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?

PLEASE give step by step solutions!

		8%
		9%
		8.5%
		7.5%

Answer 1

Option ( A) is correct answer

Detailed solution is shown below ask if any doubt

When the bond is bought at PAR of Face Value than the YTM is equal to Coupon rate of the bond. Thus the YTM of the bond when issued will be 8%

Hence 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%

Option (A) is correct

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