A buyback below par always shows a gain on extinguishment; whether it creates value depends on the tender yield and what the cash costs.
A bond bought back below par always books a gain, but it creates value only if the yield the issuer pays to retire the bond is above the cost of the money used to fund the buyback. On an illustrative EUR 300.0 million tender of a 1.25 per cent bond at 93.88, the issuer books a EUR 17.90 million gain, yet loses EUR 6.17 million of value if it refinances at 4.15 per cent, and gains EUR 7.19 million if it uses surplus cash earning 2.50 per cent. The test is one comparison: a tender yield of 3.38 per cent against the funding rate.
Worked in full in Capital Markets by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Bonds issued when rates were low now trade well below par. Buying them back at, say, 94 looks like retiring 100 of debt for 94 of cash, and the accounts agree: the difference goes through the income statement as a gain on extinguishment. But the issuer is not retiring 100 of cash today. It is retiring a stream of cheap coupons and a principal payment three years away, and it has to pay for that today with money that costs something. Whether the trade is good depends on the rate at which that stream is worth more than its price, not on the distance to par.
| Item | Value |
|---|---|
| Bond outstanding, EUR million | 500.0 |
| Coupon, annual | 1.25% |
| Remaining life, years, tender settled on a coupon date | 3 |
| Secondary market yield of the bond | 3.90% |
| Tender premium over the market price, points | 1.25 |
| Share of the bond tendered and accepted | 60% |
| Dealer-manager and other fees, points | 0.15 |
| All-in cost of a new three-year bond, concession and fees included | 4.15% |
| Yield on surplus cash | 2.50% |
The all-in cost of the new bond is above the secondary yield of the old one because a new issue pays a concession and fees; both are worked in how to calculate the all-in cost of a bond issue.
Market price = PV of 1.25 a year for three years and 100 at maturity, at 3.90% = 92.63
Tender price = 92.63 + 1.25 = 93.88; with 0.15 of fees the issuer pays 94.03 a bond
Tender yield = the rate at which the bond's cash flows are worth 94.03 = 3.38%
Accounting gain = 300.0 × (100 − 93.88 − 0.15) / 100 = EUR 17.90 million
Value created = PV of the retired flows at the funding rate − 94.03, per 100 of face
Excel: =PV(Funding,3,-1.25,-100)-TenderPrice-Fees per 100; =RATE(3,1.25,-(TenderPrice+Fees),100) for the tender yield
The tender buys EUR 300.0 million of face for EUR 281.65 million plus EUR 0.45 million of fees, and leaves EUR 200.0 million outstanding. The gain assumes the bond is carried at par; a bond issued at a discount or with capitalised issue costs would show a slightly smaller gain. The gain is the same whichever way the issuer finds the cash. The value is not.
| Funding | Rate | PV of retired flows, per 100 | Value per 100 | Value, EUR m | Accounting gain, EUR m |
|---|---|---|---|---|---|
| New three-year bond | 4.15% | 91.98 | −2.06 | −6.17 | 17.90 |
| Surplus cash | 2.50% | 96.43 | 2.40 | 7.19 | 17.90 |
Refinanced, the trade replaces 1.25 per cent debt with 4.15 per cent debt. The issuer saves EUR 3.75 million a year of old coupons but pays EUR 11.71 million on the EUR 282.10 million of new debt, EUR 7.96 million a year more, in exchange for repaying EUR 17.90 million less principal in three years. Discounted, the extra interest wins, and the "gain" is a loss of EUR 6.17 million: interest expense moved forward and reported as profit today.
Funded from cash, the comparison flips. The cash would have earned 2.50 per cent; retiring the bond earns the 3.38 per cent tender yield, 88 basis points more. The value created is EUR 7.19 million. This is the case where a below-par buyback genuinely works: an issuer with surplus liquidity, buying back its own cheap debt at a yield above what its deposits earn. The liquidity it gives up is the real cost, and it belongs in the decision. Pre-funding a maturity is the opposite trade, with its own carry, worked in how much negative carry pre-funding a bond maturity costs.
The rule: a buyback creates value when the tender yield, fees included, is above the funding rate. Here 3.38 per cent against 4.15 per cent is minus 77 basis points; against 2.50 per cent it is plus 88.
| Premium (tender price, yield) | Fund at 2.50% | 3.50% | 3.90% | 4.15% |
|---|---|---|---|---|
| 0.50 (93.13, 3.65%) | 9.44 | 1.24 | −1.95 | −3.92 |
| 1.25 (93.88, 3.38%) | 7.19 | −1.01 | −4.20 | −6.17 |
| 2.00 (94.63, 3.10%) | 4.94 | −3.26 | −6.45 | −8.42 |
| 3.00 (95.63, 2.73%) | 1.94 | −6.26 | −9.45 | −11.42 |
Even funded at the bond's own secondary yield of 3.90 per cent, the tender loses value: the premium and the fees are a transfer to the holders who tender. The break-even tender price is 91.83 if the issuer refinances and 96.28 if it uses cash. Every point of premium paid to get holders in costs EUR 3.00 million on this size.
Presenting the EUR 17.90 million gain as the case for the buyback. The gain measures the distance between the bond's price and par, which is set by where rates have gone since issue; it says nothing about whether retiring the bond today is cheaper than leaving it in place. A refinanced buyback of low-coupon debt at a premium almost always books a gain and destroys value at the same time. In some jurisdictions the gain is also taxable as income from the cancellation of debt, which makes the refinanced case worse. Compute the tender yield, fees included, and set it beside the funding rate before anyone looks at the income statement.
The book prices what an issuer pays to raise money, concession and fees included, with the cost model in the free workbooks for the book's issuer.
A below-par buyback is a decision about rates, not about par. Retiring a 1.25 per cent bond at a 3.38 per cent tender yield creates value against 2.50 per cent cash and destroys it against 4.15 per cent new debt, while the same EUR 17.90 million gain appears in the accounts either way.
To use surplus cash, reduce gross debt or capture a discount. The accounting gain is not proof of value: on the illustrative EUR 300.0 million tender at 93.88 the gain is EUR 17.90 million whichever way it is funded, but the value is minus EUR 6.17 million when refinanced at 4.15 per cent and plus EUR 7.19 million when funded from cash at 2.50 per cent.
Usually as a fixed price or a fixed spread over a reference yield, set at a premium to the secondary price to bring holders in, sometimes with an early tender payment. In the illustrative case the bond trades at 92.63 on a 3.90 per cent yield and the tender is at 93.88, a 1.25 point premium that costs the issuer EUR 3.75 million on EUR 300.0 million.
The present value of the bond's remaining cash flows at the issuer's funding rate, less fees. For a 1.25 per cent bond with three years left and 0.15 of fees, it is 91.83 when funded with new debt at 4.15 per cent and 96.28 when funded from cash earning 2.50 per cent. A tender above the break-even transfers value to the holders.
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.
Get the book on Amazon →Free companion files
Also on Amazon UK · Amazon Germany · Amazon France · Amazon Canada
Reading guide: corporate finance, valuation and markets → · All 1614 articles →
If this book helped, or didn’t, a few lines on Amazon are worth more than they look: they are what the next reader goes on. Write a review. The workbook stays free either way.