# ABC Co. issued 14-year bonds a

ABC Co. issued 14-year bonds a year ago at a coupon rate of7.7%. The bonds make semiannual payments. If the YTM on these bondsis 6.0%, what is the current bond price? (Do not roundintermediate calculations. Round the final answer to 2 decimalplaces. Omit \$ sign in your response.)

 Solution: Current bond price is      1151.95 Working Notes: Sincethe bond was issued a year ago means , it remaining life other wordyears to maturity will 1 year lesser = 14-1 = 13 years Current bond price the present value of all the cash flow duringthe remaining life of the bond , and these cash flow is discountedby YTM of the bond in other word market interest rate for the bond. And the cash flow in the life of the bond are semi annual couponsand at end of life par value of bond as redemption value. Bond Price = Periodic Coupon Payments x Cumulative PVF @ periodicYTM (for t=0 to t=n) + PVF for t=n @ periodic YTM x Face value ofBond Coupon Rate = 7.7% Annual coupon = Face value of bond x Coupon Rate = 1,000 x 7.7% =\$77 Semi annual coupon = Annual coupon / 2 = \$77/2=\$38.5 YTM= 6% p.a (annual) Semi annual YTM= 6%/2 = 3% n= no.of coupon = No. Of years x no. Of coupon in a year = 13 x 2 = 26 Bond Price = Periodic Coupon Payments x Cumulative PVF @ periodicYTM (for t= to t=n) + PVF for t=n @ periodic YTM x Face value ofBond = \$38.5 x Cumulative PVF @ 3% for 1 to 26th + PVF @ 3% for 26thperiod x 1000 = 38.5 x 17.8768424 + 1,000 x 0.463694727 =1151.953159 =\$1,151.95 Hence Current price of the bond is     1151.95 Price is more than par value of 1000 as coupon rate is higher thanYTM of the bond Cumulative PVF @ 3% for 1 to 26th is calculated = (1 – (1/(1 +0.03)^26) ) /0.03 =17.87684242 PVF @ 3% for 26th period is calculated by = 1/(1+i)^n = 1/(1.03)^26=0.46369473 Please feel free to ask if anything about above solution in commentsection of the question.

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