The make-whole redemption price worked on one euro bond, with the premium over the market price and the refinancing test it almost always fails.
A make-whole call price is the greater of par and the present value of the bond's remaining coupons and principal, discounted at the yield of a reference government bond plus a fixed spread written into the terms. On an illustrative EUR 500 million bond with a 3.875 per cent coupon and four years left, a Bund yield of 2.30 per cent plus 20 basis points gives a price of 105.173, a premium of EUR 25,863,573 over par. That is 2.676 points above where the bond trades.
Worked in full in Capital Markets by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
An investment-grade issuer sold a seven-year euro bond three years ago and wants to redeem it early. The terms let it do so at any time at the make-whole amount, plus accrued interest. Every market level below is illustrative.
| Term | Value |
|---|---|
| Nominal outstanding (EUR) | 500,000,000 |
| Coupon, annual | 3.875% |
| Years to maturity, redemption on a coupon date | 4 |
| Reference Bund yield, same remaining life | 2.30% |
| Make-whole spread | 20 bp |
| Discount rate | 2.50% |
| Yield at which the bond trades | 3.20% |
The clause, in its usual form: the redemption amount is the higher of 100 per cent of the principal and the sum of the present values of the remaining scheduled payments, discounted annually at the reference bond rate plus the spread, in each case with accrued interest added. The reference bond is chosen by a calculation agent, normally the government bond closest in maturity, a few business days before the redemption date.
Make-whole price = max(100, Σ CFt / (1 + Bund + spread)t)
Discount rate = 2.30% + 0.20% = 2.50%
Excel, with the dates and cash flows laid out: =MAX(100,PV(2.5%,4,-3.875,-100))
| Year | Cash flow | Discount factor | Present value |
|---|---|---|---|
| 1 | 3.875 | 0.975610 | 3.7805 |
| 2 | 3.875 | 0.951814 | 3.6883 |
| 3 | 3.875 | 0.928599 | 3.5983 |
| 4 | 103.875 | 0.905951 | 94.1056 |
| Total | 105.1727 |
The present value exceeds 100, so the floor does not bind and the price is 105.173. On the nominal outstanding the issuer pays 525,863,573 to retire 500,000,000 of bonds, a premium of 25,863,573. If the redemption fell between coupon dates, the discounting would use fractional periods from the redemption date and accrued interest would be paid on top.
The bond trades at a yield of 3.20 per cent, which prices it at 102.497. The make-whole pays 2.676 points more, 13,378,134 on the issue. The reason is the discount rate: the market discounts the bond's cash flows at the issuer's own credit spread, while the clause discounts them at a government yield plus a spread that is deliberately tighter. Investors are paid as if their remaining cash flows were nearly risk-free, which is what makes them whole and makes the call expensive.
The test for the issuer follows directly. Redeeming at 105.173 and refinancing pays only if new four-year money costs less than the 2.50 per cent the clause discounts at. At an illustrative new issue yield of 3.40 per cent the coupon saving is 0.475 a year, worth 1.7489 points in present value, against a premium of 5.1727: a net loss of 17,119,261. The break-even refinancing yield is exactly 2.50 per cent, below the issuer's own curve. A make-whole is a clause that permits redemption for a reason, an acquisition, a disposal, a covenant to escape, not a refinancing option.
The same discounting logic sets a new bond's price at issue, from the other side: see how a new bond's coupon and reoffer price are set. The value of one basis point on the discount rate is the bond's DV01, worked in how to calculate the DV01 of a new bond issue.
| Reference yield | 0 bp | 15 bp | 20 bp | 30 bp | 50 bp | Premium at 20 bp, EUR |
|---|---|---|---|---|---|---|
| 1.80% | 107.940 | 107.339 | 107.139 | 106.742 | 105.954 | 35,697,457 |
| 2.30% | 105.954 | 105.367 | 105.173 | 104.785 | 104.015 | 25,863,573 |
| 2.80% | 104.015 | 103.442 | 103.252 | 102.874 | 102.122 | 16,262,306 |
| 3.30% | 102.122 | 101.563 | 101.377 | 101.008 | 100.274 | 6,887,024 |
Each 50 basis points on the reference yield moves the premium by roughly ten million euros on this issue, so the timing of the call matters as much as the spread negotiated at issue. The par floor only binds if the reference yield rises above 3.675 per cent, the coupon less the spread. Every 10 basis points of make-whole spread lowers the redemption price by about 0.39 points, so the spread is worth negotiating on the term sheet, long before any call is in view.
The issue side of the same arithmetic, from mid-swaps to reoffer price and the all-in cost of the fees, is in the free workbooks for this book.
It is the excess of the make-whole redemption price over par, paid by an issuer that redeems a bond early. It compensates investors for the coupons they lose, valued at a near risk-free discount rate. On a 3.875 per cent bond with four years left, discounted at a 2.30 per cent reference yield plus 20 basis points, the premium is 5.173 points, EUR 25,863,573 on 500 million.
Because the clause discounts at a government yield plus a small spread, while the market discounts at the issuer's own credit spread. In the worked case the market yield of 3.20 per cent prices the bond at 102.497, and the make-whole at 2.50 per cent pays 105.173. The difference, 2.676 points, is why issuers often prefer a tender offer at a premium to market instead.
Rarely to refinance: the new debt would have to cost less than the clause's discount rate, 2.50 per cent in the worked case, against a market yield of 3.20. At a 3.40 per cent new issue yield, calling and refinancing loses 17,119,261. Issuers use make-wholes to remove covenants, complete an acquisition or a disposal, or clean up a capital structure, where the premium buys something other than interest savings.
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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