Question

A $1,000 par value, 30 year bond is 5 years old. It pays interest once a year at an annually compounded coupon rate of 12%. The market is returning 8% on comparable bonds. What is the bond's market price?

Answer 1

Given,

Par value = $1000

Years to maturity (n) = 30 years - 5 years = 25 years

Coupon rate = 12%

Market interest rate (r) = 8% or 0.08

Solution :-

Semi annual coupon payment (C) = $1000 x 12% = $120

Now,

Bond's market price

= C/r x [1 - (1 + r)^-n] + [par value x (1 + r)^-n]

= $120/0.08 x [1 - (1 + 0.08)^-25] + [$1000 x (1 + 0.08)^-25]

= $1500 x [1 - (1.08)^-25] + [$1000 x (1.08)^-25]

= $1500 x [1 - 0.14601790491291] + [$1000 x 0.14601790491291]

= $1500 x 0.85398209508709 + [$146.01790491291]

= $1,280.97314263 + $146.01790491291

= $1426.99