13. Jack purchases a corporate bond with par-value 30000 on January 15, 2000. Th
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13. Jack purchases a corporate bond with par-value 30000 on January 15, 2000. The bond matures at par-v alue on January 15, 2030 and pays semiannual coupons at an annual nominal rate of 5% mpounded semiannually every January 15 and July 15. The first coupon payment comes on July 15, 2000, and Jack immediately begins in accou originally priced to yield an annual rate of 6% compounded semiannually. vesting his coupon payments into a Money Market nt which earns an annual interest rate of 2% compounded semiannually. The bond is On June 15, 2020, Jack sells the bond at a price that is 8% higher than the stated market price (ie, clean price) at that time. Factoring in the sale of the bond and the coupon investments, what is Jack's overall yield on his original investment at the time that he sells the bond? Give your answer as an annual interest rate compounded semiannually. Round your percentage answer to two decimal places. Note: Between January 15, 2020 and June 15, 2020 a period of five months has passed. And, between January 15, 2020 and July 15, 2020 a period of six months has passed. Hint: Find the price at which the bond was purchased and the price at which the bond was sold, and use these along with the invested coupons to determine the rate that needs to be applied to the original purchase price in order to have it equal the value of the invested coupons and the selling price.Explanation / Answer
CALCULATION OF ORIGINAL PURCHASE PRICE OF BOND Semiannual coupon payment $750 (5/2)% of30000)=0.025*30000 Number of payment till maturity 60 (30*2) Par value $30,000 Yield per period(six months) 3% (6/2)% Present value of payments $25,848.67 (Using excel PV function with Rate=3%, Nper=60,Pmt=750,FV=30000,Type=0) Original purchase price of Bond $25,848.67 CALCULATION OF SALESL PRICE OF BOND At the time of sale, Number of payments from January 15 2021to January15,2030 19 Present value of payments on July15,2020 $27,851.43 (Using excel PV function with Rate=3%, Nper=19,Pmt=750,FV=30000,Type=0) Payment on July 15 , 2020 750 $28,601.43 Value as on June 15,2020=28601.43/(1+0.03/12) $28,530.10 Market price of the bond on June 15, 2020 $28,530.10 Sales price at 8% higher=1.08*28530.10 $30,812.51 CALCULATION OF AMOUNT RECEIVED FROM INVESTMENT OF COUPON PAYMENTS RECEIVED Semiannual coupon received $750 Number of payment received and invested 41 July15, 2000 to January 15, 2020) Semiannual interest rate= 1% Future value of payments on January 15 ,2020 $38,159.24 (Using FV function of excel with Rate=1%,Nper=41,Pmt=750, Type=1, begining of preiod) Value of 38159.24 after 5 months(on June15,2020) $ 38,318.24 (38159.24*(1+(0.01*(5/12)) TOTAL AMOUNT RECEIVED =(30812.51+38318.24)= $76,477.48 ORIGINAL INVESTMENT $25,848.67 Assume overall annual yield =r Number of years=20 years +5 months= 20.4166667 Years 25848.67*((1+r)^20.4166667)=76477.48 (1+r)=(76477.48/25848.67)^(1/20.4166667) 1+r= 1.05456672 r= 0.05456672 Annual yield= 5.46%
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