Discount Rate Bond Calculator
.bond-calc-container {
max-width: 800px;
margin: 0 auto;
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.result-value {
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Bond Valuation Calculator
$0.00
Valuation Status:
–
Total Coupon Payments:
–
PV of Coupons:
–
PV of Face Value:
–
Current Yield:
–
Total Periods:
–
Discount Rate Bond Calculator: Understanding Bond Valuation
This calculator determines the Present Value of a bond based on its coupon rate, face value, and the current market discount rate (Yield to Maturity). By inputting these metrics, investors can determine if a bond is trading at a premium, a discount, or at par.
How Bond Pricing Works
A bond's price is the sum of the present value of its future cash flows. These cash flows come in two forms:
- Coupon Payments: Regular interest payments made to the bondholder until maturity (an annuity).
- Face Value (Par Value): The lump sum repayment of the principal amount at maturity.
The "Discount Rate" entered in the calculator represents the required rate of return or the Yield to Maturity (YTM). This rate is used to discount future cash flows back to today's dollars.
The Bond Valuation Formula
The mathematical formula used to price a bond is:
Price = [ C * (1 – (1 + r)^-n) / r ] + [ F / (1 + r)^n ]
Where:
- C = Periodic coupon payment ($).
- F = Face value of the bond.
- r = Periodic discount rate (Annual Rate / Frequency).
- n = Total number of periods (Years × Frequency).
Premium vs. Discount Bonds
The relationship between the Coupon Rate and the Discount Rate determines the bond's valuation status:
- Discount Bond: Discount Rate > Coupon Rate. The bond sells for less than its face value because the market demands a higher return than what the bond's coupons provide.
- Premium Bond: Discount Rate < Coupon Rate. The bond sells for more than its face value because its coupons pay more than the current market rate.
- Par Bond: Discount Rate = Coupon Rate. The bond sells exactly at its face value.
Example Calculation
Imagine a bond with a $1,000 Face Value, a 5% Coupon Rate, and 10 Years to Maturity. If the current market interest rate (Discount Rate) rises to 6%, what is the bond worth?
- Periodic Coupon: $25 (Semiannual calculation of 5% on $1000).
- Periodic Rate: 3% (6% / 2).
- Total Periods: 20 (10 years × 2).
Using the calculator above, the bond price would be approximately $925.61. Since the price is lower than the $1,000 face value, this is a Discount Bond.
function calculateBondPrice() {
// Get Input Values
var faceValue = parseFloat(document.getElementById('bondFaceValue').value);
var couponRateAnnual = parseFloat(document.getElementById('bondCouponRate').value);
var discountRateAnnual = parseFloat(document.getElementById('bondDiscountRate').value);
var years = parseFloat(document.getElementById('bondYears').value);
var frequency = parseInt(document.getElementById('bondFrequency').value);
// Validation
if (isNaN(faceValue) || isNaN(couponRateAnnual) || isNaN(discountRateAnnual) || isNaN(years) || faceValue <= 0 || years <= 0) {
alert("Please enter valid positive numbers for Face Value and Years.");
return;
}
// Variable Preparation for Formula
// r = Periodic market rate
var r = (discountRateAnnual / 100) / frequency;
// n = Total number of periods
var n = years * frequency;
// C = Periodic coupon payment amount
var C = (faceValue * (couponRateAnnual / 100)) / frequency;
// Calculations
// 1. Present Value of Coupon Payments (Annuity Formula)
// PV_coupons = C * [ (1 – (1+r)^-n) / r ]
var pvCoupons = 0;
if (r === 0) {
pvCoupons = C * n;
} else {
pvCoupons = C * ((1 – Math.pow(1 + r, -n)) / r);
}
// 2. Present Value of Face Value (Lump Sum Formula)
// PV_face = F / (1+r)^n
var pvFace = faceValue / Math.pow(1 + r, n);
// Total Bond Price
var bondPrice = pvCoupons + pvFace;
// Current Yield = Annual Coupon Payment / Bond Price
var annualCouponPayment = faceValue * (couponRateAnnual / 100);
var currentYield = (annualCouponPayment / bondPrice) * 100;
// Determine Status
var statusText = "";
var statusClass = "";
if (bondPrice < faceValue – 0.01) { // Tolerance for float errors
statusText = "Discount Bond";
statusClass = '
Discount';
} else if (bondPrice > faceValue + 0.01) {
statusText = "Premium Bond";
statusClass = '
Premium';
} else {
statusText = "Par Bond";
statusClass = '
Par';
}
// Format Output Currency
var formatter = new Intl.NumberFormat('en-US', {
style: 'currency',
currency: 'USD',
minimumFractionDigits: 2,
maximumFractionDigits: 2
});
// Display Results
document.getElementById('result-section');
document.getElementById('bondResult').style.display = 'block';
document.getElementById('displayPrice').innerHTML = formatter.format(bondPrice);
document.getElementById('displayStatus').innerHTML = statusText + " " + statusClass;
document.getElementById('displayPVCoupons').innerText = formatter.format(pvCoupons);
document.getElementById('displayPVFace').innerText = formatter.format(pvFace);
document.getElementById('displayTotalCoupons').innerText = n;
document.getElementById('displayPeriods').innerText = n + " periods";
// Handle Current Yield division by zero if price is 0 (unlikely but safe)
if(bondPrice > 0) {
document.getElementById('displayCurrentYield').innerText = currentYield.toFixed(2) + "%";
} else {
document.getElementById('displayCurrentYield').innerText = "0.00%";
}
}