Bond Valuation

A bond is a loan you make to a government or company: you pay a price today, and in exchange the issuer promises to pay you a fixed coupon(interest payment) on a regular schedule, plus return the bond's face value (also called par value) when it matures.

Bond valuation is the process of figuring out what a bond is actually worth today — its price — given those promised future payments and the return currently available on similar bonds, called the yield.

Once a bond is issued, its coupon payments are fixed — locked in at whatever rate applied when it was created. But interest rates in the broader market don't stay fixed; they move up and down over time, and new bonds keep getting issued at whatever the current going rate is. That creates a problem for anyone trying to buy or sell an existing bond partway through its life: its price can't just stay at face value forever, because the fixed coupon it pays might now be more or less attractive than what a brand-new bond of similar risk is currently offering.

Bond valuation solves this the same way Present Value solves any future cash flow problem: treat every one of the bond's remaining payments — each coupon, plus the face value at maturity — as a separate future cash flow, and discount each one back to today using the current market yield for bonds of similar risk and maturity. The bond's price is simply the sum of all those discounted payments. If the bond's fixed coupon is more generous than what new bonds are currently paying, its price gets bid up above face value to compensate; if it's less generous than current rates, its price gets pushed down below face value, so a buyer is still getting a competitive overall return either way.

This is why bond prices and yields always move in opposite directions: when market yields rise, existing bonds with lower, locked-in coupons become less attractive relative to new bonds paying the higher going rate, so their price has to fall to keep offering a competitive return — and the reverse happens when yields fall. This relationship isn't a coincidence or a market quirk; it's a direct, mechanical consequence of discounting a fixed set of payments at a higher or lower rate, exactly the same math as Present Value.

Every remaining coupon, plus the face value, discounted at the yield:

Price = Σ [Coupon / (1+y)ᵗ]  +  Face Value / (1+y)ᴺ

• Coupon — the fixed periodic interest payment (Face Value × Coupon Rate)
• y — the market yield, the return available on similar bonds today
• N — the number of coupon payments remaining until maturity

A $1,000 face value bond with a 5% annual coupon ($50 a year) and 10 years to maturity.

Market yield = 5% (matches the coupon): price = $1,000 exactly (par)
Market yield = 7%: price ≈ $859.53 (below face value)

When the yield matches the coupon rate exactly, the bond prices at exactly its face value. When market yields rise above the coupon rate, the bond's fixed 5% payments look less attractive than what's newly available, so its price falls to compensate — the same $50-a-year, $1,000-at-maturity payment stream is worth less once a buyer could get 7% elsewhere. Try the Bond Valuation Calculator to see how the coupon, maturity, or yield changes the price.