Bond Valuation: Pricing Zero Coupon Bonds

Learn How to Price Zero Coupon Bonds

Zero coupon bonds, also known as discount bonds or pure discount bonds, are fixed-income instruments that do not pay periodic coupon payments. Instead, they are issued at a discount to their face value and provide a single payment at maturity, which includes both the return of principal and the accrued interest. Understanding the process of pricing zero coupon bonds is essential for evaluating their investment value, determining yields, and making informed decisions in debt and money markets.

Pricing Formula for Zero Coupon Bonds

The price of a zero coupon bond can be determined by discounting the future cash flow, which is the face value of the bond at maturity, using a required rate of return or discount rate. The general formula for pricing zero coupon bonds is as follows:

Bond Price = F / (1 + r)^n

Where:
F = Face value or principal payment at maturity
r = Required rate of return or discount rate
n = Number of periods (time to maturity)

Example 1:
Let's consider a zero coupon bond with the following characteristics:
Face value (F) = $1,000
Required rate of return (r) = 6%
Maturity (n) = 5 years

Using the pricing formula, we can calculate the price of this zero coupon bond:

Bond Price = $1,000 / (1 + 0.06)^5
Bond Price = $1,000 / 1.33822
Bond Price ≈ $747.26

Hence, the price of this zero coupon bond would be approximately $747.26.

Example 2:
Consider another zero coupon bond with the following characteristics:
Face value (F) = $10,000
Required rate of return (r) = 4.5%
Maturity (n) = 10 years

Applying the pricing formula, we can calculate the price of this zero coupon bond:

Bond Price = $10,000 / (1 + 0.045)^10
Bond Price = $10,000 / 1.61158
Bond Price ≈ $6,203.33

Therefore, the price of this zero coupon bond would be approximately $6,203.33.

Conclusion

Pricing zero coupon bonds involves calculating the present value of the bond's face value at maturity, discounted using a required rate of return. As zero coupon bonds do not make periodic interest payments, the entire return on investment comes from the difference between the purchase price and the face value at maturity. Understanding the pricing process allows investors to assess the attractiveness of zero coupon bonds, evaluate their yields, and make informed investment decisions in debt and money markets. It is worth noting that zero coupon bonds are particularly sensitive to changes in interest rates due to their single cash flow nature.

This article takes inspiration from a lesson found in FIN 4243 at the University of Florida.