# Zero-Coupon Bond: Definition, Formula, Example etc.

### Key Points:

• The word Coupon represents “Interest.”
• Interest is not paid for the invested amount.
• The difference between discounted purchase price and face value of the bond is the income of the investor.
• The earnings of Zero Coupon Bond are higher than the Regular Bond’s earnings.
• The maturity period of this bond is longer than Regular bond.

### What is Zero-Coupon Bond?:

Zero-Coupon Bond is a debt security where the investors will not get any interest against his invested money but he will get a big discount while purchasing the bond. At the time of maturity, when the investor will go to the liquidation he will receive the full face value amount. Normally, a zero coupon bond has a higher return than the regular bond with the same maturity.

Hence, Zero Coupon bond is the bond which has a zero interest and the investor purchase it with lower price than its face value, and reimbursed full face value amount at the time of maturity.

There are different types of Zero Coupon bond. From the start, some company is issued their bond as zero-coupon instruments. Again, some company transforms into zero coupon instruments after a financial institution divest of its interest coupon, and repackages as zero-coupon bonds.

Zero-Coupon bond also known as an accrual bond, and the word coupon represents interest.

### Pricing Formula of Zero – Coupon Bonds:

Pricing of bond is important to determine how much amount an investor will be paid at the time of purchasing the bonds. As Zero-Coupon bond purchases with a discount, hence it is important, how much discount to be determined for ascertaining the price. However, to calculate the price of a zero-coupon bond, following formula to be used:

Price of Bond = Face Value/(1+r) n

Where:

Face value is the future (maturity) value of the bond.

r is the required rate of return/interest

n is the numbers of years up to maturity.

This formula uses when the interest is compounded annually. But practically it can be paid semiannually, when the formula will be:

Price of Bond = Face Value/(1+r/2) nx2

The difference between annually and semi-annually formula is:

In semiannually, the ‘r’ is divided by two and ‘n’ is multiplied by two.

### Examples of a Zero-Coupon Bonds:

Example -1: Annual Compounding

Robi is intending 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 7% compounded annually. What price Robi will pay for the bond today?

Price of bond = \$1,000/(1+.07)5 = \$713.27

Hence, the price that Robi will pay for the bond today is \$713.27.

#### Example 2: Semi-annual Compounding

Robi is intending 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 7% compounded semi-annually. What price Robi will pay for the bond today?

Price of bond = \$1,000 / (1+0.07/2)5*2 = \$709.22

The price that Robi will pay for the bond today is \$709.22