Chaper 9 - Level 2 - Course FM Soluons ONLY CERTAIN PROBLEMS HAVE SOLUTIONS. THE REMAINING WILL BE ADDED OVER TIME.. (S08T3) Yvonne mus make a paymen of 80,000 a he end of one year. Addonally, she mus make a paymen of 40,000 a he end of wo years. Fnally, she mus make a paymen of 60,000 a he end of 3 years. She wans o purchase bonds o exacly mach her paymens. She can purchase he followng hree bonds: Bond Number Term of he Bond Annual Coupon Maury Value Year 0 00 2 2 Years 60 00 3 3 Years 70 200 Calculae he amoun of Bond 2 whch Yvonne should purchase. a. 36.50 b. 34.66 c. 37.67 d. 35.40 e. 35.7 80,000 = 00a + 60b + 70c 40,000 = 60b + 70c 60,000 = 270c From he las equaon, c = 60,000/270 Then, b = 6000 40,000 70 27 = 34.66 60 Copyrgh 203
Chaper 9 - Level 2 - Course FM Soluons 2. (S2HW) Hopkns Lfe Insurance Company s payng Keh an annuy due of 234 per year for he nex years. Calculae he Modfed duraon of Keh s annuy a an annual effecve neres rae of %. a. 3.7255 b. 4.098 c. 3.3868 d. 4.2959 e. 4.7255 D (, ) C v 234(0) v 234() v... 234(9) v 234a 0 9 9 a 9v 9 6.33492698 3.86878565 234( Ia ) 9 0. 234a a 6.75902386 3.72546053 Cv Modfed D(, ) v 3.72546053 3.72546053. Copyrgh 203
Chaper 9 - Level 2 - Course FM Soluons 3. (S08T3) Kyle purchases a year bond. The bond maures for 300 and has annual coupons of 80. Calculae he Macaulay duraon of Kyle s bond a an neres rae of 8%. a. 7.09 b. 4.87 c. 6.0886 d. 2.8246 e. 7.58 D (, ) PVBond Cv 80() v 80(2) v... 80() v 300() v Cv Prce of Bond 2 N= I/Y=8% PMT=80 FV=300 PVCPT=38.958046 80( Ia) 3000 D (, ) 38.958046 7.58 a v 80 3000v v 0.08 38.958046 4. (FHW) James has a loan of,000 whch s o be repad wh level annual paymens a an annual effecve neres rae of 2%. Calculae he Macaulay duraon of he loan usng he 2% neres rae. a. 4.58 b. 4.24 c. 3.6 d. 4.089 e. 2.5904 Cv 769.84v 769.84(2) v 769.84() v Cv 000 2.2 a v Cv.2 Cv 45846.48734 4.58 Cv 000 769.84 Ia 769.84 45846.48734 Copyrgh 203
Chaper 9 - Level 2 - Course FM Soluons 5. (FHW) The Macaulay Duraon of a perpeuy mmedae wh level annual paymens s 26. Deermne he neres rae ha was used o calculae he Macaulay Duraon. a. 0.03846 b. 0.226 c. 0.04 d. 0.037 P( ) C 2 v PIa 26 C P( ) v P( ) 26.04 25 Copyrgh 203
Chaper 9 - Level 2 - Course FM Soluons 6. (FHW) Sparks-Norrs Asse Parners (SNAP) manages he followng porfolo of bonds: D Bond Prce Macaulay Duraon 5,000 2,000 6 3 20,000 8 4 5,000 2 The duraon s calculaed a an annual effecve neres rae of 7%. Calculae he modfed duraon of SNAP s porfolo. a. 5.999 b. 5.607 c. 3.453 d. 3.694 e. 6.5 PORT DP P where D s Modfed Duraon In order o ge Modfed Duraon from Macaulay we mulply Macauly by v. DP v 5000 6v 000 8v 20000 2v 5000 P 5000 000 20000 5000 5.607 7. (FMP07) Calculae he modfed duraon of an annuy due wh paymens of 0 for years usng an neres rae of 8%. a. 3.58 b. 3.87 c. 4.7 d. 4.5 e. 4.87 Copyrgh 203
Chaper 9 - Level 2 - Course FM Soluons 8. (FMP07) Megan buys he followng bonds:.bond A wh a modfed duraon of 7 for 00;.Bond B wh a modfed duraon of 5 for 2000; and.bond C wh a modfed duraon of for 500. Calculae he modfed duraon of he porfolo. a. 6.3 b. 7.0 c. 7.3 d. 8.3 e. 8.8 9. (FMP07) John wans o absoluely mach a deb ha he owes under whch he mus make paymen of 00 n one year and 2000 n wo years. He can purchase he followng bonds:.bond A s a wo year bond wh annual coupons of 0 and a maury value of 00..Bond B maures n one year for 00 and pays a coupon of 80. Calculae he amoun of Bond B ha John should purchase. a. 758 b. 909 c. 926 d. 00 e. 88 Copyrgh 203
Chaper 9 - Level 2 - Course FM Soluons. (S07PQ) Calculae he modfed duraon of an annuy due wh paymens of 0 for years usng an neres rae of 8%. a. 3.58 b. 3.87 c. 4.7 d. 4.5 e. 4.87 9 9 9.08 0.08 0 9 C ( ) v.08.08.08.08 Cv.08 (.08)(.08)0.08 2805.50 3.58 724.69.08. (S07PQ) Megan buys he followng bonds:.bond A wh a Macaulay duraon of 7 for 00;.Bond B wh a Macaulay duraon of 5 for 2000; and.bond C wh a Macaulay duraon of for 500. Calculae he Macaulay duraon of he porfolo. a. 6.3 b. 7.0 c. 7.3 d. 8.3 e. 8.8 DP 7(00) 5(2000) (500) 7000 000 5000 6.3 P 00 2000 500 3500 Copyrgh 203
Chaper 9 - Level 2 - Course FM Soluons 2. (S2PQ) A perpeuy mmedae has a Macaulay duraon of 3.5 a an annual effecve neres rae of. Calculae. 2 3.5 2 2.5 8% 3. (S2PQ) A perpeuy due has a modfed duraon of 8 a an annual effecve neres rae of. Calculae. 2 2 2 8 4.286% 4. (S07PQ) John wans o absoluely mach a deb ha he owes under whch he mus make paymen of 00 n one year and 2000 n wo years. He can purchase he followng bonds:. Bond A s a wo year bond wh annual coupons of 0 and a maury value of 00.. Bond B maures n one year for 00 and pays a coupon of 80. Calculae he amoun of Bond B ha John should purchase. a. 0.758 b. 0.909 c. 0 926 d..000 e..88 A (0) = 2000 A =.888.888(0) + B (80) = 00 8.888 + B (80) = 00 B (80) = 88.888 B =.758 2 Copyrgh 203