Understanding Treasury Bills (T-Bills) and Their Discount Rate
Treasury Bills, commonly known as T-Bills, are short-term debt instruments issued by the U.S. Department of the Treasury. They are sold at a discount to their face value and mature at par, meaning the investor receives the face value at maturity. T-Bills are considered one of the safest investments because they are backed by the full faith and credit of the U.S. government. They are typically issued with maturities of a few days up to 52 weeks.
The T-Bill Discount Rate
The discount rate is a common way to express the yield on a T-Bill. It's calculated based on the difference between the purchase price and the face value, expressed as a percentage of the face value, and then annualized. The formula for the discount rate is:
Discount Rate (%) = [(Face Value – Purchase Price) / Face Value] * (360 / Days to Maturity) * 100
The "360 days" convention is a standard practice in the T-Bill market for annualizing yields, even though a year has 365 or 366 days. This convention simplifies calculations and is widely accepted.
Coupon Equivalent Yield (Taxable Equivalent Yield)
While the discount rate is commonly quoted, it's not a true measure of return because it's based on the face value and uses a 360-day year. The Coupon Equivalent Yield (CEY), also known as the Treasury Bill Equivalent Yield (T-Bill Equivalent Yield or TEY), provides a more comparable yield to traditional coupon-bearing bonds. It annualizes the return based on the actual purchase price and a 365-day year.
The formula for the Coupon Equivalent Yield is:
Coupon Equivalent Yield (%) = [(Face Value – Purchase Price) / Purchase Price] * (365 / Days to Maturity) * 100
This calculation gives investors a better understanding of the T-Bill's return relative to other types of investments.
Example Calculation
Let's say you purchase a $1,000 face value T-Bill for $985 that has 182 days until maturity.
Discount Rate:
[($1,000 – $985) / $1,000] * (360 / 182) * 100 = (0.015) * (1.978) * 100 = 2.97%
Coupon Equivalent Yield:
[($1,000 – $985) / $985] * (365 / 182) * 100 = (0.01523) * (2.0055) * 100 = 3.05%
This means the T-Bill offers a discount rate of approximately 2.97% and a coupon equivalent yield of approximately 3.05%.
function calculateTBillDiscountRate() {
var faceValue = parseFloat(document.getElementById("faceValue").value);
var purchasePrice = parseFloat(document.getElementById("purchasePrice").value);
var daysToMaturity = parseFloat(document.getElementById("daysToMaturity").value);
var discountRateResultDiv = document.getElementById("discountRateResult");
var couponEquivalentResultDiv = document.getElementById("couponEquivalentResult");
discountRateResultDiv.innerHTML = ""; // Clear previous results
couponEquivalentResultDiv.innerHTML = "";
if (isNaN(faceValue) || isNaN(purchasePrice) || isNaN(daysToMaturity) || faceValue <= 0 || purchasePrice <= 0 || daysToMaturity = faceValue) {
discountRateResultDiv.innerHTML = "Please enter valid positive numbers for all fields, and ensure purchase price is less than face value.";
return;
}
// Calculate Discount Rate
var discountRate = ((faceValue – purchasePrice) / faceValue) * (360 / daysToMaturity) * 100;
discountRateResultDiv.innerHTML = "
" + discountRate.toFixed(2) + "%";
// Calculate Coupon Equivalent Yield
var couponEquivalentYield = ((faceValue – purchasePrice) / purchasePrice) * (365 / daysToMaturity) * 100;
couponEquivalentResultDiv.innerHTML = "
" + couponEquivalentYield.toFixed(2) + "%";
}
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