Question

Determine present value of 7 year bonds payable with face value of $89,000 and have a stated interest rate of 14%, paid semi-annually. The market interest rate is 16%.

Answer 1

Present Value of Interest Payments = C × F × (1 ? (1 + r)^-t)/r

The present value of the face value (i.e. the maturity value) = F/(1+r)^t

Where C = Bond’s Interest Rate, F = Face value of the bond, r = interest rate, t = Time Period.

Hence Price of a bond = C × F × (1 ? (1 + r)^-t)/r    +   F/(1+r)^t

C = 7% (14%/2), F = $89,000 , r = 8% (16%/2) , t = 14 (2x7)

Total Price of Bond = 7% x $89,000 x (1 – (1 + 8%)^-14)/8% + $89,000/(1 + 8%)^14

= $6230 x 8.244 + 30301.03 = $81,662.63