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Calculating Yield on Debt

How can we evaluate the performance of debt investments?

How can we calculate Yield on Debt?

Debt yield refers to the rate of return an investor can expect to earn if he/she holds a debt instrument until maturity. Such instruments include government-backed T-bills, corporate bonds, private debt agreements, and other fixed income securities. In this article, we will explore the four different types of yields: Bank Discount, Holding Period, Money Market and Effective Annual.

 

yield

 

Bank Discount Yield (BDY)

The BDY formula is best suited to calculating yield on short-term debt instruments such as government T-bills. The formula for calculating BDY is:

 

bank discount yield

 

Where:

D – Discount/premium from face value (face value – market price)

F – Face value

360 – Number of days in a year (as per banking conventions)

– Number of days until maturity

 

BDY Example

An investor wants to buy a U.S. T-bill. The current market price is $490 and the security has a face value of $500. The T-bill matures in 200 days from today. Should the investor buy the T-bill today, what is the expected BDY?

 

bank discount yield

 

The BDY on this investment is 3.6%.

 

Holding Period Yield (HPY)

HPY measures any capital gains and/or losses from debt investments that have occurred over a specified holding period. The formula for calculating HPY is:

 

Holding period yield

 

Where:

P1 – Price of security at the end of the holding period (maturity)

P0 – Price of security at the beginning of the holding period (purchase price)

D1 – Cash distributions during holding period (coupons)

 

HPY Example

An investor buys a T-bill at a face value for $500. He then sells the T-bill at maturity for $510. What is his HPY?

 

Holding period yield example

 

The BDY on this investment is 2%. Note that T-bills are zero-coupon securities and do not pay a monthly coupon to investors. Thus, the D1 term in this example is equal to 0.

 

Money Market Yield (MMY)

MMY calculates the return on highly liquid, short-term debt instruments such as certificates of deposits, commercial paper or T-bills. MMY is different from BDY, as it computes yield based on the purchase price of the security rather than the security’s face value. The equation for MMY is:

 

money market yield

 

Where:

360 – Number of days in a year (as per banking conventions)

– Number of days until maturity

 

MMY Example

This example uses the same numbers as the HPY example above. Now, we learn that the T-bill was a 3-month T-bill that matures in 90 days. What is the investment’s MMY?

 

money market yield example

 

Using the HPY that we calculated earlier, the MMY on this investment is 8%.

 

Effective Annual Yield (EAY)

EAY is essentially the annualized version of HPY. It provides a number that is easily comparable to the annual returns of other securities. The equation for EAY is:

 

effective annual yield

 

Where:

365 – Number of days in the year (different from bank convention)

– Number of days until maturity

 

EAY Example

This example uses the same numbers as the HPY and MMY examples above, where HPY is 0.02 and t is 90 days.

 

effective annual yield example

 

The annualized return for this investment is 8.4%.

 

More Resources

CFI offers the Financial Modeling & Valuation Analyst (FMVA)™ certification program for those looking to take their careers to the next level. To learn more about related topics, check out the following resources:

  • Convertible Bond
  • Risk-Free Rate
  • Liquidity Premium
  • Fixed Income Fundamentals Course – CFI

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