Question

1. How much would the price of a 10 year semi-annual 13% coupon rate bond be, if the market interest rate is 18%? How much would it be if the interest rate drops to 10%? At which interest rate level this bond will be sold for its par value?

Answer 1

Bond Price = C x [1-{1/(1+r)ⁿ}]/r + M/(1+r)ⁿ

Where,

M = Face Value= $ 1,000 (Assumed)

C = Coupon Amount = $ 1,000 x 13 % /2 = $ 1,000 x 0.13/2 = $ 1000 x 0.065 = $ 65

r = rate of interest = 18 % p.a. or 0.18/2 = 0.09 semiannually

n = no. of periods = 10 x 2 = 20 periods

Bond price = $ 65 x [1-{1/ (1+0.09)²⁰}]/0.09 + $ 1,000/ (1+0.09)²⁰

                    = $ 65 x [1-{1/ (1.09)²⁰}]/0.09 + $ 1,000/ (1.09)²⁰

                    = $ 65 x [1-{1/ 5.604411}]/0.09 + $ 1,000/5.604411

                    = $ 65 x (1-0.178431)/0.09 + $ 178.4309

                    = $ 65 x (0.821569/0.09) + $ 178.4309

                   = $ 65 x 9.128546 + $ 178.4309

                    = $ 593.3555 + $ 178.4309 = $ 771.7864 or $ 771.79

If interest rate is 10 % p.a. or 0.05 semiannually,

Bond price = $ 65 x [1-{1/ (1+0.05)²⁰}]/0.05 + $ 1,000/ (1+0.05)²⁰

                    = $ 65 x [1-{1/ (1.05)²⁰}]/0.05+ $ 1,000/ (1.05)²⁰

                    = $ 65 x [1-{1/ 2.653298}]/0.05 + $ 1,000/ 2.653298

                    = $ 65 x (1- 0.376889)/0.05 + $ 376.8895

                    = $ 65 x (0.623111/0.05) + $ 376.8895

                   = $ 65 x 12.46221 + $ 376.8895

                    = $ 810.0437 + $ 178.4309 = $ 1,186.9332 or $ 1,186.93

When the interest rate and coupon rate will be same i.e. 13 %, the bond will trade at its par value.