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# Coupon Equivalent Rate (CER) Definition

## What Is Coupon Equivalent Rate (CER)?

The coupon equivalent rate (CER) is an alternative calculation of coupon rate used to compare zero-coupon and coupon fixed-income securities. It is the annualized yield on a zero-coupon bond when calculated as if it paid a coupon. It is also known as the bond equivalent yield (BEY) or the coupon equivalent yield (CEY)

### Key Takeaways

• The coupon equivalent rate (CER) is the annualized yield of a zero-coupon bond when calculated as if it paid a coupon
• CER allows for the comparison of zero-coupon bonds and other fixed-income securities.
• CER is a nominal yield and does not take into account compounding.

## Understanding Coupon Equivalent Rate (CER)

Coupon equivalent rate (CER) allows an investor to compare a zero-coupon bond to a coupon-paying one. While most bonds pay investors annual or semi-annual interest payments, some bonds, referred to as zero-coupon bonds, do not pay interest at all but are instead issued at a deep discount to par.

The investor makes a return on these discount bonds when the bond matures. To compare the return on coupon-paying securities with that of zero-coupons in relative terms, analysts use the coupon equivalent rate formula. The coupon equivalent rate (CER) indicates the annualized yield on a short-term debt security that is typically quoted on a bank discount basis such that the yield can be comparable with quotations on coupon-bearing securities.

In effect, it states what the coupon rate on a discount instrument (such as a zero-coupon, Treasury bill, or commercial paper) would be if the instrument carried a coupon and had been sold at face value.

Because the quoted rate of bonds is calculated on the basis of the face value, this rate for bonds issued at a discount is inaccurate for comparing them to other coupon bonds. Discount or zero-coupon bonds are not sold at face value. They are sold at a discount, and the investor typically receives more than what they invested at maturity. Thus, it is more accurate to use the CER because it uses the investor's initial investment as the basis for yield.

The formula for coupon equivalent rate is:

\begin{aligned}&\text{CR}=\frac{\text{Face Value}-\text{Market Price}}{\text{Market Price}}\times\frac{360}{\text{Days Until Maturity}}\\ &\textbf{where:}\\ &\text{CR}=\text{Coupon equivalent rate} \end{aligned}

The coupon equivalent rate (CER) is calculated as:

1. Find the discount the bond is trading at, which is face value less market value.
2. Then divide the discount by the market price.
3. Divide 360 by the number of days until maturity.
4. That number (from no. 3) is then multiplied by the number found in no. 2.

The coupon equivalent rate is an alternative way to calculate the yield of a bond and allows for a comparison of a zero-coupon bond to a bond of a different term. However, it is a nominal yield and does not take into account compounding.

The yield to maturity (YTM) is the theoretical yield an investor would receive if they held the bond to maturity. But unlike the coupon equivalent yield (CER), the yield to maturity takes into account compounding. Both are expressed as annualized rates.

## CER Example

For example, a $10,000 US T-bill that matures in 91 days is selling for$9,800. Its coupon equivalent rate would be 8.08%, or (($10,000 -$9,800) / ($9,800)) * (360 / 91), which is 0.0204 * 3.96. Compared with a bond paying an 8% annual coupon we’d choose the zero-coupon bond given it has the higher rate {8.08% > 8%]. Or consider a current zero-coupon Treasury STRIP that matures on March 15, 2022. The face value is$100 and the market price is $98.63 as of September 14, 2021. The coupon equivalent rate (CER) is 2.75%, or (($100 - $98.63) / ($98.63) * (360 / 182 ).

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