Bond Pricing & Yield to Maturity
A bond’s price is the present value of its coupons plus its face value. The yield to maturity (YTM) is the single discount rate that makes that present value equal the market price, and it is the standard measure of its yield. Price and yield move in opposite directions.
Try it yourself
A bond's price is the present value of its coupons plus face, discounted at the market yield. Move the yield and watch price trace the downward-sloping, convex curve — price moves inversely to yield.
Face value fixed at 100, so price reads as a percent of face.
Why it matters
Buying a bond is buying a fixed stream of future dollars. If the market demands a higher return (yield), it will only pay a lower price for that fixed stream. Coupon above yield gives a premium bond, coupon below yield gives a discount bond, coupon equal to yield gives par.
Formulas
Worked examples
3-year bond, $100 face, 6% annual coupon. Price it at a yield of 5%, then at 6%.
At 5%: P = 6/1.05 + 6/1.05^2 + 106/1.05^3 = $102.72, a premium (coupon above yield). At 6%: P = $100.00, exactly par (coupon equals yield).
Common mistakes
- ✗Bond prices and yields move together. They move inversely by construction.
- ✗The yield to maturity is a guaranteed return. YTM is the discount rate that equates the price to the present value of the bond’s promised cash flows. The realised return can differ if you sell before maturity or reinvest coupons at a different rate.
Revision bullets
- •Price equals present value of coupons plus face value
- •YTM is the discount rate that matches price
- •Price and yield move inversely
- •Coupon vs yield sets premium, par, or discount
Quick check
A bond trades above its face value (a premium). This means
Connected topics
Sources
- Mishkin (2018), Ch. 4Mishkin, F. S. The Economics of Money, Banking, and Financial Markets. 12th ed. Pearson, 2018. ISBN 978-1-292-26885-9.Develops bond pricing and yield to maturity for the four main credit-market instruments.