## What are Zero-Coupon Bonds?

A zero-coupon bond is a financial instrument that does not render interest. They normally trade at high discounts, and offer full face par value, at the time of maturity.

The spread between the purchase price of the bond and the price that the bondholder receives at maturity is described as the profit of the bondholder.

Normally in the case of bonds, some are issued as zero-coupon instruments right from the beginning.

However, some bonds also transform into zero-coupon bonds after they are restructured and repackaged by the owner. Zero-Coupon Bonds also fluctuate a lot in price compared to normal bonds.

## How do Zero-Coupon Bonds work?

As mentioned earlier, zero-coupon bonds do not render interest payments. The only profit or interest payment is generated at the end of the term when the bond matures.

Hence, the difference between the purchase price of the bond, and the face value of the bond tends to be the profit.

The greatest incentive for zero-coupon bondholders is the fact that they are predictable. Once the purchase is made, they know for sure that they would be getting the face value of the bond, which would be their profit.

Therefore, even before the bond matures, they are certain of their profit.

Similarly, investors do not need to worry about market fluctuation for bonds with a relatively shorter maturity duration since the bond’s face value is not contingent on market fluctuations.

## The formula for Zero-Coupon Bonds

The price of zero-coupon bonds is calculated using the formula given below:

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Price = M / (1 + r) ^ n, where

• M = maturity value of the bond. (In other words, the face value of the bond)
• R = required rate of return (or interest rate)
• N = number of years till maturity

These bonds can either offer annual compounding or semi-annual compounding. In the case where the bonds offer semi-annual compounding the following formula is used to calculate the price of the bond:

Price = M / (1 + r/2) ^ n*2

## Examples of Zero-Coupon Bonds

Calculating the price of zero-coupon bonds varies depending on whether the bonds offer annual or semi-annual compounding.

The calculation of the price of a bond is given in two illustrations below:

• Annual Compounding Bonds

Mr. Tee is looking to purchase a zero-coupon bond with a face value of \$50 and 5 years till maturity. The interest rate on the bond is 2% and will be compounded annually.

In the scenario above, the face value of the bond is \$50. However, to calculate the price that needs to be paid for the bond today, the following formula is used:

Price of the bond = M / (1 + r) ^ n = 50 / (1+0.02) ^5 = \$45.287

Therefore, \$45.3 is the amount that Mr.Tee will pay for the bond today.

• Semi-Annual Compounding Bonds

Mr. Tee is looking to purchase a zero-coupon bond with a face value of \$50 and 5 years till maturity. The interest rate on the bond is 2% and will be compounded semi-annually.

In this scenario, the face value is also \$50, but the only difference is that interest will be compounded semi-annually. Therefore, the price of the bond today will be calculated using the following formula:

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Price = M / (1 + r/2) ^ n*2 = 50 / (1 + 0.02/2) ^ 10 = \$45.264