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# Yield to Maturity: Compute price of zero coupon bonds

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a. What is the price (expressed as a percentage of the face value) of a one-year, zero-coupon corporate bond with a AAA rating?
b. What is the credit spread on AAA-rated corporate bonds?
c. What is the credit spread on B-rated corporate bonds?
d. How does the credit spread change with the bond rating? Why?

The following table summarizes the yields to maturity on several one-year, zero-coupon securities:

Security Yield (%)
Treasury 3.15
AAA corporate 3.30
BBB corporate 4.30
B corporate 5.00

a. What is the price (expressed as a percentage of the face value) of a one-year, zero-coupon corporate bond with a AAA rating?
b. What is the credit spread on AAA-rated corporate bonds?
c. What is the credit spread on B-rated corporate bonds?
d. How does the credit spread change with the bond rating? Why?

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#### Solution Preview

First, we answer part b. and c.

Credit spread is simply the difference between a bond and the T-bill.

So for AAA bond, the credit spread is 0.15%, for BBB bond is 1.15%, and for the B bond is 1.85%.

d. The lower rated the bond is, the greater the credit spread must be. The definition for credit spread is "The credit spread reflects the additional net yield an investor can earn from a security with more credit risk relative to one with less credit risk." (from Wikipedia). ...

#### Solution Summary

Yield to Maturity: Compute price of zero coupon bonds

\$2.19