A BBB-rated corporate bond has a yield to maturity of 8.4%. A U.S. Treasury secu

Question

A BBB-rated corporate bond has a yield to maturity of 8.4%. A U.S. Treasury security has a yield to maturity of 7.0%. These yields are quoted as APRs with seminannual compounding. Both bonds pay semiannual coupons at an annual rate of 7.8% and have five years to maturity.

A. What is the price (expressed as a percentage of the face value) of the Treasury bond?

B. What is the price (expressed as a percengate of the face value) of the BBB-rated corporate bond?

C. What is the credit spread on the BBB bonds?

Explanation / Answer

A. Price = Interest * PVAF(r,nyear) + Maturity value * PVF(r, n year)

= 39 * PVAF(4.2%,10) + 1000 * PVF(4.2%,10)

= 39 * 8.031 + 1000 * 0.663

= 976.209

B. Price = Interest * PVAF(r,nyear) + Maturity value * PVF(r, n year)

= 39 * PVAF(3.5%,10)+ 1000 * PVF(3.5%,10)

= 39 * 8.317 + 1000 *0.709

= 1033.363

C. Credit Spread = YTM of BBB rated - YTM of treasury security

= 8.4% - 7.00% = 1.4%

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