mheducation.com Assignments: FA18:I AOL Mail (19614) e question l HW 6 Re: BUS-F
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mheducation.com Assignments: FA18:I AOL Mail (19614) e question l HW 6 Re: BUS-F370 Midter Campus Tutoring Fantasy Football I HW 6 Saved Help Save & Exit Submit Check my work 3 A bond with a face value of $1,000 has 8 years until maturity, carries a coupon rate of 6.0%, and sells for $1,075. a. What is the current yield on the bond? (Enter your answer as a percent rounded to 2 decimal places.) 9.09 points Current vield Skipped b. What is the yield to maturity if interest is paid once a year? (Do not round intermediate calculations. Enter your answer as a percent rounded to 4 decimal places.) Book Print Yield to maturity c. What is the yield to maturity if interest is paid semiannually? (Do not round intermediate calculations. Enter your answer as a percent rounded to 4 decimal places.) Yield to maturity Mc Graw Pre3 of 1 Next >Explanation / Answer
Required - a
Current yield on a bond = Coupon / Market price * 100
= 60 / 1075 * 100 = 5.58 %
Required - b
YTM = " r " that equals the equation ....... 60 * [ 1 - (1+r)-8 ] / r + 1000 * ( 1+r)-8 = 1075
Let us try the value of above equation with ......... r = 5%
60 * [ 1 - (1.05)-8 ] / 0.05 + 1000 * (1.05)-8 = 60 * 6.463213 + 1000 * 0.676839 = 1064.63
This lower than the required 1075. That means 5% is not the YTM and infact it is lower than 5%
So, let us try with ............ r = 4.75 %
60 * [ 1 - (1.0475)-8 ] / 0.0475 + 1000 * (1.0475)-8 = 60 * 6.5290 + 1000 * 0.689871 = 1081.61
Now we find out the exact YTM that lies between 4.5% and 5 % using the simple interpolation
4.75 % ............. 1081.61
X .............. 1075
5% .............. 1064.63
( X - 4.75) / ( 5 - 4.75) = ( 1075 - 1081.61 ) / (1064.63 - 1081.61)
X - 4.75 / 0.25 = 59.07 / 69.54
X - 4.75 = 0.25 * 6.61 / 16.98 = 0.10
X = 4.85 % .............. is the required YTM
Required - C
Same technique as done in Required - b ............ take half of ..... "r" values and double the n = 8 * 2 = 16.
We will get r = 2.43 .......... so annually = 2.43 * 2 = 4.86 % ............... is the YTM
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