Question

XYZ Inc. has issued a 30-year bond with a 6% coupon rate. If the market is yielding 7%, what is the current selling price of the bond?

Answer 1

We need to make 2 assumptions here: 1. Face value of bond is $100, 2. It is an annual coupon paying bond.If any of these are know for definite and are different from what assumed, please let me know in comments.

Price of a bond is present value of all cashflows associated with the bond - namely coupons and maturity (or face value), discounted by the market rate of interest (or yield to maturity).

Mathematically, it is given by the formula:

P is Price of a bond with coupon C, interest rate i, number of periods to maturity n and face value M

In our question, F = $100 (assumed), C = 6% * $100 = $6, n = 30 years, i = 7%.

Substituting the values in equation,

P = 74.4542 + 13.1367

P = $87.5910. Answer

{if the bond has face value of $1000, this value would then be $875.910. if bond is a semi-annual coupon paying bond, the mathematical formula would then become:

P = $87.5276}