Bond anatomy and the semi-annual convention
◈ 7 cardsPar, coupon rate, coupon payment, term, yield — and the three Excel inputs a Canadian bond’s terms become: pmt = coupon × par ÷ 2, nper = years × 2, rate = yield ÷ 2.
What the certificate says
A bond is a loan cut into tradeable pieces. Its terms are fixed at issue and printed on the certificate (today, in the trust deed — Lesson 9.3):
- Par (face, principal, maturity value): what the issuer repays at maturity — $1,000 is the standard unit.
- Coupon rate: the annual interest rate on par, fixed for life. A 5.2 % bond pays 5.2 % of par a year, whatever the market does later.
- Coupon payment: the dollars actually paid. Canadian bonds pay semi-annually, so each payment is half a year's interest.
- Term to maturity: the years until par is repaid.
What the certificate does not say is the yield to maturity — the return the market requires today. Yield moves every day with the Bank of Canada, inflation and the issuer's credit; the coupon never moves. When yield rises above the coupon the bond trades below par; when it falls below, above par. Module 10 prices that; this lesson reads the inputs.
Worked example — Prairie Grid Energy 5.2 % due 2036
Prairie Grid Energy has a 5.2 % bond, $1,000 par, 10 years to maturity; the market yield for its credit is 6 %. Excel's PV needs three per-period inputs, and the semi-annual convention halves or doubles each one:
| Term on the certificate | Excel input | Conversion | Value |
|---|---|---|---|
| Coupon 5.2 % on $1,000, paid twice a year | pmt | 0.052 × 1,000 ÷ 2 | 26 |
| 10 years to maturity | nper | 10 × 2 | 20 |
| Yield 6 % | rate | 0.06 ÷ 2 | 0.03 |
=0.052*1000/2 → 26; =10*2 → 20; =0.06/2 → 0.03. All three or none — a halved rate with an unhalved coupon is the error that costs the mark. The fourth input, fv, is par: 1,000, repaid with the last coupon.
Three things that look alike
Coupon rate (5.2 %) is a contract term. Coupon payment ($26 twice a year, $52 a year) is dollars. Yield (6 %) is the market's price of the bond's risk and time — never the coupon, even on the day the bond is issued at par, when the two merely happen to be equal. A question that offers "the coupon rate" as the definition of yield is offering the trap.
Recompute
A 4.5 % bond, $1,000 par, 7 years, market yield 5 %: =0.045*1000/2 = 22.50; =7*2 = 14; =0.05/2 = 0.025. A $5,000 par holding of the same bond: pmt 112.50, the other two unchanged — par scales the payment, not the periods or the rate.