Question

Period (semi annual)	Treasury Spot Rate
1	7.00000%
2	7.04999%
3	7.09998%
4	7.12498%
5	7.13998%
6	7.16665%

What should be the price of an 8% coupon corporate bond with 3 years to maturity that is selling at a static spread of 110bp?

Answer 1

Assuming Face value = $1000

Coupon per period = (Coupon rate / No of payments per year) * Face value

Coupon per period = (8% / 2) * $100

Coupon per period = $40

Let us compute the Corporate bond price

Bond price = Coupon / (1 + (0.5 year spot rate + z-spread) / 2 ) + Coupon / (1 + (1 year spot rate + z-spread) / 2)² + Coupon / (1 + (1.5 year spot rate + z-spread) / 2)³ + Coupon / (1 + (2 year spot rate + z-spread) / 2)⁴ + Coupon / (1 + (2.5 year spot rate + z-spread) / 2)⁵ + Coupon / (1 + (3 year spot rate + z-spread) / 2)⁶ + Face value / (1 + (3 year spot rate + z-spread) / 2)⁶

Bond price = $40 / (1 + (7.00000% + 1.1%) / 2) + $40 / (1 + (7.04999% + 1.1%) / 2)² + $40 / (1 + (7.09998% + 1.1%) / 2)³ + $40 / (1 + (7.12498% + 1.1%) / 2)⁴  + $40 / (1 + (7.13998% + 1.1%) / 2)⁵ + $40 / (1 + (7.16665% + 1.1%) / 2)⁶ + $40 / (1 + (7.16665% + 1.1%) / 2)⁶

Corporate Bond price = $993.1955 or $993.20