Question

You observe the following annually-compounded (periodicity of one) spot rate curve:

Maturity (years)	Spot Rate
1	5.65%
2	5.40%
3	5.10%
4	4.90%
5	4.75%

A corporate bond with exactly 4 years until maturity pays a 5% annual coupon and is currently trading at a Z-spread of 75 bps. Based on the above spot rate curve, what is the value of the corporate bond per 100 of par?

Answer 1

Z-spread is the constant spread added to spot rates that makes the price of a security equal to the present value of its cash flows.

Maturity (Years) Rate

1 6.4%

2 6.15%

3 5.85%

4 5.65%

5 5.5%

FV = 100

Coupon Amount = (5/100)*100 = 5

Value of Bond = 5/(1.064) + 5/(1.0615)^2 + 5/ (1.0585)^3 + 5/ (1.0565)^4 + 100 / (1.0565)^4 = 97.63006