A 5% coupon bond trading at $92 tells you instantly the market demands more than 5%. Bond prices and yields move inversely, and the magnitude depends on coupon, maturity, and convexity.
A fixed-rate bond's price is the present value of its remaining cash flows, each discounted at the yield to maturity (YTM).
PMT is the periodic coupon, r the periodic YTM, N the total periods, FV par. For semiannual bonds, halve the annual coupon rate and YTM, then double the years to get N.
KEY: YTM is the single discount rate that equates PV of all promised cash flows to the bond's full price. You earn the YTM as your realized return only if you hold to maturity, every payment arrives as promised, and coupons reinvest at the YTM.
The table below shows where a fixed-rate bond's price sits against par on a coupon date, based on its coupon rate versus its yield-to-maturity.
Common mistakes
- Forgetting to halve coupon and yield for semiannual bonds. A 6% semiannual coupon pays $30 per period discounted at YTM/2 over 2 × years periods. Trap: discounting $60 once a year at the annual YTM.
- Confusing full and flat prices. Buyers pay full (flat + accrued); quotes are flat. Trap: a question asks what the buyer pays and the candidate selects the flat price.
- Reversing price/yield direction. Yields up, prices down. Trap: "YTM rose from 5% to 6%, so price increased."
Bottom line
- Bond price = PV of coupons + PV of par, each discounted at the periodic YTM
- Price and yield are inversely related and the curve is convex; equal-size yield moves produce unequal price changes
- On a coupon date: coupon > YTM = premium; coupon = YTM = par; coupon < YTM = discount
- At the same YTM, longer maturity (generally) and lower coupon amplify percentage price sensitivity; a zero-coupon bond is the most sensitive of comparable bonds
Exam shortcut
For premium/par/discount on a coupon date: compare coupon rate to YTM, no math needed. For semiannual bonds: halve the coupon rate, halve the YTM, double the years, then apply the standard PV formula. For between-coupon pricing: compute PV at the last coupon date, multiply by (1 + r)^(t/T) for full price, then subtract AI = (t/T) × PMT for flat.
The full lesson (about 3,189 words, 21 min read) adds 6 worked examples, all 7 common mistakes, a self-check, free in the app.
Learning objectives
- bond valuation prices and yields
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