A worked tap of a seven-year euro bond: ACT/ACT ICMA step by step, the clean and dirty price, the cash the issuer receives, and what the other day counts would have charged.
Accrued interest is the coupon multiplied by the days elapsed since the last coupon date, divided by the days in the coupon period. On an illustrative 3.875 per cent annual euro bond with 208 days accrued of a 365-day period, that is 3.875 × 208/365 = 2.20822 per 100, or EUR 5,520,548 on a EUR 250,000,000 tap. Investors pay it on top of the clean price and get it back in the next full coupon.
Worked in full in Capital Markets by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
The calculation matters most in the primary market when an issuer reopens an existing line. A tap settles between coupon dates, the new bonds must be fungible with the old ones and carry the same next coupon, so the buyers pre-pay the interest that has built up since the last coupon. Get the day count wrong and the settlement amount on the confirmation is wrong by tens of thousands of euros.
| Input | Value |
|---|---|
| Coupon, annual | 3.875% |
| Original issue size | EUR 500,000,000 |
| Tap size | EUR 250,000,000 |
| Last coupon date | 15 March 2026 |
| Tap settlement date | 9 October 2026 |
| Next coupon date | 15 March 2027 |
| Maturity | 15 March 2033 |
| Reoffer yield of the tap | 3.85% |
| Day count | ACT/ACT ICMA |
Step 1: count the days. From 15 March to 9 October 2026 is 208 actual days. The coupon period from 15 March 2026 to 15 March 2027 is 365 days, and 157 days remain to the next coupon.
Step 2: apply the formula. Under ACT/ACT ICMA the denominator is the actual length of the coupon period (times the number of coupons a year, which is one here).
Accrued interest per 100 = Coupon × Days accrued ÷ Days in period
= 3.875 × 208 ÷ 365 = 2.20822
Accrued interest in euros = 250,000,000 × 2.20822% = EUR 5,520,548
Excel: =3.875*COUPDAYBS(Settle,Maturity,1,1)/COUPDAYS(Settle,Maturity,1,1)
On EUR 1,000,000 of nominal that is EUR 22,082.19, the figure a trader checks first on a confirmation.
Step 3: from yield to clean and dirty price. The tap is priced at a reoffer yield of 3.85 per cent. Discounting the seven remaining coupons and the redemption, with the first cash flow 157/365 = 0.4301 of a period away, gives the dirty price; subtracting the accrued gives the clean price that is quoted.
Dirty price = Σ 3.875 ÷ 1.0385(0.4301 + k) + 100 ÷ 1.03856.4301 = 102.330
Clean price = 102.330 − 2.208 = 100.122
| Item | EUR |
|---|---|
| Clean consideration, 250,000,000 × 100.122% | 250,305,208 |
| Accrued interest, 208 days | 5,520,548 |
| Cash paid by investors at settlement | 255,825,756 |
| Full coupon paid on the tap on 15 March 2027 | 9,687,500 |
| Net interest borne by the issuer on the tap for the period | 4,166,952 |
The issuer pays a full coupon of EUR 29,062,500 on the enlarged EUR 750,000,000 line in March, but the EUR 5,520,548 it collected at settlement funds the part of the tap's coupon that relates to days before the money arrived. The net EUR 4,166,952 is exactly 157 days at 3.875 per cent on 250,000,000. Accrued interest is a timing transfer, not a cost, and it must not be counted in the proceeds when computing the all-in cost of the tap: the yield is solved on the clean consideration less fees, as in how a new bond's coupon and reoffer price are set.
Euro corporate and government bonds use ACT/ACT ICMA. Floating rate notes and money market instruments use ACT/360, sterling money market instruments ACT/365 Fixed, and many older or US corporate bonds 30/360. The same dates give different accrued amounts.
| Convention | Days | Per 100 | EUR | vs ICMA |
|---|---|---|---|---|
| ACT/ACT ICMA | 208/365 | 2.20822 | 5,520,548 | 0 |
| 30/360 | 204/360 | 2.19583 | 5,489,583 | −30,965 |
| ACT/360 | 208/360 | 2.23889 | 5,597,222 | +76,674 |
| ACT/365 Fixed | 208/365 | 2.20822 | 5,520,548 | 0 |
ACT/365 Fixed matches ICMA here only because the coupon period happens to be 365 days. In the period from 15 March 2027 to 15 March 2028, which contains 29 February, ICMA divides by 366 and the same 208 days accrue 2.20219 rather than 2.20822.
| Settlement | Days accrued | Per 100 | EUR |
|---|---|---|---|
| 15 April 2026 | 31 | 0.32911 | 822,774 |
| 15 June 2026 | 92 | 0.97671 | 2,441,781 |
| 9 October 2026 | 208 | 2.20822 | 5,520,548 |
| 15 February 2027 | 337 | 3.57774 | 8,944,349 |
A tap settling a month before the coupon raises almost a full coupon of accrued from investors. The size of the settlement cheque says nothing about the cost of the funding: the yield on the clean price does.
Every convention that decides a published number on a transaction, and what it was worth in euros, is set out in the free workbook for this case.
No. Investors buying a tap pay the accrued interest to the issuer at settlement and receive the full coupon on the next date. On an illustrative EUR 250,000,000 tap the issuer receives EUR 5,520,548 of accrued and pays EUR 9,687,500 five months later, a net EUR 4,166,952, which is exactly 157 days of interest at 3.875 per cent.
Use half the annual coupon and the actual days in the half-year period. A 4.00 per cent semi-annual bond with 92 days elapsed of a 182-day period accrues 2.00 x 92/182 = 1.01099 per 100, or 101,099 on a nominal of 10,000,000. The denominator is the period's own length, not 365.
ACT/ACT ICMA counts actual days in both the numerator and the coupon period; 30/360 treats every month as 30 days and the year as 360. On a 3.875 per cent bond settling 9 October after a 15 March coupon, ICMA gives 2.20822 per 100 and 30/360 gives 2.19583: EUR 30,965 less on a EUR 250m tap.
This article is one calculation from Capital Markets. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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