Question

Five years ago, Rock Steady Corp issued a semiannual coupon bond with seven years until maturity. This bond was originally issued at par with a $1,000 face value. The coupon rate on the bond is 8%. Today, the yield-to-maturity (YTM) is 10%. What was yield to maturity of this bond when it was issued? Show calculations.

Answer 1

When a bond is bought at PAR of Face Value then the YTM is equal to the Coupon rate on the bond. Thus the YTM of the bond when issued would be 8%

Now Lets calculate to check if the theory is correct:

Here the Face value will be discounted semi annually for 7 years thus it will be discounted at 4% for 14 times. Similarly all the coupons would be received every 6 months thus coupons would be discounted at R/2% (4%) for n*2 (2*7) =14 years. Lets calculate the PV:

Here P = 1000 (Face Value)

r = 8% (paid semi annually) thus paid 4% every 6 months

n = 7 years (compounded 6 monthly) n = 14 years

CF = 40 (Coupon)

PV of Cash Flow = PV of Face Value + PV of Coupons

= 1000/(1.04)^14 + PV of Coupons

As we know PV of Annuity(Coupons)

= C *[(1-(1+r)^-n)/r]

= 1000 * [(1-(1.04)^-14)/0.04]

So PV of Cash Flow = 1000/(1.04)^14 + 40 * [(1-(1.04)^-14)/0.04]

= (1000/1.7316764476) + 40 * [(1-(0.5774750828)/0.04]

= 577.475 + 40 * [0.4225249172/0.04]

= 577.475 + 40 * [10.56312293]

= 577.475 + 422.525

= 1000

When a bond is bought at PAR of Face Value then the YTM is equal to the Coupon rate on the bond. Thus the YTM of the bond when issued would be 8%