Bond quotation, accrued interest and the invoice price

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A quote is per 100 of par and excludes accrued interest — compute the accrued on the Canadian actual/365 basis (a half-year is 182.5 days), add it to the clean price, and the sum is the invoice.

Per 100, and clean

Bonds are quoted as a percentage of par — a price of 98.50 means $98.50 per $100 of face, or $985 per $1,000 bond, whatever the size of the holding. Excel's PRICE and YIELD functions (Module 10) return the same per-100 number. The quote is the clean price: it excludes the interest that has built up since the last coupon. That interest belongs to the seller, who held the bond for those days, and the buyer pays it on top — the accrued interest. Clean plus accrued is the dirty price, also called the invoice or settlement price: what actually changes hands.

$Invoice = \frac{Quote}{100} \times Par + Accrued interest$

Worked example — $100,000 of Tamarack 6 % at 98.50

Halton Dairy Co-op buys $100,000 par of Tamarack Foods' 6 % semi-annual bond, quoted at 98.50, for settlement 61 days after the last coupon date.

Clean price. =98.5/100*100000 = 98,500.00.

Accrued interest. The Canadian convention (the IIAC's actual/365, Canadian Bond method) accrues the annual coupon for the actual days elapsed over a 365-day year:

$A I = Par \times coupon rate \times \frac{days since last coupon}{365} = 100, 000 \times 0.06 \times \frac{61}{365} = 1, 002.74$

=100000*0.06*61/365. Equivalently, a semi-annual coupon of 3,000 over a half-year counted as 182.5 days: $3, 000 \times 61/182.5$ = the same 1,002.74. Notice what the convention does not do: it does not divide by the actual days in this coupon period. A 182-day period would give 1,005.49, a 184-day period 994.57 — the Canadian method gives 1,002.74 for either, because the divisor is fixed at 365.

Invoice. $98, 500.00 + 1, 002.74 = 99, 505.49$ ? No — 99,502.74: =98.5/100*100000+100000*0.06*61/365. Read the cents; the answer-only paper does.

Who pays whom

The buyer pays the accrued interest to the seller at settlement. At the next coupon date the buyer, now the holder of record, receives the full six-month coupon of 3,000 — of which 1,002.74 merely returns what was paid at settlement, and 1,997.26 is the buyer's own 121 days. The issuer pays one full coupon to whoever holds the bond that day; the accrued-interest exchange is how two investors split it fairly. Nobody at CDS or the issuer computes it — the dealer's confirmation does.

Recompute

Settle at 120 days instead: =100000*0.06*120/365 = 1,972.60; invoice 100,472.60 — the same 98.50 quote, a dirtier price. A 101.25 quote on $50,000 par: clean =101.25/100*50000 = 50,625.00; with a 5 % coupon 90 days in, accrued =50000*0.05*90/365 = 616.44, invoice 51,241.44. The quote tells you the clean price per 100; the calendar tells you the rest.