Bond Valuation Calculator
Calculate the fair value of a bond from its face value, coupon rate, years to maturity, current market rate, and payment frequency. Compare the fair value to the current price to decide whether the bond is trading at a premium, discount, or par.
What Is Bond Valuation?
Bond valuation is the process of determining the fair price of a bond — the present value of all future cash flows the bond will pay. Those cash flows are the coupon payments (periodic interest) and the return of face value at maturity.
A bond's fair value moves in the opposite direction of interest rates. When market rates rise above the bond's coupon rate, the bond's fixed coupon payments become less attractive, so the bond's price falls — trading at a discount. When market rates fall below the coupon rate, the bond's payments become more attractive, so the price rises — trading at a premium.
Bond Valuation Formula
The fair value of a bond is the sum of the present values of all coupon payments plus the present value of the face value:
Bond Price = Σ [C ÷ (1 + r/2)^t] + [F ÷ (1 + r/2)^n]
- C — coupon payment per period (= Face Value × Coupon Rate ÷ Frequency)
- F — face value (par value, returned at maturity)
- r — annual market rate (yield to maturity)
- n — total number of payment periods (= years × frequency)
The formula for the fair value with semi-annual payments uses r/2 as the per-period discount rate and n = 2 × years as the number of periods.
Worked Example
A bond has a $1,000 face value, 6% annual coupon, 10 years to maturity, and the market rate is 8%:
Semi-annual coupon payment = $1,000 × 6% ÷ 2 = $30 per period
Number of periods = 10 years × 2 = 20 periods
Per-period discount rate = 8% ÷ 2 = 4%
PV of coupons = $30 × [(1 − (1.04)^−20) ÷ 0.04] = $407.65
PV of face value = $1,000 ÷ (1.04)^20 = $456.39
Fair value = $407.65 + $456.39 = $864.04
The bond trades at a discount because the 6% coupon is below the 8% market rate — investors demand a higher return than the coupon provides, so the price falls.
Premium, Discount, or Par?
- Discount (coupon < market rate) — the bond's coupon is below what investors can get elsewhere, so the price falls below face value.
- Par (coupon = market rate) — the bond's coupon matches the market rate, so the price equals face value.
- Premium (coupon > market rate) — the bond's coupon exceeds the market rate, so investors pay extra to get those higher coupon payments.
As the bond approaches maturity, its price converges toward face value — this is called "pull-to-par." A discount bond's price rises toward par; a premium bond's price falls toward par.
Frequently Asked Questions
What is the difference between bond price and face value?
Face value (or par value) is the amount the bond will pay at maturity — typically $1,000 for US corporate bonds. The bond price is what the bond currently trades for on the secondary market, which can be above (premium) or below (discount) face value. Only at maturity does the price equal face value.
What is yield to maturity (YTM)?
YTM is the total return an investor earns if they buy the bond at its current price and hold it to maturity. It accounts for both coupon payments and the difference between the purchase price and face value. YTM is the single number that fully describes a bond's return — when people say "bond yields," they usually mean YTM.
Why do bond prices fall when interest rates rise?
Because existing bonds have fixed coupon payments. If new bonds are issued at higher rates, older bonds become less attractive — investors can get better returns elsewhere. To sell the older bond, the price must drop until its yield matches the market. This is why bond prices and interest rates have an inverse relationship. Longer maturity means greater sensitivity to rate changes.
What is duration?
Duration measures a bond's sensitivity to interest rate changes. A bond with duration of 5 years will change in price by about 5% for every 1% change in interest rates. Higher duration = greater price sensitivity. Duration is a more useful risk measure than maturity because it accounts for coupon payments as well as the time to maturity.
What is the current yield?
Current yield is the annual coupon payment divided by the current bond price. It is a quick way to compare the cash income from a bond to its price. But current yield ignores the gain or loss from the price moving toward face value at maturity — YTM is the more complete measure of return.
What is the difference between coupon rate and yield?
The coupon rate is fixed at issuance — it determines the actual cash payment each year. The yield is the return the investor earns at the current price, which changes as bond prices move. A bond with a 6% coupon bought at $864 has a YTM of 8% — the higher yield comes from buying at a discount to face value. The lower the price, the higher the yield.