan is recognised at the cash received less separately incurred transaction costs. Paragraph 11.18 then requires fees, transaction costs, premiums and discounts to be spread over the expected life of the instrument through the EIR, rather than expensed up front.
Building the amortised cost table
Paragraph 11.15 sets amortised cost as the amount at initial recognition, less principal repaid, plus or minus the cumulative amortisation of any difference between that amount and the maturity amount. In practice each period works like this:
| Column | How it is calculated |
|---|---|
| Opening amortised cost | Initial carrying amount, then last period's closing balance |
| Interest at the EIR | Opening amortised cost × EIR for the period (paragraph 11.16(b)) |
| Cash paid or received | Contractual coupon and any capital repayment |
| Closing amortised cost | Opening + interest − cash |
By maturity the closing balance equals the final repayment, so the fees and any discount have been released through interest over the life of the instrument.
Worked example from FRS 102
The FRC's own example follows paragraph 11.20. On 1 January 20X0 an entity buys a bond for CU900, paying transaction costs of CU50. It receives interest of CU40 a year in arrears for five years, and the bond is redeemed for CU1,100 on 31 December 20X4. The initial carrying amount is CU950.
| Year | Opening | Interest at 6.9583% | Cash received | Closing |
|---|---|---|---|---|
| 20X0 | 950.00 | 66.11 | (40.00) | 976.11 |
| 20X1 | 976.11 | 67.92 | (40.00) | 1,004.03 |
| 20X2 | 1,004.03 | 69.86 | (40.00) | 1,033.89 |
| 20X3 | 1,033.89 | 71.94 | (40.00) | 1,065.83 |
| 20X4 | 1,065.83 | 74.16 | (40.00) | 1,100.00 |
The calculator's default inputs reproduce this example. Enter the principal as 1,000 with a 4% coupon to give CU40 a year, the cash paid as 900, costs of 50 and a redemption amount of 1,100. It returns an EIR of 6.9584% (6.95845% to five decimal places). The FRC prints the rate as 6.9583% and shows final-year interest of 74.16, where the calculator gives 74.17; these are rounding differences in the published table, and every other figure matches to the penny. Total interest income over the five years is CU350: CU200 of coupons plus the CU150 difference between the CU950 carrying amount and the CU1,100 redemption.
Annuity loans and payment frequency
For a repayment loan with level instalments, choose the annuity profile. The calculator works out the instalment from the coupon rate and term, then solves the EIR from the instalments and the initial carrying amount. With half-yearly, quarterly or monthly payments the rate is solved per period. The table then adds up each year's periods, and the headline shows the annual equivalent rate, (1 + periodic rate) raised to the number of periods a year, minus 1. That is a compounding convention, not a consumer credit APR.
What this calculator does not cover
- Below-market and interest-free loans. Director, employee and intercompany loans at a non-market rate are financing transactions under paragraph 11.13, measured at the present value of the payments at a market rate. Paragraph 11.13A gives some small entities an exemption;
- Variable rates. Paragraph 11.19 re-estimates cash flows as market rates change;
- Changes in estimates. Paragraph 11.20 requires a catch-up adjustment at the original EIR when expected cash flows change, for example on early repayment;
- Impairment and expected credit losses. Neither impairment under FRS 102 nor IFRS 9 loss allowances are modelled;
- Irregular cash flows. Payment holidays, stepped coupons and part repayments need a bespoke schedule.
Getting the accounting right
Expensing loan arrangement fees on day one, rather than spreading them through the EIR, does not follow paragraph 11.18. Our FRS 102 accounts team sets up amortised cost schedules for bank debt, loan notes and intercompany balances, and our IFRS accounts service covers the IFRS 9 equivalent. Companies funding research can also use our R&D tax credit calculator.