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How is a bond tap priced, and what does the issuer receive?

The coupon is already fixed, so the price does the adjusting, and the accrued interest investors pay in is not money the issuer keeps.

Julian R. Sterling · from Capital Markets

A tap is priced off the existing bond: the re-offer yield is set where the outstanding line trades plus a small concession, the clean price is solved from that yield on the old coupon, and investors also pay the interest accrued since the last coupon date. On an illustrative €250 million tap of a 3.25 per cent bond re-offered at 3.70 per cent with 4.40 years left, the clean price is 98.189, the issuer receives €245.47 million of principal plus €4.88 million of accrued interest, and its all-in cost after 0.15 per cent of fees is 3.738 per cent, not 3.25.

Worked in full in Capital Markets by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →

Issuers tap an existing line instead of launching a new bond to build a larger, more liquid issue, to avoid a new set of documents, and often to pay a smaller concession than a new maturity would need. The arithmetic differs from a new issue in two ways: the coupon is already fixed, so the price does the adjusting, and settlement falls between coupon dates.

The assumptions

An illustrative euro corporate tap. Market levels are assumptions.

Input	Value
Existing line outstanding	€500m
Tap size	€250m
Coupon, annual, ACT/ACT (ICMA)	3.25%
Last coupon date / next coupon date	15 Mar 2026 / 15 Mar 2027
Maturity	15 Mar 2031
Settlement of the tap	20 Oct 2026
Interpolated mid-swap rate	2.95%
Re-offer spread, concession included	0.75%
Re-offer yield	3.70%
Underwriting fees, on nominal	0.15%

The re-offer spread is where the outstanding bond is quoted in the secondary market, plus whatever concession the books demand. How that concession is measured is worked in how a new bond's coupon and re-offer price are set; the tap simply applies the result to a coupon that cannot move.

The calculation, step by step

The cash is close to €250 million, which is exactly what misleads. Of the €249.97 million, €4.88 million is not funding at all. On 15 March 2027 the issuer pays a full year's coupon on the tap, €8,125,000, to investors who held it for five months: €4,875,000 of that is the accrued interest they paid in on settlement, handed back, and only €3,250,000 is interest earned. The money the issuer can actually keep is the principal net of fees, €245,097,521, against €250 million to repay in 2031.

The result: what the tap costs

The cost of a tap is the yield that discounts the bond's remaining cash flows to the price the issuer really received: the dirty price less fees, 100.139 − 0.15. Solving gives an all-in yield of 3.738 per cent, the 3.70 re-offer yield plus 3.8 basis points of fees spread over 4.40 years. The 3.25 per cent coupon is irrelevant to the cost. It only decides how much of the cost is paid as coupon and how much as the €4,527,479 discount to par that the issuer repays at maturity.

Tap or new line? If a new 4.4-year bond would need, say, 0.10 per cent more concession than the tap, the tap saves 10 basis points on €250 million for 4.40 years, about €1,147,134 in present value at 3.70 per cent. The line also grows to €750m, which can help secondary liquidity. Against that, a tap below par carries original issue discount, which some issuers and investors treat differently for tax and accounting, and a deep discount can make the merged line awkward.

What if the yield is different?

Same €250m tap of the 3.25% line, settlement 20 Oct 2026.

Re-offer yield	Clean price	Principal received, €	Versus par, €
3.30%	99.786	249,464,065	−535,935
3.50%	98.983	247,458,078	−2,541,922
3.70%	98.189	245,472,521	−4,527,479
3.90%	97.403	243,507,146	−6,492,854
4.10%	96.625	241,561,707	−8,438,293

Each 20 basis points of yield moves the price by roughly 0.8 points on this maturity, about €2 million on the tap. Where rates have risen since the original issue, a tap of an old low-coupon line lands well below par, and the issuer's treasury should expect the question of why it raised less than it borrowed.

The common mistakes

• Quoting the coupon as the cost. The tap costs 3.738 per cent all-in. Reporting 3.25 per cent understates the cost of funds by almost half a point.
• Counting accrued interest as proceeds. The €4,875,000 goes back out at the next coupon date. Budget it as a timing item, not as cash raised.
• Comparing dirty prices. A dirty price of 100.139 looks like a premium issue. The clean price, 98.189, is the one comparable with the original issue price and with other bonds.
• Using the wrong day count. A euro bond on ACT/ACT accrues on actual days over the actual period; applying 30/360 shifts the accrued and the clean price.

Takeaway

A tap is priced like a secondary trade: yield in, clean price out, accrued on top. The issuer's cost is the yield on what it keeps after fees and after handing back the accrued, 3.738 per cent here. The full cost walk for a bond issue, fees and concession included, is in how to calculate the all-in cost of a bond issue, and the curve and register behind these conventions are in the free workbook for this case.

Questions readers ask

What is a bond tap issue?

A tap is a further issue of an existing bond on identical terms, same coupon, same maturity, so that it merges with the original line, often immediately and sometimes after a temporary code. Because the coupon cannot change, the price adjusts: a 3.25 per cent bond tapped when the market wants 3.70 per cent is sold below par, at 98.189 in the illustrative case.

Why do investors pay accrued interest on a tap?

Because the next coupon is paid in full on every bond, including the new ones. Investors in an illustrative €250 million tap settling 219 days into the coupon period pay 1.95 per 100, €4,875,000, on settlement, and get it back inside the €8,125,000 coupon paid at the next coupon date. For the issuer it is a timing item, not funding.

Is a tap cheaper than a new bond?

Often, because a tap of a line investors already hold usually needs a smaller concession than a new maturity. If a new bond needed 0.10 per cent more, a €250 million tap with 4.40 years to run saves about €1,147,134 in present value at 3.70 per cent. The comparison should be made on all-in yield after fees, not on coupon.

Also on this site

• How are a new bond's coupon and reoffer price calculated?Mid-swap 2.734% plus 118 bp gives a 3.914% reoffer yield; the coupon is rounded down to 3.875% and the price solves to 99.765. Worked example.
• How do you calculate accrued interest on a bond?Coupon times days since the last coupon over days in the period: 3.875 x 208/365 is 2.20822 per 100, EUR 5,520,548 on a EUR 250m tap of a euro bond.
• How do you calculate the all-in cost of a bond issue?Solve the yield on net proceeds: 47.4 bp of fees on a seven-year bond at 4.32 per cent give an all-in 4.40 per cent, mid-swaps plus 130.04 bp.
• How do you calculate a new issue concession on a bond?Reoffer spread minus fair value interpolated on the issuer's curve: 122 less 117.81 is 4.19 bp, EUR 1,241,953 on 500 million. Log interpolation says -0.78.
• How do you calculate a convertible bond's conversion premium?Conversion price over share price, less one. A 30% premium on a 40.00 share sets conversion at 52.00, parity at 76.92 and, at par, an implied volatility of 27.3%.
• How do you compare euro and dollar bond funding costs?Spread each bond over its own swap curve, then add the basis: 108 bp over dollar swaps less an 18 bp basis is 90 bp, 32 bp cheaper than euros at 122.

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