Understanding the fair market value of a bond is essential for any fixed-income investor. This Bond Price Calculator helps you determine what a bond should be trading for based on its coupon payments, maturity date, and the current market interest rates (Yield to Maturity).
Key Definitions
Face Value: Also known as the par value, this is the amount the bondholder will receive when the bond reaches maturity. Most corporate bonds have a face value of $1,000.
Coupon Rate: The fixed annual interest rate paid by the bond issuer. A 5% coupon on a $1,000 bond pays $50 per year.
Yield to Maturity (YTM): The total return anticipated on a bond if it is held until it matures. This is essentially the market interest rate for bonds of similar risk and duration.
Years to Maturity: The time remaining until the issuer must repay the Face Value.
The Bond Pricing Formula
The price of a bond is the sum of the present values of all future coupon payments plus the present value of the face value. The formula used is:
Imagine a bond with the following characteristics:
Face Value: $1,000
Coupon Rate: 6% (Annual)
Yield to Maturity: 4%
Years to Maturity: 5
Since the Yield to Maturity (4%) is lower than the Coupon Rate (6%), the bond will sell at a Premium (above $1,000). Using the calculator, you would find that the bond price is approximately $1,089.04.
Relationship Between Yield and Price
Bond prices and yields have an inverse relationship. When the market interest rates (YTM) rise, existing bonds with lower fixed coupon rates become less attractive, causing their prices to drop. Conversely, if market rates fall, the price of existing bonds will rise.
function calculateBondPrice() {
var faceValue = parseFloat(document.getElementById("faceValue").value);
var couponRate = parseFloat(document.getElementById("couponRate").value) / 100;
var ytm = parseFloat(document.getElementById("ytm").value) / 100;
var years = parseFloat(document.getElementById("yearsToMaturity").value);
var frequency = parseInt(document.getElementById("paymentFrequency").value);
if (isNaN(faceValue) || isNaN(couponRate) || isNaN(ytm) || isNaN(years)) {
alert("Please enter valid numerical values for all fields.");
return;
}
var periodicCoupon = (faceValue * couponRate) / frequency;
var periodicYield = ytm / frequency;
var totalPeriods = years * frequency;
var bondPrice = 0;
// Present Value of Coupons
if (periodicYield === 0) {
bondPrice = (periodicCoupon * totalPeriods) + faceValue;
} else {
// PV of Annuity (Coupons)
var pvCoupons = periodicCoupon * (1 – Math.pow(1 + periodicYield, -totalPeriods)) / periodicYield;
// PV of Face Value (Lump Sum)
var pvFaceValue = faceValue / Math.pow(1 + periodicYield, totalPeriods);
bondPrice = pvCoupons + pvFaceValue;
}
// Display Result
var resultDiv = document.getElementById("bondResult");
var priceSpan = document.getElementById("calculatedPrice");
var statusPara = document.getElementById("bondStatus");
resultDiv.style.display = "block";
priceSpan.innerHTML = "$" + bondPrice.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2});
if (bondPrice > faceValue) {
statusPara.innerHTML = "This bond is trading at a Premium because the coupon rate is higher than the yield.";
} else if (bondPrice < faceValue) {
statusPara.innerHTML = "This bond is trading at a Discount because the coupon rate is lower than the yield.";
} else {
statusPara.innerHTML = "This bond is trading at Par.";
}
}