Question

A 4% annual coupon corporate bond with two years remaining to maturity has a Z-spread of 200 bps. The two-year, 2% annual payment government benchmark bond is trading at a price of 98.106. The one-year and two-year government spot rates are 2% and 3%, respectively, stated as effective annual rates.Assume all interest paid annually.

(a)Calculate the corporate bond price.

(b)Calculate the G-spread, the spread between the yields-to-maturity on the corporate bond and the government bond having the same maturity.

Answer 1

Assuming Face value = $100

Coupon per period = Coupon rate * Face value

Coupon per period = 4% * $100

Coupon per period = $4

Let us compute the Corporate bond price

Bond price = Coupon / (1 + 1 year spot rate + z-spread) + Coupon / (1 + 2 year spot rate + z-spread)² + Face value / (1 + 2 year spot rate + z-spread)²

Bond price = $4 / (1 + 2% + 2%) + $4 / (1 + 3% + 2%)² + $100 / (1 + 3% + 2%)²

Corporate Bond price = $98.177   

Let us compute the government benchmark bond YTM

Bond price = Coupon / (1 + YTM) + Coupon / (1 + YTM)² + Face value / (1 + YTM)²

98.106 = $2 / (1 + YTM) + $2 / (1 + YTM)² + $100 / (1 + YTM)²

Using Texas Instruments BA 2 plus calcultor

SET N = 2, PMT = 2, FV = 100, PV = -98.106

CPT --> I/Y = 2.9897

Yield to Maturity (YTM) of government benchmark bond = 2.9897%

Let us compute the Corporate bond YTM

Bond price = Coupon / (1 + YTM) + Coupon / (1 + YTM)² + Face value / (1 + YTM)²

98.177 = $4 / (1 + YTM) + $4 / (1 + YTM)² + $100 / (1 + YTM)²

Using Texas Instruments BA 2 plus calcultor

SET N = 2, PMT = 4, FV = 100, PV = -98.177

CPT --> I/Y = 4.9801

Yield to Maturity (YTM) of Corporate bond = 4.9801%

G-spread = Yield to Maturity of Corporate bond - Yield to Maturity of government benchmark bond

G-spread = 4.9801% - 2.9897%

G-spread = 1.9904% or 199.04 basis points