(A) ASSUME THERE IS A BOND THAT MATURES IN 16.5 YEARS. THE BOND HAS A PAR VALUE
ID: 2710048 • Letter: #
Question
(A) ASSUME THERE IS A BOND THAT MATURES IN 16.5 YEARS. THE BOND HAS A PAR VALUE OF $1,000.00, PAYS INTEREST SEMI-ANNUALLY, AND HAS A CURRENT PRICE OF $954.33. THE YIELD TO MATURITY ON THE BOND IS CURRENTLY 7.9%. TO THE NEAREST PENNY, HOW MUCH INTEREST IS PAID EACH YEAR ON EACH BOND?
(B) SUPPOSE THIS BOND IS A ZERO COUPON BOND. THE YIELD TO MATURITY IS STILL 7.9%. TO THE NEAREST PENNY, WHAT IS YOUR ESTIMATE OF ITS CURRENT PRICE?
(C) SUPPORSE YOU HAD A CHOICE OF INVESTING IN EITHER OF THESE BONDS – THE ONE THAT PAYS CASH INTEREST AND THE ZERO COUPON BOND – BUT NOT BOTH. WHICH WOULD YOU CHOSE. IN ONE OR TWO SENTENCES JUSTIFY YOU ANSWER.
Explanation / Answer
FV = 1000 ; YTM = 7.9% ; Current Price = $ 954.33 ; Time To maturity = 16.5 years
Present Value of Coupon Payments + Present Value Of Maturity Value of Bond = 954.33
Present Value of Coupon Payments + 1000/(1+7.9%/2)^33 = 954.33
Present Value of Coupon Payments = 954.33 - 278.47 = 675.86
Coupon Payments * PVIFA(33 periods, 3.95%) = 675.86
Coupon Payments * 18.2664 = 675.86 = $37
Semi Annual Coupon = $37
Annual Coupon Interest = 37 * 2 = $74
If the bond is a zero coupon bond, there is only maturity payment at the end of 33 periods (16.5 *2) and hence its current price will be the present value of maturity amount which has been calculated above as $ 278.47
Investing in coupon bond and zero coupon bond will give the same return of 7.9%. However this is only true if the bond is trading at its fundamental value calculated above. If this is not the case, interest paying bond will be more attractive