# Zero Coupon Bond

A zero-coupon bond (also called a zero) is a bond which pays no coupon payments. Its yield results from the difference between its issue price and maturity value and its current value equals the present value of its face value.

A zero-coupon bond is also called a deep discount bond because it is typically issued at a price which is significantly different from its face value. As the bond gets closer to its maturity, the value of the bond increases.

A zero-coupon bond differs from a traditional bond in the following ways:

- A regular bond pays periodic coupon payments while a zero-coupon bond does not pay any periodic cash flows;
- The return on a traditional bond results from both interest payments and price movement while a zero-coupon bond's total return results from difference between issue price and maturity value;
- A zero-coupon bond has zero reinvestment risk while a traditional bond has significant reinvestment risk;
- A zero-coupon bond has higher interest rate risk than a traditional bond.

When coupon-paying bonds are broken down into their principal and coupon components such that each payment is a zero-coupon bond, such zero-coupon components are called **strips**.

## Formula

### Value of a Zero-Coupon Bond

Because a zero-coupon bond has only one cash flow which occurs at the time of maturity of the bond, its price/value equals the present value of that cash flow discounted at the required rate of return.

The following formula can be used to work out value of a zero-coupon bond:

Value of Zero-Coupon Bond = | Face Value |

(1 + Yield)^{n} |

Where **yield** is the periodic bond yield and **n** refers to the total compounding periods till maturity.

### Yield on a Zero-Coupon Bond

Given the current price (or issue price) of a zero-coupon bond (denoted as **P**), its face value (also called maturity value) of **FV** and total number of **n** coupon payments, we can find out its yield to maturity using the following equation:

Zero-Coupon Bond Yield = | Face Value | ^{1/n} | − 1 | ||

P |

## Example

On 1 January 20X3, Andrews invested $50,000 in 100 zero-coupon bonds of $1,000 par value 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 20X3 is 6.8%. Find the value of the zero-coupon bond as at 31 December 2013 and Andrews expected income for the financial year 20X3 from the bonds.

Value (31 Dec 20X3) = | $1,000 | = $553.17 |

(1 + 6.8%)^{9} |

Value of 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).

by Obaidullah Jan, ACA, CFA and last modified on

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