Discount Yield
The rate of return a bond generates annually as a percentage when sold at a discount to its par value
What Is Discount Yield?
The discount yield is the rate of return a bond generates annually as a percentage when sold at a discount to its par value. It calculates the yield on treasury bills or municipal bonds sold at a discount.
It is also referred to as the bank discount yield (BDY). The quoted prices financial institutions use for these fixed-income securities represent the percentage of the bond’s face value and are determined by discounting the bond based on 360 days.
It is most frequently used to calculate the yield on short-term bonds or treasury bills sold at a discount. These short-term instruments include municipal notes and commercial paper issued by municipalities.
These money market instruments are generally investments with a maturity of less than one year. For example, Treasury bills have a maximum maturity of 26 weeks. Such devices don’t carry periodic interest payments and are issued at a price lower than their face value.
If the bond is held until Maturity, the return on investment (ROI) is determined by the yield computation of the discount bond. If it sold before Maturity, the rate of return earned would be different. This new rate of return would be based on the sale price of the bond (security).
Key Takeaways
- Discount Yield is the annual rate of return generated by a bond sold at a discount to its par value. It is also known as the bank discount yield.
- It is commonly used to calculate the yield on short-term bonds and treasury bills sold at a discount, such as municipal notes and commercial paper, with maturities of less than one year.
- The formula to calculate the discount yield is (Face Value - Purchase Price) / Face Value x 360 / Number of days to maturity.
- Discount yield is different from bond equivalent yield, which considers the applicable total interest and is used to compare yields between different bonds.
- Discount Yield and bond equivalent yield calculations are important for investors to assess the rate of return on their investments and compare the yields of various fixed-income securities.
How to Calculate the Discount Yield
The formula for discount yield is:
DY = (Face Value-Purchase Price)/Face Value x 360/Nb of days to Maturity
This formula means the purchase price at which you bought the bond is subtracted from the face value of this bond at Maturity.
This number is the discount amount of the bond, which is then divided by its face value to get the percentage discount of its face value.
To break it down more and simplify it:
- (Face Value - Purchase Price): The discount amount pertained to the face value of the bond
- (Face Value - Purchase Price) / Face Value: The percentage discount of this bond’s face value
- (360 / Nb of Days to Maturity): The number of days left till the bond matures
All money market instruments such as treasury bills, zero-coupon bonds, municipal bonds, and commercial paper have the same calculation to get the DY.
Although they constitute the same formula for getting the yield, they differ from each other:
- A Commercial Paper is an unsecured promissory note that corporations issue to finance their short-term obligations, such as funding for a new project.
- A treasury bill is low-debt short-term government security with a maturity lasting 52 weeks.
- Zero coupon bonds are discount bonds that don’t pay any interest during the life of the bonds.
- Government entities issued municipal bonds to raise money for roads, buildings, schools, and other projects.
Practical Examples
Here are a few examples to get familiar with the concept:
Example 1: You purchase a bond at 970$ with a face value of 1000$. The bond was purchased at a discount of 30$. The bond matures in 60 days. The discount yield in this case is:
DY = (Face Value - Purchase Price)/Face Value x 360/Nb of Days to Maturity
= (1000 - 970)/1000 x 360/60
= 0.18
=18%
Example 2: A bond that has a face value of 1000$ and matures in 120 days is selling today at an 80$ discount from face value. Discount yield is:
DY = Discount Price/Face Value x 360/Nb of Days to Maturity
= 80/1000 x 360/120
= 0.24
= 24%
Example 3: A bond with a face value of 10000$ and a purchase price of 9500$ has a DY of 15%. The number of days left to maturity:
Nb of Days to Maturity = Discount Price/Face Value x 360/DY
= 500/10000 x 360/0.15
= 120 days
If the DY was 20%, the Nb of days to maturity after calculation would be 90 days.
Hence, you see an inverse correlation. When the Nb of days to maturity is less, the yield would be more.
Also, the higher the discount price, the higher the DY.
The Difference between Discount Yield and Bond Equivalent Yield
As mentioned before, the discount yield is most frequently used to calculate the yield on short-term bonds and treasury bills sold at a discount. Securities use the discount yield when sold at a discount. This is to calculate the investor’s rate of return.
Bond equivalent yields (BEY) can sometimes be confused with bank discount yields. There is a common misconception between them, but the bond equivalent yield is generally the total yield on bonds after taking into account the total interest applicable.
It is calculated by dividing the difference of the face value by the purchase price and then dividing it by the purchase price. Then multiply it by 360 days over its number of days to maturity.
It’s the same as the yield, but the face value in the denominator is replaced with the purchase price.
Another simpler calculation would be:
Bond Equivalent Yield = 365 * DY / 360 - (T*DY)
- “T” is the number of days to maturity.
The bond equivalent yield purpose is mainly used to help investors get the equivalent yield between two or more bonds and calculate the value of the deep discount or zero-coupon bonds on an annualized basis.
Discount Yield FAQs
It is the rate of return a bond generates annually as a percentage when sold at a discount to its par value.
It is done by dividing the discount over the face value, multiplying it by 360, and dividing it by the days left to maturity.
Put, no. The bond equivalent yield is generally the total bond yield after considering the applicable genuine interest. In contrast, the discount yield is applied on short-term bonds and discounted treasury bills.
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