Question

A $1000 par value bond with 6 years to maturity pays semi-annual coupons at a rate of 12% APR, with next coupon paid 6-months from today. If the bond is currently priced at $1,049.35, what is it's yield to maturity?

Answer 1

Solution:

In the case of Bond Pricing, the cash flows value and the discount rate should always be consistent i.e. if  cash flows are received semiannually, time interval and required rate of return is also compounded semiannually,

Par Value $ 1000

Bond Price $ 1049.35

Remaining Life of the Bond = 6 years * 2 = 12 years

Coupon Rate = 12%/2 = 6% Semi-annual rate

YTM = [Coupon + (Maturity Value - Bond Price)/ Remaining life of the Bond] / [(Maturity Value + Bond Price)/2]

= [ $ 1000 * 6% + ($ 1000 - $ 1049.35)/12 ] / ($ 1000 + $ 1049.35)/2

= [$ 60 - $ 4.11] / $ 1024.675

= 5.45% semi annual

or YTM = 10.91% annualized

Effective Annual YTM, = (1+10.91%/2)² - 1

= 11.21%