Mah 7 Tes Fall 01 November 7, 01 1. You are given he following spo ineres rae curve: Time Spo Rae r 0.5.% 1.0.5% 1.5.9%.0 4.4%.5 5.0%.0 5.7%.5 6.5% 4.0 7.5% Calculae he accumulaed value of a hree year annuiy immediae wih annual paymens of 500. PV 500 500 500 165.8654 1.05 (1.044) (1.057) AV 165.8654(1.057) 161.4468
. A bond has he following characerisics a 8% ineres: a. Price = 10,000 b. Modified Duraion = 17 c. Macaulay Convexiy = 50 Esimae he price of his bond using boh he duraion and he convexiy if he ineres rae was 7%. MacDur ModDur 1 i MacDur 17(1.08) MacCon MacDur 50 17(1.08) ModConv 15.80978 (1 i) (1.08) ( i i0 ) P( i) P( i0)[1 ModDur( i i0) ModConv( )] (.07.08) Pi ( ) 10, 000[1 17(.07.08) 15.80978( )] 11857.90466
. Telma has agreed o pay 100,000 o her parens in 8 years. She wans o fully immunize her ineres rae risk by purchasing he following wo zero coupon bonds: a. Bond 1 maures for 10,000 a he end of 6 years. b. Bond maures for 6000 a he end of 15 years. The annual effecive ineres rae is 4%. Calculae he number of Bond ha Telma will buy. (Assume parial bonds can be purchased.) Presen Value Liabiliy 8 100, 000(1.04) 7069.005 P1=amoun spen on Bond 1 P=amoun spen on Bond Mach Prices: P1+P=7069.005 Mach Duraion: P1(6) P(15)=7069.005(8) P1=7069.005-P (7069.005-P)(6)+P(15)=58455.164 48414.1-6P+15P=58455.164 9P 14618.041 P=167.56011 15 16,7.56011(1.04) 9, 4.984 4.878 6000 6000 # Bonds 4.878
4. Sarah owns a 5 year bond wih annual coupons of 500 and a mauriy value of 10,000. Sarah sells he bond monhs afer he 10 h coupon has been paid. The bond is sold o produce an annual yield rae of 6%. Calculae he clean value of his bond a he ime of sale based on he heoreical mehod. f 1 D B (1 j) 10 f N 5 I / Y 6 PMT 500 FV 10, 000 CPT PV=871.66484 ndamort P1=P=10 BAL=908.775101 1 1 D 908.775101(1.06) 9161.61958 1.06 1 AccCoupon=500( ) 1.80514.06 C D AC 908.979907
5. Trena has agreed o pay Jayme he following paymens: a. 0,000 a he end of years; b. 50,000 a he end of 5 years; and c. 10,000 a he end of 8 years. You are given ha v 0.9. Calculae he Modified Duraion of Trena s liabiliy. v ModDur C () v Cv 5 8 0, 000()(.9) 50, 000(5)(.9) 10, 000(8)(.9) (.9)[ ] 5 8 0, 000(.9) 50, 000(.9) 10, 000(.9) 0659.8768 (.9)( ).571514 5819.171
6. Trena has agreed o pay Jayme he following paymens: a. 0,000 a he end of years; b. 50,000 a he end of years; and c. 10,000 a he end of years. You are given he following hree bonds: a. A one year bond wih annual coupons of 100 and a mauriy value of 000 wih a price of 000. b. A wo year bond wih annual coupons of 80 and a mauriy value of 1000 wih a price of 100. c. A hree year bond wih annual coupons of 50 and a mauriy value of 1800 wih a price of 1580. Deermine he amoun of he wo year bond ha should be purchased o exacly mach he cash flows of Trena s liabiliy. (Assume ha you can purchase parial bonds.) Cash Flows Time 1 Benefi 0,000 50,000 10,000 Bond A 100 Bond B 80 1080 Bond C 50 50 1850 A(100) B(80) C(50) 0, 000 B(1080) C(50) 50, 000 C(1850) 10, 000 10, 000 C 5.405405405 of Bond C 1850 50, 000 50(5.405405405) B 46.04604605 of Bond B 1080 0, 000 50(5.405405405) 80(46.04604605) A 1.4087907 of Bond C 100 We wan o purchase 46.05 of he wo year bond.
7. The common sock of Kroeger LTD pays a quarerly dividend. The nex dividend is expeced o be.00 and is payable in monhs. Thereafer, each dividend is expeced o be 0.10 larger han he previous dividend. In oher words, he firs dividend will be.00, he second dividend will be.10, he hird dividend will be.0, ec. Calculae he price of Kroeger common sock o yield 1% compounded quarerly. (4) i.1 0.0 4 4 P Q 0.10 177.78 i i 0.0 (0.0)
8. The Baa Insurance Company has he following wo asses: a. A zero coupon bond which maures for 10,000 in five years and has an annual yield of 8%. b. A bond wih a price of 0,000 which has a Macaulay Duraion of and a Macaulay Convexiy of 11. All values were calculaed a an annual effecive ineres rae of 8%. Le Le Por D Mod be he Modified Duraion of his porfolio of asses a an ineres rae of 8%. Por C Mod be he Modified Convexiy of his porfolio of asses a an ineres rae of 8%. Calculae C Por Mod D. Por Mod 5 A 10000(5) v MacDur 5 5 10000v 5 A 10000(5) v MacConv 5 5 10000v MacDur ModDur Por Por 6805.8197 0000 (5) ().507787408 0000 6805.8197 0000 6805.8197.4795104 MacConv ModConv ModConv Por Por Por 6805.8197 0000 (5) (11) 14.55451186 0000 6805.8197 0000 6805.8197 14.55451186.507787408 15.4855105 (1.08) ModDur Por 1.755904
9. A 0 year bond has annual coupons of 400. The bond maures for 1,000. Calculae he Macaulay Duraion of his bond a an annual effecive ineres rae of 5.5%. MacDur C () v 400(1) v 400() v... 400(0) v 1000(0) v 0 0 C v 400v 400 v... 400v 1000v 0 0 Numeraor: P&Q Formula 400 0 0 =400a ( a 0 v ) 1000(0) v 0 0 0.055 400(11.950848) 77.777(11.950848 6.85457967) 89109.5047 10950.0705 Denominaor: Financial Calculaor N=0 I/Y=5.5 PMT=400 FV=1000 CPT PV=95.69577 10950.0705 MacDur= 14.1787906 95.69517
10. You are given he following hree bonds: a. A one year bond wih annual coupons of 100 and a mauriy value of 000 wih a price of 000. b. A wo year bond wih annual coupons of 80 and a mauriy value of 1000 wih a price of 100. c. A hree year bond wih annual coupons of 50 and a mauriy value of 1800 wih a price of 1580. Deermine he hree year spo ineres rae. Bond A 100 000 r1 0.05 (1 r ) Bond B 1 80 1080 100 (1 r ) 1.14498688 r 0.069718976 1.05 (1 r ) Bond C 1580 50 50 1850 1.05 (1.069718976) (1 r ) r 0.07511817
11. Calculae he modified convexiy for a year bond wih annual coupons of 00 and a mauriy value of 5000 using an annual effecive ineres rae of 8%. MacCon MacDur ModConv (1 i) 00(1) v 00() v 500() v MacDur 00v 00v 500v.88615046 00(1) v 00(4) v 500(9) v MacConv 00v 00v 500v 8.60444.88615046 8.60444 ModConv 9.50689566 (1.08)
1. Heaher purchases a callable bond o yield 7% converible semi-annually. The bond pays semiannual coupons a a rae of 8% converible semi-annually. The bond maures a he end of 10 years for is face amoun of 4000. The bond is callable a he end of 5 years for a call value of 400. The bond is also callable a he end of 7 years for a call value of 4100. Calculae he price ha Heaher paid for he bond. PMT I/Y N FV CPT PV 160.5 10 400 408.115869 160.5 14 4100 480.188585 160.5 0 4000 484.48066 The price Heaher paid is $480.188585
1. The preferred sock of STOAKES Inc sells has a quarerly dividend of 4 wih he nex dividend paid in monhs. Calculae he price of he preferred sock o produce an annual yield of 10%. (4) i 4 1.10 (1 ) 4 (4) i 0.0411689 4 Div PV increase wih 1 monh of ineres (4) i ( ) 4 1 4 = (1.0411689) 167.0695 0.0411689