Question

A $1,000 zero-coupon bond makes payment of the face value at maturity. How would you value the price of a zero-coupon bond and decide if you should buy the zero-coupon bond? Is the bond selling at premium, at discount or at par?

Answer 1

Zero-coupon bonds make no interest payment. Only the face value of the bonds is paid at the maturity. The price of zero-coupon bond can be calculated with the use of following formula:

Price of Zero-Coupon Bond = Face Value of Zero-Coupon Bond/(1+Interest Rate or Yield to Maturity or Required Rate of Return)^Years

Based on the above formula, it can be concluded that the price of zero-coupon bond will be less than $1,000. That, is, the bonds will be issued at a discount. For Instance, let us calculate the price of a 20 year zero-coupon bond with a face value of $1,000 and Yield to Maturity of 5%.

Price of Zero-Coupon Bond = 1,000/(1+5%)^20 = $376.89

The zero-coupon bond would generally be bought in order to gain from the difference between the purchase value and the face value. The investor purchases the bonds at the lower price and gets repaid the face value at the time of maturity. In the above example, the investor would buy the bonds at $376.89 and will get $1,000 for each bond held by him on maturity. Zero-coupon bonds are issued at discount in order to attract the investors to buy them. It is important to note that higher the interest rate/yield to maturity/required rate of return, the lower will be the bond price assuming other things remain constant. Similarly, longer the maturity period, lower will be the bond price assuming other things remaining constant. Therefore, the investor should take into account both the required rate of return and maturity period while evaluating the price of bond and making a decision to invest.