Calculate Bond Maturity

[diemhuongpham]

Dear all,

Please help instruct to calculate this exercise as below:

Bond A has a coupon rate 8%, maturity of 15 years and is trading at par. Bond B has the same bond rating as bond A, has 7.5% coupon rate paid semiannually and it trades 5% below par. What is the maturity of Bond B?

Much thanks all,

 

[David Harper CFA FRM]

Hi @diemhuongpham Interesting. The question requires that we make an assumption (it makes the assumption) that if the bonds have the same rating, then the must have the same yield (aka, yield to maturity). It's important to understand why equivalent ratings do not (necessarily) imply equivalent yields, even beyond the fact that ratings are ordinal measures; e.g., if identical ratings might instead imply equivalent credit spreads (additions to the risk free rate curve), in which case, the implied yields would not be identical.

If we look beyond this presumption and accept the intention of the question, we can infer the yield of Bond A must be 8.0% (equal to its coupon rate when price equals par) such that we are solving for the maturity of 5% discounted bond with 7.5% s.a. coupon that yields 8.0%. With the calculator: 4 I/Y, -95 P/V, 3.75 PMT, 100 FV and CPT N = 41.03; i.e., 20 years. I hope that's helpful,