One year ago, Phutki Corp. issued a $1,000 par value, 11 percent (annual payment

Question

One year ago, Phutki Corp. issued a $1,000 par value, 11 percent (annual payment) coupon bond. At the time the bond was issued it had 15 years to maturity. Currently this bond is selling for $1,000 in the bond market. Phutki Corp. is now planning to issue a $2,000 par value bond with a coupon rate of10%(semi-annualpayments)thatwillmature25yearsfromtoday. Assumingthattheriskinessof the new bond is the same as the previous bond (i.e., the YTM on the new bond is equal to the current YTM on the previous bond), how much will investor's pay for this new bond?

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Explanation / Answer

Previous bond price, 1000 =(1000*0.11)((1+k)^15 -1)/(k(1+k)^15 + 1000/(1+k)^15 at k = 0.11 (=11%) , RHS = 1000 = LHS Hence ytm = k = 0.11 = 11 % Semi-annual coupon rate = 10/2 % = 0.10/2, periods = 25*2 =50, semi-annual yield = 0.11/2 = 0.055 New bond price, P = (1000*0.10/2)(1.055^50 -1)/(0.055*1.055^50) +1000/1.11^25 => = 920.18 ($) (ANSWER)

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