Zero coupon bond value = F ÷ (1+ r)t
F = face value of bond
r = rate or yield
t = time to maturity
Zero coupon bond is also known as pure discountbond or sometimes also as discount bond. Basically, zero coupon bond do notpays periodic payments rather you will get one lump sum amount at the end ofterm. The amount which a user gets on maturity date is known as face value. Asit appears from name ‘discount bond’ is sold below from its face value ororiginal price with standard dividend payments periodically.
As it can be seen in the formula above that the original price or face value of zero coupon bond is discounted to present value. Yield would be used in the formula to calculate the original value of the zero bond. The value of bond may fluctuate after issuance of the bond as the current interest rates of the market will influence prices.
Zero Coupon Bond Illustration
Lets suppose a zero coupon bond is issued for 5 years havinga face value of $150 along with a rate of 7%, now we put all these values inexpression above;
= $150 ÷ (1.07)5
So, the original price of bond would be$106.951 which we get from zero coupon bond value formula. Moreover, the facevalue after 5 years would be $100 for this bond.
Zero coupon bond illustration with changing rate
If we assume with above example that theinterest rate changes to 4% after the issuance of the bond while it was 7% atthe time of issuance. Here we can see about the impact by using same formula;
= $150 ÷ (1.04)5
After solving the equation you can seethe difference clearly.