TBILLPRICE function

The TBILLPRICE function in Excel is used to calculate the price of a Treasury bill (T-bill) based on its bond-equivalent yield, the face value, and the number of days to maturity. Treasury bills are sold at a discount, and their price is typically less than their face value. The TBILLPRICE function allows you to determine how much you would pay for a T-bill based on these parameters.

Syntax

TBILLPRICE(settlement, maturity, rate, redemption)

Parameters

1. settlement: The settlement date of the Treasury bill. This is the date after the issue date when the T-bill is traded to the buyer. It must be a valid Excel date.
2. maturity: The maturity date of the Treasury bill. This is the date when the face value of the T-bill is paid back to the investor. It must be a valid Excel date.
3. rate: The bond-equivalent yield of the Treasury bill. This is the annualized yield expressed as a percentage (not as a decimal).
4. redemption: The redemption value of the T-bill, which is typically $100.

How It Works

The TBILLPRICE function calculates the price of a Treasury bill based on the bond-equivalent yield and other input values. The formula for calculating the price of a T-bill is:

$$\text{Price} = \text{Redemption} \times \left( 1 – \frac{\text{Rate} \times \text{Days to maturity}}{360} \right)$$

Where:

• Rate is the bond-equivalent yield of the T-bill,
• Days to maturity is the number of days from the settlement date to the maturity date,
• Redemption is the face value of the T-bill (usually $100).

The TBILLPRICE function returns the price you would pay for the T-bill (per $100 face value), based on the given yield and other parameters.

Example

Suppose you have the following details for a T-bill:

• Settlement date: January 1, 2025
• Maturity date: July 1, 2025
• Bond-equivalent yield: 4% (0.04 as a decimal)
• Redemption value: $100

To calculate the price of the T-bill, you would use the following formula in Excel:

=TBILLPRICE(DATE(2025,1,1), DATE(2025,7,1), 0.04, 100)

This would return the price of the T-bill based on the provided yield, settlement date, and maturity date.

Important Notes

• The rate input should be in decimal form. For example, for a 4% bond-equivalent yield, the rate would be entered as 0.04.
• The TBILLPRICE function assumes a 360-day year for calculating the discount.
• The result is the price per $100 face value of the T-bill, and the price is typically less than $100 due to the discount.

Summary

The TBILLPRICE function in Excel calculates the price of a Treasury bill based on its bond-equivalent yield, settlement date, maturity date, and redemption value. It is useful for determining how much you would pay for a T-bill given the bond-equivalent yield, which is based on the T-bill’s discount relative to its face value.