HW Sol 3 - University of Texas at Dallas School of...

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Unformatted text preview: University of Texas at Dallas School of Management Finance 6301 Professor Day Corporate Finance Fall 2010 Solution Set 3 1. A U.S. government bond having 11 years to maturity has a coupon rate of 6 percent. The bond is currently trading at a price that gives the bond a semiannually compounded yield (to maturity) of 5.5 percent. Assuming that at the end of one year the bond offers investor's a yield to maturity of 5.0 percent, a. determine the return to holding the bond for one year Given that the current yield to maturity is 5.5 percent, the price of a bond having a 6 percent coupon rate and 6 years to maturity is B = 1 2 " $ 60 " [ 1 . 055 2 ( 1 " 1 ( 1 + . 055 2 ) 2x11 ) ] + $ 1000 ( 1 + . 055 2 ) 2x11 , = $30 x16.3435 + 0.55055 x $1000 , = $1040.86 . If we assume that the bond's yield to maturity is 5.0 percent at the end of the year (i.e., the yield to maturity falls to 5 percent), the price of the 6 percent coupon bond at the end of one year (given that the bond now has only 10 years to maturity) is B 1 = 1 2 " $ 60 " [ 1 . 050 2 ( 1 " 1 ( 1 + . 050 2 ) 2x10 ) ] + $ 1000 ( 1 + . 050 2 ) 2x10 , = $30 x15.58916 + 0.61027 x $1000 , = $1077.94 . Denote the original price of the bond at date by B and denote the new price of the bond by B 1 . Then if we denote the yearly coupon payments from the bond by C , the rate of return from holding the 6 percent 11- year bond for one year can be expressed as r = B 1 + C B- 1 = $ 1077 . 94 + $ 60 $ 1040 . 86- 1 = 0.0933 (9.33 percent). 2 The return computation above fails to account for the fact that first of the two coupon payments received could be reinvested to earn additional interest income. For example, if we assume that the $30 coupon payment received in the middle of the year can be reinvested at the semiannually compounded yield to maturity for the bond at date 1 (i.e., 5.0 percent), the annual rate of return to holding the bond is r' = B 1 + 1 2 x C + 1 2 x C x (1 + y 2 ) B- 1 = $ 1077 . 94 + $ 30 + $ 30 . 75 $ 1040 . 86- 1 = 0.0940 ( 9.40 percent). which is slightly in excess of the yearly return computed on the previous page. b. assuming that the bond is priced to yield 7.0 percent at the end of the year, determine the return from holding the bond. If the bond's yield to maturity is 7.0 percent at the end of the year (the required yield increases to 7 percent), the price of the 6 percent coupon bond (having 10 years to maturity) is B 1 = 1 2 " $60 " 1 .07 2 (1 # 1 (1 + .07 2 ) 2x10 ) + $1000 (1 + .07 2 ) 2x10 = $30 " 14.212403 + $1000 " 0.502566 = $928.94 The rate of return from holding the 6 percent 11- year bond for one year is r = $928.94 + $60 $1040.86 " 1 = " 0.0499 ( " 4.99 percent) c. assuming that the bond is priced to yield 6.0 percent at the end of the year, determine the return from holding the bond....
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HW Sol 3 - University of Texas at Dallas School of...

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