Question

Consider the following information from September 15, 2015, for a coupon bond with a face value of $1,000 and a maturity date of September 15, 2017: Coupon rate: 5% Yield to maturity: 7.5% a. What was the bond’s current yield? b. Why is the bond’s yield to maturity greater than its coupon rate?

Answer 1

a. Current yield = Interest / Present value

= $50 / $955.11

= 5.23%

Note:- Present value of bond = Face / (1+ yiled)^{number of payment} + Interest [1 - (1+yield)^{-number of payment}] / yield

=1000 / (1+ 0.075)²+ ($1000*5%)[1 - (1+0.075)^-2] / 0.075

=1000 / (1.075)²+ 50 [1 - (1.075)^-2] / 0.075

=1000 / (1.075)²+ 50 [1 - 1/(1.075)²] / 0.075

=1000 / 1.15563 + 50 [1 - 1/1.15563] / 0.075

= 865.33 + 89.78

= 955.11

b. bond’s yield to maturity greater than its coupon rate because Bond present value ($955.11) is less than its par value ($1000) ,