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Solve for the Effective Interest Rate — IFRS 9 Worked Example | CALC SERIES #16

When a bond is purchased at a discount, the EIR must be calculated before building the amortisation table. Here's the IRR equation, the trial-at-7% verification, the full 3-year table, and why using the coupon rate as the EIR silently understates interest income every year.

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Solve for the Effective Interest Rate — IFRS 9 Worked Example | CALC SERIES #16

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In this video

  1. 0:00 Introduction — when you need to solve for the EIR
  2. 0:22 The scenario — bond at €94,750, face €100k, 5% coupon, 3 years
  3. 0:55 IFRS 9 B4.1.1 — EIR = rate that discounts cash flows to purchase price
  4. 1:20 Setting up the IRR equation: €94,750 = PV of €5k, €5k, €105k
  5. 1:55 Trial at 7% — discount each cash flow, sum = €94,750 ✓
  6. 2:30 EIR amortisation table — Y1 €6,633 / Y2 €6,747 / Y3 €6,869
  7. 3:00 Year 1 journal entries — EIR interest + coupon receipt
  8. 3:35 Bond amortises from €94,750 to €100,000 at maturity
  9. 4:00 Common mistake — using coupon rate 5% as EIR
  10. 4:30 Recap — IRR equation, trial, verify, table

Key terms in plain English

Internal rate of return (IRR)
The discount rate that makes the net present value of a series of cash flows equal to zero. For a bond purchased at a discount, the IRR of the cash flows (coupon payments plus face value repayment, minus purchase price) equals the effective interest rate.
Bond at a discount
A bond where the purchase price is less than the face value. This occurs when the market rate of interest exceeds the coupon rate — investors demand a higher return than the coupon provides, so the price falls below face value.
Discount amortisation
The gradual increase in the carrying amount of a bond purchased at a discount, from purchase price to face value at maturity, using the effective interest method. The difference between EIR interest income and coupon cash received represents the discount being amortised.
Gross carrying amount
The amortised cost of a financial asset before deducting any loss allowance. Under IFRS 9, interest income on non-credit-impaired assets is calculated on the gross carrying amount at the EIR.

Full explanation

When you need to solve for the EIR

IFRS 9 Appendix B paragraph B4.1.1 defines the effective interest rate as the rate that exactly discounts the estimated future cash flows to the gross carrying amount — the purchase price. For a bond issued at par, the EIR equals the coupon rate. For a bond issued at a discount, the EIR is higher than the coupon rate and must be calculated.

In practice, the EIR is found using the IRR function in Excel or a financial calculator. In an exam, trial and error at a plausible rate (typically between the coupon rate and a rate that gives a PV well below the purchase price) is the expected approach.

The scenario: bond purchased at €94,750

Face value: €100,000. Coupon: 5% per annum = €5,000 per year. Maturity: 3 years. Cash flows: €5,000 (Year 1), €5,000 (Year 2), €105,000 (Year 3 — final coupon plus principal). The bond was purchased for €94,750. The EIR is the rate r such that: €94,750 = €5,000/(1+r) + €5,000/(1+r)² + €105,000/(1+r)³.

Trial at 7% — verification

€5,000 / 1.07 = €4,673. €5,000 / 1.07² = €4,367. €105,000 / 1.07³ = €85,710. Sum: €4,673 + €4,367 + €85,710 = €94,750. The equation balances. EIR = 7%.

EIR amortisation table

Year 1: Opening €94,750 × 7% = €6,633 interest income. Coupon received €5,000. Closing: €94,750 + €6,633 − €5,000 = €96,383.

Year 2: Opening €96,383 × 7% = €6,747. Coupon €5,000. Closing: €98,130.

Year 3: Opening €98,130 × 7% = €6,869. Coupon and principal received €105,000. Closing: €0 (bond fully repaid). Total interest income over three years: €20,249.

Journal entries for Year 1

At purchase: Dr Bond investment €94,750 / Cr Cash €94,750.

Interest income (EIR): Dr Bond investment €6,633 / Cr Interest income €6,633.

Coupon received: Dr Cash €5,000 / Cr Bond investment €5,000.

Net effect on bond investment: €94,750 + €6,633 − €5,000 = €96,383 closing balance.

Common mistake: using the coupon rate as the EIR

If 5% is used instead of 7%, Year 1 interest income is 5% × €100,000 (face value) = €5,000 — equal to the coupon. The bond investment balance never changes: it stays at €94,750 year after year instead of amortising up to €100,000. Over three years, interest income is understated by €20,249 − €15,000 = €5,249. The bond is also presented below its recoverable amount at maturity, which could trigger unnecessary concerns about impairment. IFRS 9 is explicit: the EIR is applied to the gross carrying amount — the amortised cost balance — not the face value.