Question

The Shield Corporation has BB-rated bonds with a yield to maturity of 6.40% APR. A U.S Treasury, with the same maturity, currently has a yield to maturity of 4.14% APR. Both bonds pay semi-annual coupons at a 6.24% APR and have 5.00 years until maturity. (assume $1,000 face value)

What is the current price of the Shield Corporation bond?

What is the current price of the Treasury bond?

Answer 1

The current price of the shield corporation bond is computed as shown below:

Coupon payment = 6.24% / 2 x $ 1,000 (Since bonds are semi annual hence divided by 2 )

= $ 31.20

YTM = 6.40% / 2 (Since bonds are semi annual hence divided by 2 )

= 3.20%

N = 5 x 2

= 10

So the bonds price will be

= $ 31.20 / 1.032¹ + $ 31.20 / 1.032² + $ 31.20 / 1.032³ + $ 31.20 / 1.032⁴ + $ 31.20 / 1.032⁵ + $ 31.20 / 1.032⁶ + $ 31.20 / 1.032⁷ + $ 31.20 / 1.032⁸ + $ 31.20 / 1.032⁹ + $ 31.20 / 1.032¹⁰ + $ 1,000 / 1.032¹⁰  

= $ 993.24 Approximately

The current price of the treasury bond is computed as shown below:

Coupon payment = 6.24% / 2 x $ 1,000 (Since bonds are semi annual hence divided by 2 )

= $ 31.20

YTM = 4.14% / 2 (Since bonds are semi annual hence divided by 2 )

= 2.07%

N = 5 x 2

= 10

So the bonds price will be

= $ 31.20 / 1.0207¹ + $ 31.20 / 1.0207² + $ 31.20 / 1.0207³ + $ 31.20 / 1.0207⁴ + $ 31.20 / 1.0207⁵ + $ 31.20 / 1.0207⁶ +$ 31.20 / 1.0207⁷ + $ 31.20 / 1.0207⁸ + $ 31.20 / 1.0207⁹ + $ 31.20 / 1.0207¹⁰ + $ 1,000 / 1.0207¹⁰

= $ 1,093.97 Approximately

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