Question

Company X has 8% coupon bonds on the market with 20 years to maturity. If the bonds make semiannual payments and they are sold for 97.5% of par, what is the YTM? What is the current yield? What is the effective annual yield?

Answer 1

Let us assume face value of bond is 1000

Market value is 975

Coupon rate is 8%

Semi annual coupon rate is 4%

When market rate is equal to 4% then value of bond will be 1000

Value of bond when market rate is 5%

=40(PVIFA 5% 40p) + 1000/(1.05)^40

=40(17.1591)+ 142

= 828.4

Now by using interpolation method we can find yield

= 4 +(1000-975)/(1000-828.4)

= 4.1285%

Annual rate = 8.256

2) current yield is = coupon /mv

= 40/975 =4.10

Annual rate is 8.205

3) effective Annual yield on bond

Semi annual yield = 4.145%

Effective rate = (1+0.041285)^2 - 1 = 8.427%