Discount, par, premium and pull to par
◈ 8 cardsCompare the coupon rate with the market yield — not dollars with dollars — to predict discount, par or premium; then hold the yield still and watch the price close on par as maturity nears.
Get more, pay more
A bond's coupon is fixed; the market's required yield is not. Set them side by side and the price follows:
- Coupon rate below the yield → the bond pays less than the market requires → it must sell below par — a discount.
- Coupon rate equal to the yield → par.
- Coupon rate above the yield → investors get more than they require and pay for it → above par — a premium.
The comparison is between two rates, never between the coupon dollars and the price, and never between the price and the previous trade.
Worked example — Prairie Grid at three yields
Hold the 5.2 % coupon, 10 years, $1,000 par, and move only the market yield:
| Market yield | Excel | Price | Because |
|---|---|---|---|
| 6 % | =-PV(0.03,20,26,1000) | 940.49 | 5.2 % < 6 % → discount |
| 5.2 % | =-PV(0.026,20,26,1000) | 1,000.00 | 5.2 % = 5.2 % → par |
| 4.5 % | =-PV(0.0225,20,26,1000) | 1,055.87 | 5.2 % > 4.5 % → premium |
At par the arithmetic is exact: a bond whose coupon equals its yield is worth exactly its face, whatever the term. That is also why a new issue is priced at par — the underwriter sets the coupon equal to the yield the market wants that day.
Pull to par
Now freeze the yield at 6 % and let time pass. The discount bond, still paying 5.2 %:
| Years left | Excel | Price | Below par by |
|---|---|---|---|
| 10 | =-PV(0.03,20,26,1000) | 940.49 | 59.51 |
| 5 | =-PV(0.03,10,26,1000) | 965.88 | 34.12 |
| 1 | =-PV(0.03,2,26,1000) | 992.35 | 7.65 |
| 0 | — | 1,000.00 | 0 |
The gap closes because fewer and fewer below-market coupons remain to be compensated for. At maturity the issuer pays par, so the price must arrive there. A premium bond does the mirror: at a constant 4.5 % yield, 1,055.87 → 1,031.03 (5 years) → 1,006.77 (1 year) → 1,000. The holder of a premium bond sees the price fall toward par over the years even though nothing went wrong — the premium was the market's price for above-market coupons, and it is used up as they are paid.
Pull to par is what the current yield ignores (Lesson 10.5) and what YTM captures (Lesson 10.4): a discount bond's YTM exceeds its coupon precisely because the price climbs to par on top of the coupons.
Recompute
Prairie Grid at 7 %, 10 years: =-PV(0.035,20,26,1000) = 872.09 — a deeper discount for a wider gap. At 7 % with 3 years left: =-PV(0.035,6,26,1000) = 952.04 — the same gap, less time to matter. The rule, cold: compare the coupon rate with the required yield; the price is on the side of the difference.