Question

You are provided the following information about a bond that was issued 7 years ago. The bond has a par value of $1000, has 8 years until maturity, and carries a 10% coupon with interest being paid annually. What is the effective yield to maturity if we assume the bond is currently priced at $896.64 and you are additionally informed that coupons are paid semi-annually?

Select one:

a. 6.02%

b. 12.41%

c. 10%

d. 12.04%

Answer 1

Solution:

Yield to maturity is to be carried out by trial & error method but it can also be calculated with the approximate formula as follows:

YTM = [I+(F-P) / n] / (F+P) / 2 Where,

I= Periodic coupon amount = $ 50

F = Redemption amount = $ 1000

P= Current market price = $ 896.64

n= No. of periods = 8years *2 = 16 Periods

YTM = [50+(1000-896.64)/16] / (1000+896.64)/2

= 50 + (103.36)/16 / 1896.64/2

= 50+6.46 / 948.32

= 56.46 / 948.32

= 0.0595 i.e 5.95%

Effective annual YTM= (1+Periodic YTM)^2 - 1

= (1+0.0595)^2 - 1

=1.1225-1

= 0.1225 i.e 12.25%

Which is approximately equal to 12.41%

So Effective yield to maturity is 12.41%

I am also doing the same in excel for your reference .