# All You Need to Know About the Bond Equivalent Yield Formula

The following article deals with the necessity of using the bond equivalent yield formula for restating the yield of a fixed income security in terms of semiannual interest rate.

Aparna Iyer

Last Updated: Feb 28, 2018

Understanding BEY

The Bond Equivalent Yield (BEY), also known as equivalent coupon yield and investment rate yield, calculates the total yield on investments while taking into account the interest applicable on the bonds. The calculation provides an insight into the comparative study between fixed income securities and securities accompanied with annual yields.

The Formula

The discount rate for the T-bill is converted to a coupon equivalent using the bond equivalent yield formula. The formula helps to restate the yield on a T-bill or any other debt instrument in terms of semiannual investment yield, in order to facilitate direct comparison with an interest bearing coupon security, viz. T-bond, T-note. For T-bills with a maturity of 182 days or less, discount rate/discount yield on the T-bill can be converted to bond equivalent yield (to maturity) using the following formula:

*BEY= (365 x DR)/(360-(N x DR))*where:

DR = Discount Rate or Discount Yield (in decimal)

N = Time between settlement date and maturity date (in days)

Need for the Formula

The investor's return on investment (ROI) or return, if the bond is held till maturity is called the yield to maturity or simply the yield. The yield needs to be determined so that one can compare alternative fixed income investments. The yield on a T-bill is calculated using either the discount yield formula, or the investment yield formula.

*Discount Yield Formula or Discount Rate = [(FV - PP)/FV] x [360/M]*where:

FV = Face Value

PP = Purchase Price

M = Maturity of T-bill (in days)

*Investment Yield Formula = [(FV - PP)/PP] x [365 or 366/M]*