## DEFINITION of '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 effective yield on a zero-coupon bond when calculated as if it paid a coupon.

The formula for CER is given as:

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## BREAKING DOWN 'Coupon Equivalent Rate - CER'

Not all bonds are made equal. 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 effective annual 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 he or she 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. For example, a \$10,000 T-bill that matures in 91 days is selling for \$9,800. Its rate is currently quoted as:

Quoted rate = (Discount value / Face value) x (360 / Days to maturity)

---where the discount value is the difference between the face value and market value of the bond.

Quoted rate = [(\$10,000 - \$9,800) / \$10,000] x (360 / 91)

= (\$200/\$10,000) x (360/91)

= 0.02 x 3.956

= 0.0791, or 7.91%

However, the CER uses the initial investment to calculate the yield:

Coupon equivalent rate = (Discount value / Market price) x (360 / Days to maturity)

= (\$200/\$9,800) x (360/91)

= 0.0204 x 3.956

= 0.0807, or 8.07%

The first part of the equation is the standard return formula and shows the return on investment. The second portion of the formula annualizes the first part of the formula.

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