Bond Price Calculator
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Bond Valuation Results
How to Calculate Bond Price with Coupon Rate
Valuing a bond is a critical skill for fixed-income investors. Unlike stocks, where valuation is often subjective, bond pricing is based on a mathematical formula that discounts future cash flows to their present value. This Bond Price Calculator helps you determine the fair market value of a bond by considering its face value, coupon rate, yield to maturity (YTM), and time remaining until maturity.
Understanding the Core Variables
Before using the calculator, it is essential to understand the specific inputs required for the bond pricing formula:
- Face Value (Par Value): The amount the bond issuer promises to pay back at maturity. Typically, this is $1,000 or $100 for corporate and government bonds.
- Annual Coupon Rate: The interest rate the bond pays annually based on its face value. For example, a 5% coupon on a $1,000 bond results in $50 of income per year.
- Yield to Maturity (YTM): The total return anticipated on the bond if it is held until it matures. This acts as the discount rate in the calculation, reflecting the current market interest rate for similar risk bonds.
- Years to Maturity: The length of time remaining until the bond's principal is repaid.
- Frequency: How often interest payments are made. Most US bonds pay semi-annually (twice a year), while some European bonds pay annually.
The Bond Pricing Formula
The price of a bond is the sum of the present value (PV) of its future coupon payments and the present value of the face value repayment at maturity.
Bond Price = PV(Coupons) + PV(Face Value)
1. Present Value of Coupons (Annuity)
The coupons represent a series of fixed payments (an annuity). The formula is:
PVcoupons = C * [ (1 – (1 + r)-n) / r ]
2. Present Value of Face Value (Lump Sum)
The principal repayment is a single lump sum received at the end. The formula is:
PVface = F / (1 + r)n
Where:
C = Coupon payment per period
r = Market interest rate per period (YTM / Frequency)
n = Total number of payment periods (Years * Frequency)
F = Face Value
Example Calculation
Let's calculate the price of a standard corporate bond using these metrics:
- Face Value: $1,000
- Coupon Rate: 5% (Pays $50 per year)
- Frequency: Semi-annual (Pays $25 every 6 months)
- YTM (Market Rate): 4%
- Years to Maturity: 10 Years
Since the bond pays semi-annually, we adjust the variables:
Total Periods (n) = 10 * 2 = 20 periods
Periodic Rate (r) = 4% / 2 = 2% (0.02)
Periodic Coupon (C) = ($1,000 * 5%) / 2 = $25
Step 1: Calculate PV of Coupons
PV = 25 * [ (1 – (1.02)-20) / 0.02 ]
PV = 25 * 16.3514 = $408.79
Step 2: Calculate PV of Face Value
PV = 1,000 / (1.02)20
PV = 1,000 / 1.4859 = $672.97
Step 3: Total Bond Price
Price = $408.79 + $672.97 = $1,081.76
Because the coupon rate (5%) is higher than the market yield (4%), this bond trades at a Premium (above par value).
Premium vs. Discount vs. Par
The relationship between the coupon rate and the YTM determines the bond's status:
- Premium Bond: Coupon Rate > YTM. The price will be higher than the face value.
- Discount Bond: Coupon Rate < YTM. The price will be lower than the face value.
- Par Bond: Coupon Rate = YTM. The price will equal the face value.
Use the calculator above to quickly determine these values without performing manual compound interest calculations.