Zero-Coupon Bond: Definition, How It Works, and How to Calculate

What Is a Zero-Coupon Bond?

A zero-coupon bond is an investment in debt that does not pay interest but instead trades at a deep discount. The profit is realized at its maturity date when the bond is redeemed for its full face value.

A zero-coupon bond is also known as an accrual bond.

Understanding Zero-Coupon Bonds

Some bonds are issued as zero-coupon instruments. Other bonds are transformed into zero-coupon instruments after a financial institution strips them of their coupons and repackages them as zero-coupon bonds.

Because they offer payment at face value at maturity, zero-coupon bonds tend to fluctuate in price on the secondary market much more than coupon bonds.

What Is a Bond?

For a company or a government, a bond is a tool for borrowing money. Investors who purchase bonds are effectively acting as lenders to the issuing entity.

The investors earn a return in the form of coupon payments, which are made semiannually or annually, throughout the life of the bond.

When the bond matures, the bondholder is repaid an amount equal to the face value of the bond. The par or face value of a corporate bond is typically stated as $1,000.

If a corporate bond is issued at a discount, this means investors can purchase the bond below its par value. For example, an investor who purchases a bond for $920 at a discount will receive $1,000 when it reaches its maturity date. The $80 return plus coupon payments are the investor's earnings for holding the bond.

But not all bonds have coupon payments. Those that do not are referred to as zero-coupon bonds.

How Zero-Coupon Bonds Work

Zero-coupon bonds are issued at a deep discount and repay the par value at maturity. The difference between the purchase price and the par value represents the investor's return. The payment received by the investor is equal to the principal invested plus the interest earned, compounded semiannually, at a stated yield.

The interest earned on a zero-coupon bond is an imputed interest, meaning that it is an estimated interest rate for the bond and not an established interest rate. For example, a bond with a face value of $20,000 that matures in 20 years, with a 5.5% yield, may be purchased for roughly $6,855. At the end of the 20 years, the investor will receive $20,000.

The difference between $20,000 and $6,855 (or $13,145) represents the interest that compounds automatically until the bond matures. Imputed interest is sometimes referred to as "phantom interest."

The imputed interest on the bond is subject to federal income tax. Therefore, although no coupon payments are made on zero-coupon bonds until maturity, investors may still have to pay federal, state, and local income taxes on the imputed interest that accrues each year.

Purchasing a municipal zero-coupon bond, buying zero-coupon bonds in a tax-exempt account, or purchasing a corporate zero-coupon bond that has tax-exempt status are a few ways to avoid paying income taxes on these securities.

Pricing a Zero-Coupon Bond

The price of a zero-coupon bond can be calculated as:

Price = M ÷ (1 + r)ⁿ

where:

• M = Maturity value or face value of the bond
• r = required rate of interest
• n = number of years until maturity

If an investor wishes to make a 6% return on a bond, with $25,000 par value, that is due to mature in three years, they will be willing to pay the following:

$25,000 / (1 + 0.06)³ = $20,991.

If the debtor accepts this offer, the bond will be sold to the investor at $20,991 / $25,000 = 84% of the face value. Upon maturity, the investor gains $25,000 - $20,991 = $4,009, which translates to 6% interest per year.

The greater the length of time until the bond matures, the less the investor pays for it, and vice versa.

The maturity dates on zero-coupon bonds are usually long-term, with initial maturities of at least 10 years. These long-term maturity dates let investors plan for long-range goals, such as saving for a child’s college education. With the bond's deep discount, an investor can put up a small amount of money that grows over time.

Zero-coupon bonds can be issued from a variety of sources, including the U.S. Treasury, state and local government entities, and corporations.

Most zero-coupon bonds trade on the major exchanges.

The Bottom Line

Zero-coupon bonds are an alternative to the better-known coupon bonds that pay regular interest to their investors. Zero-coupon bonds pay no interest but are purchased at a deep discount and repaid at full price.

Most zero-coupon bonds are long-term issues; 10 or more years is common. They are often used to finance a long-range goal, such as paying for a child's college education.

One big thing to consider: The owners of zero-coupon bonds pay a "phantom interest" tax on the bonds' earnings through the years they hold them.