# Zero Coupon Bond

Zero coupon bond is a bond that pays no interest (coupon) over its life and is issued at a significant discount to its face value. The present value of the bond increases as it reaches maturity and the investors are compensated through this accrued interest which is paid at once at the maturity. A zero coupon bond is alternatively called a deep discount bond or more informally a zero.

Due to the time value of money, the present value of a single sum of money increases over time as it reaches maturity. The investors' income for a period equals the value of zero coupon bond at the end of the period minus the value of the zero coupon bond at the start of the period.

Sometimes normal coupon-paying bonds are broken down into their principal and coupon components such that each payment is a coupon bond in itself. Such zero coupon components are called strips.

## Formula: Value of a Zero Coupon Bond

In finance, value of any security equals the present value of its cash flows. A zero coupon bond has only one cash flow equal to its face value which occurs at the time of maturity of the bond.

Value of a Zero Coupon Bond = | Face Value |

(1 + Effective Rate of Interest)^{years to maturity} |

## Example

On 1 January 2013, Andrews invested $50,000 in 100 $1,000 par value zero coupon bonds issued by Stonehenge Travel Plc. The bonds were issued at a yield of 7.18%. The forecasted yield on the bonds as at 31 December 2013 is 6.8%. Find the value of the zero coupon bond as at 31 December 2013 and Andrews expected income for the financial year 2013 from the bonds.

Value of the zero coupon bond as at 31 December 2013 = $1,000 ÷ (1 + 6.8%)^{9} = $553.17

Value of Andrews total holding = 100 × $553.17 = $55,317

Expected accrued income = value at the end of a period − value at the start of a period = $55,317 − $50,000 = $5,317

This gain of $5,317 is made up of the unwinding of discount (the increase in present value as it nears maturity) plus 'capital gain' portion that results from positive movement in market yield on the bond.

The value of zero coupon bond will continue to increase till it reach $100,000 at the time of its maturity. Total dollar amount of interest earned by Andrews would be $50,000 ($100,000 minus $50,000).

Written by Obaidullah Jan