Discount Yield

The expected annual percentage rate of return earned on a bond when it is sold at a discount on its face value

What is Discount Yield?

Discount yield is the expected annual percentage rate of return earned on a bond when it is sold at a discount on its face value. The discount yield is also popularly referred to as the bank discount yield (BDY).

 

Discount Yield

 

Summary

  • Discount yield is the expected annual percentage rate of return earned on a bond when it is sold at a discount on its face value.
  • It is also popularly referred to as the bank discount yield (BDY).
  • Discount yield is commonly calculated for municipal bonds, Treasury bills (T-bills), zero-coupon bonds, commercial paper, most money market instruments, and so on.

 

How is the Discount Yield Calculated?

Discount yield is calculated as follows:

 

Discount Yield - Formula

 

The components of the discount yield formula are as follows:

  • (Face Value – Purchase Price) is the total discount amount applied to the face value of the bond.
  • (Face Value – Purchase Price) / Face Value is the percentage value of the total discount on the bond to its face value.
  • 360 / No. of Days (or Months) to Maturity is the number of days (or months) remaining until maturity, because the bond is held until maturity.

 

Popular Usage

Discount yield is commonly calculated for municipal bonds, Treasury bills (T-bills), zero-coupon bonds, commercial paper, most money market instruments, and so on.

  • Municipal bonds: Municipal bonds are low-risk debt securities issued by the government, or municipality, primarily to finance its public expenditures. These are exempt from most federal and provincial taxes.
  • Treasury bills: Treasury bills are low-risk debt securities issued by the U.S. government, with a short term maturity of one year or less. While the interest income earned from T-bills is subject to federal income tax policies, it is exempt from most state and local taxes.
  • Zero-coupon bonds: A zero-coupon bond is a debt security that has no periodic interest payments. However, it is sold at a sizeable discount from its face value, ultimately rendering a profit at maturity to the bondholder.
  • Commercial paper: A commercial paper is a short-term debt security issued by corporations. They are typically issued to finance/meet with short-term liabilities.

 

Practical Example

Say, for example, you purchase a bond for $9,600. It matures to a total value of $10,000. It means the bond was purchased at a discount of $400. It was issued on December 1, 2019, and is to mature in 90 days.

Consequently, the discount yield for this bond can be calculated as follows:

 

Discount Yield - Sample Calculation

 

Therefore, the discount yield of the bond is 0.16 or 16%.

 

Limitations to the Discount Yield Measure

Some limitations to the discount yield measure include:

 

1. Time convention

For simplification of calculation, the discount yield is annualized, taking into account a 360-day year rather than the actual 365-day year. It creates a slight problem because the interest on bonds and Treasury bills is paid on a 365-day basis. The calculation time convention often leads to a mismatch in values.

 

2. Based on face value

While there is not usually much difference, some mismatch and errors can creep up considering that discount yield is calculated based on the bond issued’s face value rather than the actual dollar amount invested, i.e., the purchase price.

 

What is the Bond Equivalent Yield (BEY)?

Bond equivalent yields (BEY) are often considered along with bank discount yields and sometimes also confused with each other. BEY is the total yield on bonds after taking into account the total interest applicable, i.e., the simple semi-annual interest on an actual day-count basis.

The bond equivalent yield (BEY) is calculated as follows:

 

Bond Equivalent Yield (BEY)

 

Where:

  • DR is the discount rate (which is basically the discount yield expressed in decimal form)
  • t is the number of days left between settlement and maturity

 

The BEY is different from the BDY in the sense that it takes the actual dollar amount invested, i.e., the purchase price, into account, and the fact that it takes the actual-day count, i.e., the 365-day year, into account rather than the 360-day year convention.

 

More Resources

CFI is the official provider of the global Capital Markets & Securities Analyst (CMSA)™ certification program, designed to help anyone become a world-class financial analyst. To keep advancing your career, the additional resources below will be useful:

  • Commercial Paper
  • Money Market
  • Treasury Bills (T-Bills)
  • Zero-Coupon Bond

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