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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?

#### 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

## Bonds and Yield Related Questions

Can you please assist me with theses questions?

3. A bond has a coupon rate of 8.5% and 18 years until maturity. If the yield to maturity is 6.7%, what is the price of the bond?

5. A bond sells for \$864.50 and has a coupon rate of 6%. If the bond has 16 years until maturity, what is the yield to maturity of the bond?

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16. Bond X is a premium bond with an 8% coupon, a Yield to Maturity of 6 percent, and 15 years to maturity. Bond Y is a discount bond with 8% coupon, a Yield to Maturity of 10 %, and also 15 years to maturity. If interest rates remain unchanged, what do you expect the price of these bonds to be 1 year from now? In 5 years? In 10 years? In 14 years? In 15 Years? What's going on here?

18. Bond J is a 4% coupon bond. Bonk K is a 10% coupon bond. Both bonds have 10 years to maturity and have a Yield To Maturity of 7%. If interest rates suddenly rise by 2%, what is the percentage price change of these bonds? What if rates suddenly fall by 2% instead? What does this problem tell you about the interest rate risk of lower-coupon bonds?

25. A bond with a coupon rate of 7% sells at a yield to maturity of 8%. If the bond matures in 13 years, what is the Macaulay duration of the bond? What is the modified duration?