Question

Assume a par value of $1,000. Caspian Sea plans to issue a 10.00 year, semi-annual pay bond that has a coupon rate of 7.86%. If the yield to maturity for the bond is 8.11%, what will the price of the bond be?

Answer 1

Par value = $1000

Years to maturity = 10 years

Coupon rate = 7.86%

Yield to maturity = 8.11% or 0.0811

Solution :-

Semi annual coupon payment (C) = $1000 x 7.86% x 1/2 = $39.30

Semi annual periods (n) = 10 years x 2 = 20

Semi annual yield to maturity (r) = 0.0811/2 = 0.04055

Now,

Price of the bond = C/r x [1 - (1 + r)^-n] + [Par value x (1 + r)^-n]

= $39.30/0.04055 x [1 - (1 + 0.04055)^-20] + [$1000 x (1 + 0.04055)^-20]

= $39.30/0.04055 x [1 - (1.04055)^-20] + [$1000 x (1.04055)^-20]

= $39.30/0.04055 x [1 - 0.45158647765507] + [$1000 x 0.45158647765507]

= $39.30/0.04055 x 0.54841352234493 + [$451.586477655]

= $531.50805 + $451.586477655

= $983.09