Bonds are debt instruments where an issuer owes the holders a debt and is obliged to pay interest (the coupon) and/or to repay the principal at a later date (maturity). The "worth" or price of a bond in the secondary market is not always its face value. It fluctuates based on prevailing interest rates, time to maturity, and the creditworthiness of the issuer.
How the Bond Worth Calculator Works
This calculator estimates the present value of a bond, which represents its theoretical worth in the current market. The calculation is based on the bond's future cash flows (coupon payments and the principal repayment) discounted back to their present value using the current market yield (also known as the required rate of return or yield to maturity).
The Formula:
The core of the calculation is the Net Present Value (NPV) formula, adapted for bonds. The bond's worth (Price) is the sum of the present values of all future coupon payments and the present value of the face value received at maturity.
Price = ∑ [ C / (1 + r)^t ] + [ FV / (1 + r)^n ]
Where:
C = Annual Coupon Payment (Face Value * Annual Coupon Rate)
r = Current Market Yield (as a decimal)
t = The period number (1, 2, 3, …, n)
FV = Face Value (Par Value) of the bond
n = Total number of periods (Years to Maturity)
Note: For simplicity, this calculator assumes annual coupon payments. In reality, many bonds pay semi-annually, which would require adjusting the formula to reflect twice the number of periods with half the coupon payment each period.
Key Inputs Explained:
Face Value (Par Value): The amount the bondholder will receive when the bond matures. This is typically $1,000 for corporate bonds.
Annual Coupon Rate: The fixed interest rate the bond pays annually, expressed as a percentage of the face value.
Current Market Yield: The prevailing rate of return investors expect for similar bonds in the market. This is the discount rate used in the calculation.
Years to Maturity: The remaining time until the bond's face value is repaid.
Interpreting the Results:
If Market Yield > Coupon Rate: The bond's worth will likely be less than its face value (a discount bond). Investors demand a higher return than the bond offers, so its price drops to compensate.
If Market Yield < Coupon Rate: The bond's worth will likely be more than its face value (a premium bond). The bond offers a higher return than the market currently demands, so its price increases.
If Market Yield = Coupon Rate: The bond's worth will be approximately equal to its face value.
Understanding bond valuation is crucial for investors to make informed decisions about buying or selling bonds in the secondary market.
function calculateBondWorth() {
var faceValue = parseFloat(document.getElementById("faceValue").value);
var couponRate = parseFloat(document.getElementById("couponRate").value);
var marketRate = parseFloat(document.getElementById("marketRate").value);
var yearsToMaturity = parseFloat(document.getElementById("yearsToMaturity").value);
var resultElement = document.getElementById("result-value");
resultElement.textContent = "–"; // Reset before calculation
// Input validation
if (isNaN(faceValue) || faceValue <= 0) {
alert("Please enter a valid Face Value greater than zero.");
return;
}
if (isNaN(couponRate) || couponRate < 0) {
alert("Please enter a valid Annual Coupon Rate (0 or greater).");
return;
}
if (isNaN(marketRate) || marketRate <= 0) {
alert("Please enter a valid Current Market Yield greater than zero.");
return;
}
if (isNaN(yearsToMaturity) || yearsToMaturity <= 0) {
alert("Please enter a valid Years to Maturity greater than zero.");
return;
}
var couponPayment = faceValue * (couponRate / 100);
var marketYieldDecimal = marketRate / 100;
var bondPrice = 0;
// Calculate present value of coupon payments
for (var t = 1; t <= yearsToMaturity; t++) {
bondPrice += couponPayment / Math.pow(1 + marketYieldDecimal, t);
}
// Calculate present value of face value
bondPrice += faceValue / Math.pow(1 + marketYieldDecimal, yearsToMaturity);
// Format the result to two decimal places
resultElement.textContent = "$" + bondPrice.toFixed(2);
}