Bond Valuation Calculator
Estimate bond value using face value, coupon, yield, and years.
About the Bond Valuation
A bond is a loan you make to a government or a company. They pay you a fixed amount of interest every year — the coupon — and hand back the face value at the end. The catch is that once rates in the wider market move, your fixed coupon is suddenly worth more or less than what new bonds pay, and the price of your bond adjusts until the two are competitive. This calculator does that adjustment: it prices a bond from its face value, coupon rate, the current market yield and the years left to maturity.
How to use it
- Enter the face value — the amount repaid at maturity, usually $1,000.
- Enter the coupon rate, the fixed annual interest the bond pays.
- Enter the current market yield for bonds of similar risk and maturity.
- Enter the years remaining until maturity. The price updates as you type.
The formula
A bond is worth the present value of everything it will pay you: a stream of coupon payments, plus the face value returned at the end.
Price = C × [1 − (1 + y)−n] ÷ y + F ÷ (1 + y)n
Where C is the annual coupon payment in dollars (face value × coupon rate), y is the market yield as a decimal, n is years to maturity, and F is the face value. The first term values the coupons, the second values the lump sum at the end. Everything is discounted, because a dollar arriving in ten years is worth less than a dollar today.
Worked examples
| Face value | Coupon | Market yield | Years | Price | Trading at |
|---|---|---|---|---|---|
| $1,000 | 5% | 6% | 10 | $926.40 | a discount |
| $1,000 | 5% | 5% | 10 | $1,000.00 | par |
| $1,000 | 6% | 4% | 10 | $1,162.22 | a premium |
| $1,000 | 5% | 6% | 2 | $981.67 | a small discount |
Compare the first and last rows. Same bond, same 1% gap between coupon and yield — but the ten-year bond loses $73.60 and the two-year loses only $18.33. That is duration: the longer you are locked into a below-market coupon, the more the price has to fall to make up for it.
Common mistakes
- Entering the coupon as a dollar amount. The coupon field is a rate. A $1,000 bond paying $50 a year has a 5% coupon, not a 50.
- Confusing coupon rate with yield. The coupon is fixed the day the bond is issued and never changes. The yield is what the market demands today. When they differ, the price moves.
- Using the coupon rate as your return. If you buy at a discount, your actual return is higher than the coupon, because you also collect the gap between the price you paid and the face value at maturity.
- Forgetting that this is a clean price. Bonds are usually quoted without the interest accrued since the last payment. A broker will add that on top when you actually buy.
Terms explained
- Face value (par)
- The amount repaid at maturity. Almost always $1,000 for corporate bonds. The coupon rate is a percentage of this, not of what you paid.
- Coupon rate
- The fixed annual interest rate the issuer promises. A 5% coupon on a $1,000 bond pays $50 a year, usually as $25 twice.
- Market yield
- The return investors currently demand for lending to a borrower of this quality for this long. This is the number that moves.
- Discount / premium
- Below face value means the coupon is worse than the market offers. Above means it is better. Exactly at face value is called par.
- Yield to maturity (YTM)
- The total annualised return if you buy at today's price and hold to the end, counting both coupons and the pull back to face value.
- Duration
- How sharply the price reacts to a change in yield. Longer maturities and lower coupons mean more duration and a bumpier ride.
Common questions
- Why is the price below face value?
- Because the yield you entered is above the coupon. Nobody pays full price for a bond paying less than the market offers, so the price falls until the buyer's total return matches what they could get elsewhere.
- What happens at maturity?
- You receive the face value, regardless of what the price did in between. A bond bought at a discount pulls upward toward face value as maturity approaches — that gain is part of your return.
- Is a higher yield better?
- It means more income, but usually more risk. Yields rise when a borrower starts to look less safe, so an unusually high yield is the market pricing in a chance you do not get paid.
- How do I calculate the annual interest payment?
- Multiply the face value by the coupon rate. A $1,000 bond with a 4.5% coupon pays $45 a year. Most bonds split that into two payments of $22.50, six months apart.
- What is the difference between price and yield?
- They are two views of the same thing and always move in opposite directions. Fixing one determines the other: if the price falls, the fixed coupon becomes a larger percentage of what you paid, so the yield rises.
- Does this handle semi-annual coupons?
- This prices on an annual basis, which is the standard textbook treatment and accurate enough for comparing bonds. A semi-annual bond is worth a little more, because you receive half the coupon six months earlier and can reinvest it.
- Why did my bond fall in value when nothing went wrong?
- Almost certainly because interest rates rose. Your coupon is fixed, so when new bonds start paying more, yours has to get cheaper to stay competitive. Held to maturity you still receive the full face value.
- Is this the same as bond interest expense?
- No. Interest expense is what the issuing company records in its accounts for the cost of borrowing. This calculator takes the investor's side: what the bond is worth to someone buying it.