## 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.

### 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:

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)

**t **– 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?

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:

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?

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:

Where:

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

**t **– 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?

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:

Where:

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

**t **– 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.

The annualized return for this investment is **8.4%**.

### More Resources

We hope you enjoyed CFI’s explanation of yield on debt. 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: