The reoffer spread is what investors earn. The issuer pays that plus its fees and expenses, spread over the life of the bond at the annuity factor, not by the number of years.
Deduct the underwriting commission and the issue expenses from the reoffer price, then solve for the yield at which the bond's coupons and redemption discount back to those net proceeds. On the Ardennes Industries seven-year bond in Capital Markets, 47.4 basis points of upfront costs take the issuer's cost from a reoffer yield of 4.32 per cent to an all-in yield of 4.40 per cent, or mid-swaps plus 130.04 basis points: 8.04 basis points a year on top of the 122 the market saw.
Worked in full in Capital Markets by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
The reoffer spread is what investors earn. The all-in cost is what the issuer pays, and it is the right number to compare with a loan, a private placement or a bond of a different tenor, because each comes with a different mix of upfront and running costs. The conversion is one division, provided it is done with the annuity factor and not by dividing by the number of years.
| Item | EUR | bp of size |
|---|---|---|
| Underwriting commission | 1,750,000 | 35.0 |
| Legal fees | 285,000 | 5.7 |
| Rating agency fees | 195,000 | 3.9 |
| Listing and paying agent | 65,000 | 1.3 |
| Roadshow | 75,000 | 1.5 |
| Upfront costs | 2,370,000 | 47.4 |
The bond pays a 4.25 per cent annual coupon and was reoffered at mid-swaps of 3.10 per cent plus 122 basis points, a yield of 4.32 per cent and a price of 99.5848. The fair value on the issuer's own curve, by linear interpolation, is 117.81, so the new issue concession is 4.19 basis points.
Net price = reoffer price − commission − expenses (per 100 nominal)
All-in yield = the yield at which the bond's cash flows are worth the net price
Shortcut: running cost in bp = upfront cost in bp ÷ annuity factor at the reoffer yield
In Excel: =YIELD(Settle,Maturity,4.25%,99.1108,100,1,0) or, with a cash-flow column, =IRR(C2:C9) where C2 is minus the net proceeds. The annuity factor is =(1-(1+y)^-7)/y.
Step 1, the net price. 99.5848 − 0.35 − 0.124 = 99.1108. Gross proceeds are EUR 497,923,900; net proceeds EUR 495,553,900.
Step 2, solve for the yield. The yield at which seven coupons of 4.25 and a redemption at 100 are worth 99.1108 is 4.40 per cent, mid-swaps plus 130.04 basis points: 8.04 basis points a year more than the reoffer yield.
Step 3, check with the shortcut. The annuity factor at 4.32 per cent over seven years is 5.9317. The commission is 35 ÷ 5.9317 = 5.90 basis points a year, the expenses 12.4 ÷ 5.9317 = 2.09, together 7.99. Added to the reoffer spread that gives 129.99, within a twentieth of a basis point of the exact answer.
| Component | bp a year |
|---|---|
| Fair value on the issuer's curve (linear) | 117.81 |
| New issue concession | 4.19 |
| Commission and expenses, running | 8.04 |
| All-in spread | 130.04 |
Of the 12.22 basis points the issuer pays above its own secondary curve, 66 per cent is fees and expenses and the rest is the concession. In euros the three lines are EUR 1,750,000 of commission, 620,000 of expenses and a concession worth 1,241,953 in present value: EUR 3,611,953 in all, or 72.24 basis points of the nominal amount.
The same upfront cost is spread over fewer years on a shorter bond, so it weighs more per year.
| Tenor, years | Annuity factor | Running cost, bp | Exact add-on, bp | Fees ÷ tenor, bp |
|---|---|---|---|---|
| 3 | 2.7583 | 17.18 | 17.24 | 15.80 |
| 5 | 4.4121 | 10.74 | 10.78 | 9.48 |
| 7 | 5.9317 | 7.99 | 8.01 | 6.77 |
| 10 | 7.9832 | 5.94 | 5.95 | 4.74 |
| 15 | 10.8737 | 4.36 | 4.37 | 3.16 |
The exact add-on in this table assumes a bond priced at par; the seven-year figure differs slightly from the 8.04 above because the actual bond was issued below par. Commission is the other lever: at 20 basis points the all-in spread would be 127.49, at 50 basis points 132.59. Each 15 basis points of commission on a seven-year bond is worth about 2.5 basis points a year.
Compare like with like. A five-year bank loan with a 50 basis point arrangement fee and a ten-year bond with 47.4 basis points of costs are not comparable on their margins. Convert each upfront cost at its own tenor's annuity factor, or solve each all-in yield, before ranking them.
The common mistake is to spread the fees in a straight line: 47.4 divided by seven years is 6.77 basis points, against the correct 7.99. Dividing by the tenor ignores that the fee is paid today while the coupon it is compared against is paid over seven years, so it understates the cost by 1.22 basis points a year here, and by a larger proportion on longer bonds: at fifteen years the straight line gives 3.16 against 4.36. The second mistake is to leave the concession out: it appears on no invoice, but the issuer pays it in coupon for the life of the bond.
All-in cost = the yield on net proceeds; to a close approximation, reoffer spread plus upfront costs divided by the annuity factor. On the Ardennes bond that is 122 + 7.99, or 130 basis points over mid-swaps. The cost workbook in the free companion files for Capital Markets builds the full bill from the fee letter, the invoices and the concession, and how to calculate a new issue concession shows where the 4.19 basis points come from and why they could have been minus 0.78.
Divide the fee in basis points by the annuity factor at the issue yield over the bond's life. On a seven-year bond at 4.32 per cent the factor is 5.9317, so a 35 basis point commission costs 5.90 basis points a year and 47.4 basis points of total upfront costs 7.99.
Because the fee is paid today and the coupon is paid over time, so the straight line ignores discounting. On a seven-year bond it gives 6.77 basis points a year against the correct 7.99, and on a fifteen-year bond 3.16 against 4.36.
The coupon or reoffer yield, the underwriting commission, the invoiced expenses for legal, rating, listing and roadshow, and economically the new issue concession. On the Ardennes bond the all-in spread of 130.04 basis points is 117.81 of fair value, 4.19 of concession and 8.04 of fees and expenses.
The full cost of the issue, with the fee, the expenses and the concession, is worked in chapters 6 to 8 of 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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