MA373 F15 Homework Chapter 6 Solutions

# MA373 F15 Homework Chapter 6 Solutions - Chapter 6 Section...

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October 20, 2015 Copyright Jeffrey Beckley 2013, 2014, 2015 Chapter 6 Section 2 1. Hanjie purchases a 10 year zero coupon bond for 500 and will be paid 1000 at end of 10 years. Calculate the annual effective return received by Hanjie. Solution: Remember the formula, n j n P Fra Cv . Since this is a zero coupon bond, our formula simplifies to n j P Cv .We are given that P=500, n=10, C=1000 and we need to find j. 10 10 1/10 500 1000 0.5 1 0.5 1 0.071773 v j j We could also find this value using our calculator. 500 10 1000 / 7.1773 PV N FV CPT I Y   2. A 20 year bond with a par value of 10,000 will mature in 20 years for 10,500. The coupon rate is 8% convertible semi-annually. Calculate the price that Abhijit would pay if he bought the bond to yield 6% convertible twice a year. Solution: Once again, start with the formula n j n P Fra Cv . We are given that 10,000 F ; 10,500 C ; 20*2 40 n ; 0.08 0.04 2 i ; and 0.06 0.03 2 j . We can find the coupon 10,000*0.04 400 Fr . Now we can plug these values in to find P. 40 40 1 1.03 400 10500 1.03 0.03 12,464.76 n j n P Fra Cv P P You may also use your calculator: 40 / 3 400 10500 12464.76 N I Y PMT FV CPT PV    

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October 20, 2015 Copyright Jeffrey Beckley 2013, 2014, 2015 3. (F11HW) A 20 year bond with a 20,000 par value pays semi-annual coupons of 500 and is redeemable at par. Jaiyi purchases the bond for 21,000. Calculate Jaiyi’s semi-annual yield to maturity on the bond. Solution: n j n P Fra Cv We know 500; Fr 20,000; C 21,000 P . This gives us We cannot solve this algebraically so we will solve it using our calculator. 40 21000 500 20000 / 2.3072 N PV PMT FV CPT I Y   This give us (2) 0.023072 2 i . Our answer is 0.023072*2 4.614% convertible semi-annually. 4. Marissa purchases 20 year bond. The bond matures for 100,000. The bond has annual coupons. The first coupon is 1000. The second coupon is 2000. The third coupon is 3000. The coupons continue to increase until the 20 th coupon is 20,000. Marissa purchase the bond to yield an annual effective rate of 8%. Calculate the price that Marissa pays for the bond. Solution: n j n P Fra Cv is equivalent to ( ) n j P PV Coupons Cv . We know 20; n 100,000; C 0.08 j . First, let’s find the present value of the coupons. Coupons: 1000, 2000, 3000,…..,20,000. We can use the shortcut to the P,Q formula with P=Q=1. 20 20 20 20 20 20 ( ) 1000 1000 0.08 1 1.08 1.08 20 1.08 0.08 1000 78,907.93815 0.08 a v PV Coupons Ia Now we can find the price of the bond. 20 78,907.93815 100,000 1.08 100,362.76 P . 5. Jie bought a 10 year bond four years ago. The bond matures for 100,000 which is the par value. The bond has a coupon rate of 9.2% convertible semi-annually. Jie paid 102,000 for the bond.
October 20, 2015 Copyright Jeffrey Beckley 2013, 2014, 2015 Today the bond has exactly six years until maturity. Calculate the price at which Jie could sell the bond if: a.

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