Question

Suppose a five-year, $1000 bond with annual coupons has a price of $950 and a yield to maturity of 6%. What is the bond's coupon rate?

Answer 1

Suppose the annual coupon amount be C.

Bond price = C x PVIFA (n, i) + F x PVIF (n, i)

                    = C x PVIFA (5, 6%) + F x PVIF (5, 6%)

                    = C x [{1-(1+0.06)^-5}/0.06] + $ 1,000 x (1+0.06)^-5

                    = C x [{1-(1.06)^-5}/0.06] + $ 1,000 x (1.06)^-5

                    = C x [(1-0.747258172866057)/0.05] + $ 1,000 x 0.747258172866057

                    = C x (0.252741827133943/0.05) + $ 747.258172866057

                   = C x 4.21236378556572 + $ 747.258172866057

$ 950 = C x 4.21236378556572 + $ 747.258172866057

C x 4.21236378556572 = $ 950 - $ 747.258172866057

                                       = $ 202.741827133943

C = $ 202.741827133943/4.21236378556572 = $ 48.1301799784405

C = Face value x coupon rate/annual coupon frequency

$ 48.1301799784405 = $ 1,000 x coupon rate

Coupon rate = $ 48.1301799784405/ $ 1,000 = 0.0481301799784405 or 4.813 %

Coupon rate of the bond is 4.813 %