To value a bond, add two present values: the discounted stream of coupon payments plus the discounted face value you receive at maturity, both discounted at the bond’s yield to maturity. Learning how to value a bond comes down to gathering four inputs, plugging them into a present value formula, and interpreting the result against the market. Once the mechanics click, you can price a plain coupon bond, a zero-coupon bond, or a callable bond using variations of the same equation.
The Four Inputs
Every bond valuation starts with the same four numbers.
Face value is the principal the issuer repays at maturity, also called par value. Corporate bonds almost always carry a $1,000 face value, and that figure is the standard reference point for pricing.
Coupon rate is the annual interest rate the issuer promises, expressed as a percentage of face value. A 6% coupon on a $1,000 bond means $60 per year. In the U.S., most bonds split that into two semi-annual payments, so a 6% coupon pays $30 every six months.1TreasuryDirect. Understanding Pricing and Interest Rates Treasury notes and bonds follow the same semi-annual convention.2eCFR. 31 CFR 356.30 – When Does the Treasury Pay Principal and Interest on Securities
Maturity is when the issuer must return your principal. The time remaining determines how many payment periods you’ll discount.
Yield to maturity (YTM) is the discount rate. It represents the total annual return you’d earn if you bought the bond at its current price and held it to maturity. YTM reflects prevailing interest rates, the issuer’s creditworthiness, and market risk appetite. When people quote “the yield” on a bond, they usually mean YTM.
One related term: a basis point is one-hundredth of a percentage point (0.01%). Yields quoted in basis points are common, so a 50 basis point move takes a rate from 3.00% to 3.50%.
The Bond Valuation Formula
A coupon-paying bond delivers two types of cash flows: a stream of equal interest payments, which is an ordinary annuity, and a single lump-sum repayment of principal at the end. Calculate the present value of each separately, then add them. The underlying logic is the time value of money. A dollar received years from now is worth less than a dollar today, so future payments are discounted at the YTM to find their present worth.
Present Value of the Coupon Payments
The coupon stream is an ordinary annuity. Its present value is:
PV of coupons = PMT × [(1 − (1 + r)−n) / r]
PMT is the dollar amount of each coupon payment. r is the YTM per period (semi-annual for most U.S. bonds). n is the total number of periods.
Take a bond with a $1,000 face value, a 6% coupon rate, 5 years to maturity, and a 5% YTM:
- PMT: $1,000 × 6% ÷ 2 = $30 per semi-annual period
- r: 5% ÷ 2 = 2.5%, or 0.025
- n: 5 years × 2 = 10 periods
Plugging in: $30 × [(1 − (1.025)−10) / 0.025] = $30 × 8.7521 = $262.56. That’s the present value of all ten future coupon payments.
Present Value of the Face Value
The principal repayment is a single lump sum, discounted with the basic present value formula:
PV of face value = FV / (1 + r)n
Using the same inputs: $1,000 / (1.025)10 = $1,000 / 1.2801 = $781.20.
Add the Two Components
The bond’s value is the sum: $262.56 + $781.20 = $1,043.76.
The result matches what you’d expect. A 6% coupon beats the 5% market rate, so the bond trades at a premium of roughly $44 above par. If the YTM were 7% instead, the same bond would price below $1,000, reflecting its coupon disadvantage. The formula is identical in both cases; only the discount rate changes.
Valuing a Zero-Coupon Bond
Zero-coupon bonds, including U.S. Treasury STRIPS, pay no periodic interest. They’re issued at a deep discount, and the entire return comes from the difference between purchase price and the face value received at maturity. Drop the annuity component:
Price = FV / (1 + r)n
Consider a 10-year zero-coupon bond with a $1,000 face value and a 3% YTM, compounded semi-annually. The semi-annual rate is 1.5% and the number of periods is 20:
Price = $1,000 / (1.015)20 = $1,000 / 1.3469 = $742.47
You’d pay about $742 today and receive $1,000 in ten years. The $258 spread is your return. Because there are no coupon payments to cushion price movements, zero-coupon bonds are far more sensitive to interest rate changes than coupon bonds of the same maturity.
Valuing a Callable Bond
A callable bond gives the issuer the right to redeem it before maturity at a specified call price. Issuers exercise the call when rates drop far enough to make refinancing worthwhile, so investors risk losing a high-coupon bond precisely when they’d most want to keep it.
For callable bonds, substitute the first call date for the maturity date and the call price for the face value:
Price = PMT × [(1 − (1 + r)−n) / r] + Call Price / (1 + r)n
Here n is the number of periods until the first call date, and the call price replaces face value in the lump-sum term. The discount rate that makes this equation balance against the market price is the yield to call (YTC).
Investors compare YTC to YTM and focus on whichever is lower. That worst-case figure is called yield to worst, and it represents the minimum return you can expect assuming the issuer acts in its own interest. When YTC sits below YTM, the issuer has a strong incentive to call, so YTC becomes the more realistic measure of your expected return.
Price and Yield Move in Opposite Directions
The inverse relationship between price and yield is the single most important concept in bond investing, and it also serves as a sanity check on any valuation. When market rates rise, existing bonds with lower fixed coupons become less attractive, so their prices fall until the effective yield matches the new market rate. When rates drop, those same coupons look generous, and the price climbs.
Three pricing scenarios follow:
- At par ($1,000). Coupon rate and YTM are identical. The bond pays exactly the market rate, so there’s no reason to deviate from face value.
- At a premium (above $1,000). Coupon rate exceeds YTM. Investors pay extra for above-market fixed payments.
- At a discount (below $1,000). Coupon rate falls short of YTM. The price drops below par, and the built-in gain at maturity makes up the difference.
Check the scenario before you finalize your answer. If the coupon rate is higher than the YTM and your formula returns a price below $1,000, something went wrong.
Clean Price vs. Dirty Price
The valuation formula gives you the dirty price, or full price: the total economic value of the bond, including interest that has accrued since the last coupon date. Bonds quoted on trading screens or in the financial press show the clean price, which strips out that accrued interest. The distinction matters because what you actually pay at settlement is the dirty price.
Accrued interest compensates the seller for holding the bond through part of a coupon period without receiving a payment:
Accrued interest = (days since last coupon / days in coupon period) × coupon payment
Corporate bonds typically use a 30/360 day-count convention, treating each month as 30 days and the year as 360. Treasury bonds use actual/actual. The convention is specified in the bond’s terms.
When you buy between coupon dates, you pay the clean price plus accrued interest. On the next coupon date, you receive the full coupon payment, which reimburses you for the accrued portion you advanced to the seller.
How the Value Changes When Rates Move: Duration
Knowing a bond’s value at one point in time is useful. Knowing how much that value will change when rates move is often more useful. Duration is the tool for that.
Macaulay Duration
Macaulay duration is the weighted average time until you receive the bond’s cash flows, with each payment weighted by its present value as a proportion of total price. It’s expressed in years. A five-year coupon bond has a Macaulay duration shorter than five years because the coupon payments pull the weighted average forward. A zero-coupon bond’s Macaulay duration equals its maturity exactly, since there’s only one cash flow.
Modified Duration
Modified duration adjusts Macaulay duration to estimate the percentage price change for a given yield change:
Modified duration = Macaulay duration / (1 + YTM per period)
The result tells you the approximate percentage price change for a 100 basis point move in rates. A bond with a modified duration of 4.5 would drop roughly 4.5% if yields rose one percentage point, and gain about 4.5% if yields fell by the same amount.
The estimate works well for small yield changes. For larger moves, the price-yield relationship curves rather than staying linear. That curvature is called convexity, and it refines the duration estimate when rates move significantly.
Doing It in a Spreadsheet
Running the present value formulas by hand builds understanding, but most valuations happen in a spreadsheet. Excel’s PRICE function returns the clean price per $100 of face value and handles settlement dates, day-count conventions, and coupon frequencies automatically.3Microsoft. PRICE Function The syntax is:
PRICE(settlement, maturity, rate, yld, redemption, frequency, [basis])
Rate is the annual coupon rate, yld is the YTM, redemption is the amount per $100 face value at maturity (typically 100), and frequency is 1 for annual, 2 for semi-annual, or 4 for quarterly. The optional basis argument controls the day-count convention: 0 for the 30/360 standard common in corporate bonds, 1 for the actual/actual used by Treasuries.
The companion YIELD function works in reverse. Given a bond’s current price, it returns the YTM. Financial calculators from HP and Texas Instruments have equivalent time value of money functions. Brokerage platforms display calculated values as well, but running the math yourself once or twice is what makes those screen numbers meaningful.