Documentation/Calc Functions/TBILLEQ

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    Function name:

    TBILLEQ

    Category:

    Financial Analysis

    Summary:

    Calculates the bond equivalent yield of a US Treasury bill (sometimes known as a T-Bill). This is an estimate of the annual yield that a bond would need to provide similar growth to the Treasury bill, and can be a useful metric for comparing different investment opportunities.

    Treasury bills are short-term securities, issued by many governments of the world. A Treasury bill is purchased at a discount to its face value on the settlement date and pays no interest. It is subsequently sold at its full face value on the maturity date, which is within one year in most cases.

    Note pin.svg

    Note:
    The logic underlying the TBILLEQ function relates specifically to US Treasury bills. Therefore, it may not be applicable for Treasury bills issued by other governments.

    Syntax:

    TBILLEQ(Settlement; Maturity; Discount)

    Returns:

    Returns a real number, which is the bond equivalent yield for a Treasury bill having the specified characteristics. The number returned is a percentage expressed as a decimal fraction (for example, the returned value 0.075 would represent 7.5%).

    Arguments:

    Settlement is a date (in quotation marks) or a date-time serial number, or a reference to a cell containing one of those types, which specifies when a trade is "settled". On this date the transfer of the Treasury bill to the buyer is completed, and the buyer makes the appropriate payment.

    Maturity is a date (in quotation marks) or a date-time serial number, or a reference to a cell containing one of those types, which specifies when the Treasury bill matures. On maturity, the holder is repaid the full value of the bill.

    Discount is a positive real number (expressed as a percentage, such as 2.5%, or a decimal fraction, such as 0.025), or a reference to a cell containing that number, which is the discount rate. An auction determines the discount rate to be paid for each US Treasury bill issue.

    • If either Maturity or Settlement is not a valid date, then TBILLEQ reports a #VALUE! error.
    • If either Maturity or Settlement contain time components, then these are ignored by TBILLEQ.
    • If Discount is non-numeric, then TBILLEQ reports a #VALUE! error.
    • If Discount is less than or equal to 0.0, then TBILLEQ returns an invalid argument error (Err:502).
    • If the Settlement date is not before the Maturity date, then TBILLEQ returns an invalid argument error (Err:502).
    • If [math]\displaystyle{ \text{DAYS360}(Settlement;\:Maturity; \: \text{TRUE}()) \: \gt \:360 }[/math], then Maturity is too long after Settlement and TBILLEQ returns an invalid argument error (Err:502).

    Additional details:

    • The formula for TBILLEQ is:
    [math]\displaystyle{ \text{TBILLEQ}~=~\frac{365 \times rate}{360 \: - \: \left(days \times rate \right)} }[/math]
    where days is the number of days between the settlement (purchase) date and maturity (redemption) date. days is calculated using a day count convention that assumes the actual number of days in each month, with the year comprising 360 days. rate is the percentage discount rate of the Treasury bill.

    Examples:

    Formula Description Returns
    =TBILLEQ(A1; A2; A3) where cell A1 contains the date 2022-11-15, A2 contains the date 2023-03-31, and A3 contains the value 5%. Here the function calculates the bond equivalent yield for the specified Treasury bill, returning the value 0.0516704416761042 (5.17%). 0.0516704416761042
    =TBILLEQ(DATE(2022; 11; 15); DATE(2023; 3; 31); 5%) Here the function calculates the bond equivalent yield for the same Treasury bill as in the previous example, but utilizes the DATE function instead of typing formatted date values. The function again returns the value 0.0516704416761042 (5.17%). 0.0516704416761042
    =TBILLEQ("1999-03-31"; "1999-06-01"; 0.0914) Here the function calculates the bond equivalent yield for the specified Treasury bill, returning the value 0.094151493565943 (9.42%). 0.094151493565943

    Related LibreOffice functions:

    TBILLPRICE

    TBILLYIELD

    ODF standard:

    Section 6.12.47, part 2

    Related (or similar) Excel functions:

    TBILLEQ