What it means
A bond is a loan that pays fixed interest and returns the original amount at the end. Because a dollar received in five years is worth less than a dollar today, each future payment has to be reduced, or discounted, to its value today.
Adding these discounted amounts together gives the fair price. The rate used for discounting is the yield, which is the return the market currently demands for a bond of that risk and length.
If the market yield is higher than the bond's coupon (its fixed interest rate), the bond sells below face value, at a discount. If the market yield is lower, it sells above face value, at a premium.
This explains why bond prices and interest rates move in opposite directions. When rates rise, the fixed payments of an existing bond look less attractive, so its price falls.
When rates drop, the same payments become more valuable and the price rises. Finance teams use bond valuation in several places.
Treasury departments value their own debt, investors value holdings for reporting, and corporate finance staff test what a new issue could raise. Accountants also use the same method to measure certain liabilities at fair value.
The standard method assumes the bond is paid in full and on time. For riskier issuers, the discount rate is raised to reflect the chance of default, which lowers the price.
Features like early repayment rights can also change the result.
In practice
Real-world examples
Example 1
A pension fund manager is offered a corporate bond with a 4% coupon while similar bonds yield 5%. She runs the valuation and finds the fair price is below face value. She bids only at that level, since paying face value would mean accepting a lower return than the market offers.
Example 2
A food manufacturer wants to issue five-year bonds to fund a new plant. Its treasurer values different coupon levels using the current yield for its credit rating. The analysis shows which coupon would let the bonds sell at face value, so the company raises the full amount.
Example 3
A small business owner holds a bond in her retirement account and sees its market price fall after central bank rates rise. Valuation shows the drop is the expected result of a higher discount rate, not a sign that the issuer is in trouble. She decides to hold the bond to maturity and collect every payment in full.
Think of it
Bond valuation is like calculating what future rent payments are worth today. You're finding the present value of a series of cash flows.
Formula
Calculation
Bond price = Coupon / (1 + y) + Coupon / (1 + y)^2 + ... + (Coupon + Face value) / (1 + y)^n, where y is the market yield and n is the number of years.
Suppose a bond has a face value of $1,000, pays a 6% annual coupon and has two years left. The coupon is 1,000 x 0.06 = $60 a year. The market yield is 5%.
Year 1 payment: 60 / 1.05 = $57.14. Year 2 payment plus face value: 1,060 / 1.1025 = $961.45.
Price = 57.14 + 961.45 = $1,018.59. The bond trades at a premium because its coupon is higher than the market yield.Case study
Seen in the real world
Calder Valley Utilities is a fictional company that issued $20,000,000 of bonds paying a fixed 5% coupon. A year later, market yields for similar companies rise to 7%. The finance team revalues the bonds to report the fair value of its debt.
The valuation shows the bonds are now worth less than face value, because new investors could earn 7% elsewhere. The gap between the old price and the new price is the market's way of adjusting a 5% coupon to a 7% world. This illustrative example highlights an important point for managers: the company still owes the full $20,000,000, so the lower market value does not reduce what it must repay. It does, however, matter if the company plans to buy the bonds back, which would now be cheaper.
The treasurer also uses the exercise to test the opposite scenario. If yields later fall below the coupon, the bonds would be worth more than face value, and buying them back would cost the company a premium. Running both cases helps the board decide whether to hold the debt or refinance it, and the numbers come from one simple present value model.
Watch out
Common mistakes
- Believing a bond is always worth its face value until maturity. Its market price moves with yields and can sit above or below face value for years.
- Using the coupon rate to discount the payments. The correct rate is the current market yield, which reflects today's required return.
- Ignoring credit risk. A weaker issuer needs a higher discount rate, which lowers the value even if the promised payments are identical.
Questions
People also ask
Why does a bond price fall when rates rise?
Because new bonds pay more, so the fixed payments of the older bond are worth less when discounted at the higher rate.
What is the difference between yield and coupon?
The coupon is the fixed interest set when the bond is issued, while the yield is the return the market requires today.
Does valuation change what the issuer owes?
No, the issuer still owes the face value at maturity, and the valuation only changes the market price investors would pay.
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