Zero-Coupon Bond: Definition, Function, and Calculation

A zero-coupon bond is a type of bond that doesn’t pay periodic interest (coupons). Instead, it is sold at a deep discount to its face value

What is a Zero-Coupon Bond?

Zero coupon bonds are bonds that do not pay interest during the life of the bonds. Instead, investors buy zero coupon bonds at a deep discount from their face value, which is the amount the investor will receive when the bond “matures” or comes due.

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

The difference between the purchase price of a zero-coupon bond and its par value(face value) indicates the investor’s return.

Understanding Zero-Coupon Bond

As a zero-coupon bond does not pay periodic coupons, it trades at a discount to its face value. To understand why, consider the time value of money.

The time value of money is a concept that states that money is more valuable now than it will be in the future; for example, an investor would prefer to receive $100 today rather than $100 in one year. By receiving $100 today, the investor can put it in a savings account and earn interest (resulting in more than $100 in a year).

Extending the concept above to zero-coupon bonds, an investor who buys the bond now must be compensated with a higher future value. A zero-coupon bond must trade at a discount because the issuer must provide a return to the investor for purchasing the bond.

Zero coupon bonds typically have long maturity dates, with many lasting ten, fifteen, or more years. These long-term maturity dates enable investors to plan for long-term objectives, such as paying for a child’s college education. With the deep discount, an investor can put up a small sum of money that will grow over time.

How Zero-Coupon Bonds Work

Zero-coupon bonds are sold at a significant discount to their face value and repay the full face value when they mature. The investor’s profit comes from the difference between the buying price and the bond’s face value.

The total amount received at maturity includes the initial investment and the interest, which accrues over time and compounds semiannually/Annually at a specified rate.

For example, if a zero-coupon bond has a face value of $1,000 and matures in 5 years, you might buy it today for $700.

Over the 5 years, the bond doesn’t pay any interest, but at maturity, you get the full $1,000.

The $300 difference is your profit, which is effectively the interest earned over the bond’s life. This makes it simple and predictable for investors, especially for long-term savings goals.

Pricing a Zero-Coupon Bond

The price of a zero-coupon bond is calculated by discounting its face value back to the present value using the bond’s yield to maturity (YTM).

Since these bonds do not pay periodic interest, the formula focuses solely on the compounding effect over time.

The formula is:

Price = Face Value / (1 + r)^n

Where:

Price is the current value of the bond.
Face Value is the amount the investor will receive at maturity.
r is the annual yield (expressed as a decimal).
n is the number of years until maturity.

For example, if a zero-coupon bond has a face value of $10,000, a YTM of 5%, and matures in 5 years, its price would be:

Price = 10,000 / (1 + 0.05)^5 = ₹7,835.26

This means you would pay $7,835.26 today for a bond that will pay $10,000 at the end of 5 years.

Think About It Zero-coupon bonds grow quietly! No interest payments mean no distractions—just a single payout at maturity, making them super predictable.

Reinvestment Risk and Interest Rate Risk

Reinvestment Risk

Zero-coupon bonds have no reinvestment risk because they do not pay periodic interest (coupons). Since there are no interim cash flows that need to be reinvested at prevailing market rates, the investor avoids the risk of reinvesting proceeds at lower interest rates.

This makes zero-coupon bonds ideal for investors seeking predictable returns.

Interest Rate Risk

Zero-coupon bonds are highly sensitive to changes in interest rates. Since the entire return is realized at maturity and is based on discounting, any change in interest rates significantly impacts the bond’s price.

For instance, when interest rates rise, the present value of the bond decreases sharply, and when rates fall, the bond’s price increases significantly.

This high sensitivity is due to the longer duration of zero-coupon bonds compared to coupon-paying bonds.

Final Thoughts

Zero-coupon bonds are a simple, predictable investment option. By eliminating periodic interest payments, they offer a fixed return at maturity. Ideal for long-term goals, they avoid reinvestment risk but are sensitive to interest rate changes. Their discounted price makes them accessible and appealing for disciplined, patient investors seeking steady growth.

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