Explain bond valuation with the following example:Calculate the market price of a $1,000 face value bond with a 14% coupon rate with 30 years until maturity. Current market rate is 9%.
The fair market price of a bond is given by the sum of the present value of all the cash inflows over the life of the bond.
P = C/(1+d) + C/(1+d)^2 +... C/(1+d)^n + M/(1+d)^n where C is the annual interest received, d is the discount rate, M is the maturity value and n is the life of the bond.
The series C/(1+d) + C/(1+d)^2 +... C/(1+d)^n can be evaluated as C*(1 - (1+d)^n)/d
This process is illustrated by calculating the value of the bond described in the problem.
Here, the interest payments are at a rate of 14% or $140, the maturity value is $1000 and the discount rate is 9%. This gives:
P = 140/(1.09) + 140/(1.09)^2 +... + 140/(1.09)^30 + 1000/(1.09)^30
=> 140(1 - (1.09)^-30)/(0.09) + 1000/(1.09)^30
=> 1438.31 + 75.37
The value of the bond is $1513.68