A bond that pays no interest and trades at a discount to its face value
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What is a Zero-Coupon Bond?
A zero-coupon bond is a bond that pays no interest and trades at a discount to its face value. It is also called a pure discount bond or deep discount bond. U.S. Treasury bills are an example of a zero-coupon bond.
Summary
- A zero-coupon bond is a bond that pays no interest.
- The bond trades at a discount to its face value.
- Reinvestment risk is not relevant for zero-coupon bonds, but interest rate risk is relevant for the bonds.
Understanding Zero-Coupon Bonds
As a zero-coupon bond does not pay periodic coupons, the bond 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 illustrates that money is worth more now than an identical sum in the future – an investor would prefer to receive $100 today than $100 in one year. By receiving $100 today, the investor is able to put that money into a savings account and earn interest (thereby having more than $100 in a year’s time).
Extending the idea above into zero-coupon bonds – an investor who purchases the bond today must be compensated with a higher future value. Therefore, a zero-coupon bond must trade at a discount because the issuer must offer a return to the investor for purchasing the bond.
Pricing Zero-Coupon Bonds
To calculate the price of a zero-coupon bond, use the following formula:
Where:
- Face value is the future value (maturity value) of the bond;
- r is the required rate of return or interest rate; and
- n is the number of years until maturity.
Note that the formula above assumes that the interest rate is compounded annually. In reality, zero-coupon bonds are generally compounded semi-annually. In such a case, refer to the following formula:
Note that the formula above looks similar to the previous one, with the only difference being the required rate of return (r) being divided by 2 and the number of years until maturity (n) being multiplied by two. Since the bond compounds semi-annually, we must divide the required rate of return by two and multiply the number of years until maturity by two to account for the total number of periods the bond will be compounded for.
Example of a Zero-Coupon Bonds
Example 1: Annual Compounding
John is looking to purchase a zero-coupon bond with a face value of $1,000 and 5 years to maturity. The interest rate on the bond is 5% compounded annually. What price will John pay for the bond today?
Price of bond = $1,000 / (1+0.05)5 = $783.53
The price that John will pay for the bond today is $783.53.
Example 2: Semi-annual Compounding
John is looking to purchase a zero-coupon bond with a face value of $1,000 and 5 years to maturity. The interest rate on the bond is 5% compounded semi-annually. What price will John pay for the bond today?
Price of bond = $1,000 / (1+0.05/2)5*2 = $781.20
The price that John will pay for the bond today is $781.20.
Reinvestment Risk and Interest Rate Risk
Reinvestment risk is the risk that an investor will be unable to reinvest a bond’s cash flows (coupon payments) at a rate equal to the investment’s required rate of return. Zero-coupon bonds are the only type of fixed-income investments that are not subject to investment risk – they do not involve periodic coupon payments.
Interest rate risk is the risk that an investor’s bond will decline in value due to fluctuations in the interest rate. Interest rate risk is relevant when an investor decides to sell a bond before maturity and affects all types of fixed-income investments.
For example, recall that John paid $783.53 for a zero-coupon bond with a face value of $1,000, 5 years to maturity, and a 5% interest rate compounded annually. Assume that immediately after John purchased the bond, interest rates change from 5% to 10%. In such a scenario, what would be the price of the bond?
Price of bond = $1,000 / (1+0.10)5 = $620.92
If John were to sell the bond immediately after purchasing it, he would realize a loss of $162.61 ($783.53 – $620.92).
To conclude:
- Reinvestment risk is not relevant for zero-coupon bonds; and
- Interest rate risk is relevant for zero-coupon bonds.
More Resources
Thank you for reading CFI’s guide on Zero-Coupon Bond. To keep learning and developing your knowledge of financial analysis, we highly recommend the additional resources below:
FAQs
A zero-coupon bond is a debt security instrument that does not pay interest. Zero-coupon bonds trade at deep discounts, offering full face value (par) profits at maturity.
How do you solve for zero coupon bonds? ›
The target purchase price of a zero coupon bond, assuming a desired yield, can be calculated using the present value (PV) formula: price = M / (1 + i)^n. M is the face value at maturity, i is the desired yield divided by 2, and n is the number of years remaining until maturity times 2.
Is zero coupon bonds a good deal? ›
A zero-coupon bond will usually have higher returns than a regular bond with the same maturity because of the shape of the yield curve. Zero-coupon bonds are more volatile than coupon bonds, so speculators can use them to profit more from anticipated short-term price movements.
What is a zero-coupon bond quizlet? ›
What is a zero coupon bond? A bond that pays no coupons. It only pays the face value on the maturity date.
What is a zero-coupon bond for dummies? ›
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.
What are examples of zero-coupon bonds? ›
Examples of zero-coupon bonds include US Treasury bills, US savings bonds, long-term zero-coupon bonds, and any type of coupon bond that has been stripped of its coupons. Zero coupon and deep discount bonds are terms that are used interchangeably.
How do you solve coupon bonds? ›
The formula for the coupon rate consists of dividing the annual coupon payment by the par value of the bond. For example, if the interest rate pricing on a bond is 6% on a $100k bond, the coupon payment comes out to $6k per year.
How do you calculate zero-coupon bond spot rate? ›
The spot rate is calculated by finding the discount rate that makes the present value (PV) of a zero-coupon bond equal to its price. These are based on future interest rate assumptions. So, spot rates can use different interest rates for different years until maturity.
How to calculate the duration of a zero-coupon bond? ›
However, for zero-coupon bonds, duration equals time to maturity, regardless of the yield to maturity. The duration of level perpetuity is (1 + y) / y. For example, at a 10% yield, the duration of perpetuity that pays $100 annually will equal 1.10 / . 10 = 11 years.
Why would someone invest in a zero coupon bond? ›
The Zero Coupon bonds eliminate the reinvestment risk. Zero-Coupon bonds do not let any periodic coupon payments, and hence a fixed interest on Zero Coupon bonds is guaranteed. Fixed returns: The Zero Coupon bond is a perfect choice for those who prefer long-term investment and earn a lump sum.
Therefore, a zero-coupon bond must trade at a discount because the issuer must offer a return to the investor for purchasing the bond.
Are zero coupon bonds junk bonds? ›
Zero-coupon bonds emphasize the discount element of income to the exclusion of coupons; junk bonds emphasize the risk element contained in the interest yield on such securities; and indexed bonds simply match the rate of return, through either coupons or discounts, to some specified index in the hope of accurately ...
Why are zero coupon bonds risky? ›
If interest rates rise, the value of your zero coupon bond on the secondary market will likely fall. Long-term zeros can be particularly sensitive to changes in interest rates, exposing them to what is known as duration risk.
Which of the following best describes a zero-coupon bond? ›
Answer and Explanation: The correct answer is option d. A bond that has no coupons and pays a face value at maturity.
What is a zero-coupon bond of any maturity? ›
E) A zero-coupon bond of any maturity will have more interest rate price risk than any coupon bond, even a perpetuity. A shorter-term zero-coupon bond can have less price risk than a longer term coupon-paying bond, such as a perpetuity.
What are zero-coupon bonds an example of ___________? ›
Zero coupon bonds are an example of a original issue.
Why would someone invest in a zero-coupon bond? ›
The Zero Coupon bonds eliminate the reinvestment risk. Zero-Coupon bonds do not let any periodic coupon payments, and hence a fixed interest on Zero Coupon bonds is guaranteed. Fixed returns: The Zero Coupon bond is a perfect choice for those who prefer long-term investment and earn a lump sum.
What is a zero-coupon bond equivalent? ›
The coupon equivalent rate is a calculation of the effective yield on a zero-coupon bond. The effective yield is the annual rate of return attached with a period of interest rate, while a zero-coupon bond is a type of bond that provides no periodic interest to the bondholders.
What is the result of zero-coupon bonds? ›
A bond with a coupon rate of zero, therefore, is one that pays no interest. However, this does not mean the bond yields no profit. Instead, a zero coupon bond generates a return at maturity. 1 Bond investors look at a number of factors when assessing the potential profitability of a given bond.
