Question

Workman Software has 4.1 percent coupon bonds on the market with 14 years to maturity. The bonds make semiannual payments and currently sell for 91.57 percent of par. What is the YTM?

What is the effective annual yield (i.e., EAY or EAR)?

Answer 1

Lets assume par value to be $1000

Current value of bond = Par value x 91.57%

= 1000 x 91.57%

=915.7 $

Interest = 1000 x 4.1% x 1/2

= 20.5$

n = no of coupon payments = 14 x 2 = 28

YTM = Interest +(Face value -current market price/n) / (Face value + current market price/2)

= 20.5 + (1000-915.7 / 28) / (1000+915.7 / 2)

= 20.5 + (84.3/28) / (1915.7/2)

= 20.5 + 3.0107 / 957.85

= 23.5107/957.85

=0.024545

i.e 2.4545%

Thus annual YTM = 2.4545% x 2 = 4.9091%

Effective annual yield = (1+ Nominal YTM/n)^n

n = no. of compounding period

Effective annual yield = (1+4.9091%/2)^2 - 1

=(1+2.4545%)^2 - 1

=(1+0.024545)^2 - 1

=1.024545^2 - 1

=1.049692 - 1

= 0.049692

=4.9692 %