Question

# 22. Consider a 2-year zero-coupon bond and a 2-year coupon bond that both have a face...

22. Consider a 2-year zero-coupon bond and a 2-year coupon bond that both have a face value of \$100. The coupon bond has a coupon interest rate equal to 5%. Both bonds currently have the same yield to maturity of 6%. Which statement is FALSE?
A) Both bonds are trading at a discount.

B) The zero-coupon bond is trading at a discount but the coupon bond is trading at a premium.

C) The internal rate of return for both bonds is equal to each other.
D) The coupon bond declines stronger in price than the zero-coupon bond when their yield to maturity rises from 6% to 7% (compare the declines in \$ terms).
Ans: B

Price of zero coupon bond can be calculated by using the following excel formula:
=PV(rate,nper,pmt,fv)
=PV(6%,2,0,-100)
= \$89

Price of coupon bond can be calculated by using the following excel formula:
=PV(rate,nper,pmt,fv)
=PV(6%,2,-5,-100)
= \$98.17

The price of both bonds are below the face value. That means both bonds are trading at a discount. Thus, Statement B is false.

The statement "The zero-coupon bond is trading at a discount but the coupon bond is trading at a premium" is false.

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