P Fra Cv. Since this is a zero coupon bond, our formula simplifies to that P=500, n=10, C=1000 and we need to find j. 10

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1 Chapter 6 Sectio 1. (F11HW) Yacy purchases a 10 year zero coupo bod for 500 ad will be paid 1000 at ed of 10 years. Calculate the aual effective retur received by Yacy. Solutio: Remember the formula, P Fra Cv. Sice this is a zero coupo bod, our formula simplifies to that P=500, =10, C=1000 ad we eed to fid v 10 1/ We could also fid this value usig our calculator. PV 500 N 10 FV 1000 CP I / Y P Cv.We are give. (F11HW) A 0 year bod with a par value of 10,000 will mature i 0 years for 10,500. he coupo rate is 8% covertible semi-aually. Calculate the price that Adrew would pay if he bought the bod to yield 6% covertible twice a year. Solutio: Oce agai, start with the formula P Fra Cv We are give that F 10,000 ; C 10,500 ; 0* 40 ; i 0.04; ad We ca fid the coupo Fr 10,000* Now we ca plug these values i to fid P. P Fra Cv P P 1, You may also use your calculator: N 40 I / Y 3 PM 400 FV CP PV

2 3. (F11HW) A 0 year bod with a 0,000 par value pays semi-aual coupos of 500 ad is redeemable at par. Audrey purchases the bod for 1,000. Calculate Audrey s semi-aual yield to maturity o the bod. Solutio: P Fra Cv We kow Fr 500; C 0,000; P 1,000. his gives us We caot solve this algebraically so we will solve it usig our calculator. N 40 PV 1000 PM 500 FV 0000 CP I / Y.307 i his give us semi-aually. () Our aswer is * 4.614% covertible 4. (F11HW) Marissa purchases 0 year bod. he bod matures for 100,000. he bod has aual coupos. he first coupo is he secod coupo is 000. he third coupo is he coupos cotiue to icrease util the 0 th coupo is 0,000. Marissa purchase the bod to yield a aual effective rate of 8%. Calculate the price that Marissa pays for the bod. Solutio: P Fra Cv is equivalet to P PV ( Coupos ) Cv. We kow 0; C 100,000; First, let s fid the preset value of the coupos. Coupos: 1000, 000, 3000,..,0,000. We ca use the shortcut to the P,Q formula with P=Q=1. 0 a 0v 0 PV ( Coupos) 1000Ia , Now we ca fid the price of the bod. 0 P 78, , , (S1HW) Siqi bought a 10 year bod four years ago. he bod matures for 100,000 which is the par value. he bod has a coupo rate of 9.% covertible semi-aually. Siqi paid 10,000 for the bod.

3 oday the bod has exactly six years util maturity. Calculate the price at which Siqi could sell the bod if: a. he bod is sold to yield the same yield that was used to whe Siqi bought the bod. b. he bod is sold to yield 8% covertible semi-aually. Solutio: P Fra Cv N 10* 0; C 100,000 ; P Usig our calculator we should first solve for i r ; Fr (0.046) 4600 ; N 0 PV PM 4600 FV CP I / Y () i Keep i mid that a) We ow have 1 semiaual periods left util maturity. 1 P Fra Cv 4600a 100,000 v his value ca easily be obtaied usig your calculator. 1 ND AMOR P1 8 P 8 BAL 101, or N 1 I / Y PM 4600 FV CP PV b) Now we will use As above we ca either use 1 P Fra Cv 4600a 100,000 v ad ust plug i the ew 1 iterest rate or use our calculator. N 1 I / Y 4 PM 4600 FV CP PV (S1HW) Katherie buys a bod to yield 8% covertible semi-aually for a price of 19, he bod has a coupo rate of 7% covertible semi-aually. he bod matures for 0,000 which is its face value. Determie how may years util the bod matures. Solutio: P Fra Cv where deotes the umber of semiaual paymets ; P 19, ; r ; Fr 0000(.035) 700 ; We eed to use our calculator to fid. PV I / Y 4 PM 700 FV 0000 CP N semiaual periods is equal to 6.5 years.

4 7. (S09) Charles buys a 50 year bod with semi-aual coupos. he bod matures for Each semi-aual coupo is 5 durig the first year. Each semi-aual coupo is 10 durig the secod year. he semi-aual coupo cotiues to icrease each year util each semi-aual coupo is 50 i the 50th year. Calculate the price that Charles should pay to receive a yield of 10% covertible semi-aually. Solutio: P PV ( Coupos ) Cv C 1000 () 0.1 i 0.05 i he coupos are a series of paymets whose PV is foud but usig the formula that does t follow the rules. 50 a 50v PV ( Coupos) P v (S09) A 8 year bod has a par value of X. he redemptio value is X+500. he bod pays quarterly coupos at a rate of 6% covertible quarterly. Jacque bought this bod for to yield 8% covertible quarterly. Calculate X. Solutio: P Fra Cv 8*4 3; C X ; P ; r 0.015; Fr X ; 4 P Fra Cv Xa ( X 500) v v X a v

5 Chapter 6, Sectio 3 9. (S09) A five year bod with a par value of 1000 pays aual coupos of 10%. he bod has a maturity value of 100. Calculate the premium or discout whe this bod is purchased to yield 9% aually. (Be sure to state whether it is a premium or a discout.) Solutio: P Fra Cv Fr 0.1(1000) 100 ; 5; 0.09; C 100 P Fra Cv a v his shows that we are buyig it for less that maturity value which meas we are buyig this at a discout. he amout of discout= C P (S1HW) Justi buys a bod at a discout of 500. he bod is a 15 year bod with a par value of 8,000 ad a coupo rate of 6% covertible semi-aually. he bod matures for its par value. Calculate the yield covertible twice a year o this bod. Solutio: Usig your calculator: PV 7500 N 30 PM 40 FV 8000 CP I / Y ( ) % covertible semiaually.

6 11. (S08) Haah is cosiderig buyig two bods both priced to produce the same yield rate. he first bod is a 0 year bod with aual coupos of 500. he bod matures for 10,500. he purchase price of this bod is 7,000. he secod bod is a 15 year bod which matures for 8,000 ad pays aual coupos of 100t i year t. I other words, the coupo is 100 i the first year, 00 i the secod year, etc util it is 1,500 i year 15. Calculate the amout of premium or discout i the purchase of the secod bod. Be sure to state whether it is discout or premium. Solutio: Use your calculator to fid I: PV 7500 N 30 PM 40 FV 8000 CP I / Y Use I to calculate the price of the secod bod: P 100 Ia 8000v Where Ia P =6.51 Discout

7 Chapter 6, Sectio 5 1. (F11HW) A 0 year bod with a par value of 10,000 will mature i 0 years for 10,500. he coupo rate is 8% covertible semi-aually. he bod is bought to yield 6% covertible twice a year. Determie the book value of the bod immediately after the 10 coupo is paid. Solutio: Use your calculator to fid price: I / Y 3 N 40 PM 400 FV CP PV Do ot clear your calculator but chage to N 10 ad the CP FV Now, fid P P a v Now we ca solve for the face value after the 10 th coupo paymet a Cv C (F11HW) A five year bod with a par value of 1000 will mature i 5 years for Aual coupos are payable at a rate of 6%. Calculate the Bod Amortizatio Schedule if the bod is bought to yield 8% aually. Solutio: I / Y 8 N 5 PM 60 FV 1000 CP PV Use the AMOR fuctio o the calculator. For example, year 1 is P1 1ad P 1. Year PRN IN Book Value

8 14. (F11HW) Calculate the Bod Amortizatio Schedule if the bod i Problem 13 is bought to yield 5%. Solutio: I / Y 5 N 5 PM 60 FV 1000 CP PV Use the AMOR fuctio o the calculator. Year PRN IN Book Value (F11HW) A 40 year bod with a par value of 5000 is redeemable at par ad pays semi-aual coupos at a rate of 7% covertible semi-aually. he bod is purchased to yield 6% covertible semi-aually. Calculate the amortizatio of the premium i the 61 st coupo. Solutio: I / Y 3 N 80 PM 175 FV 5000 CP PV Use the AMOR fuctio with P 1 =61 ad P =61 PRN=13.84

9 16. (S08) A bod with a par value of 1000 is bought to yield 8% covertible semiaually. he bod pays semi-aual coupos at a rate of 6% compouded semiaually. he bod matures for C. If the Book Value of the Bod immediately after the 5 th Coupo is 1100, fill i the followig table: Solutio: Do the part is yellow first. Do the gree box ext. ime Coupo Iterest Pricipal Book Value 14 / It = th Coupo Sice Pricipal is 1100 (Give) 1000(.03) 30 =>It = a geometric sequece 6 th Coupo 1000(.03) (.04) = =1114 We ca get our calculator to do this problem as follows: I / Y 4 N 5 PM 30 FV 1100 CP PV Use the AMOR fuctio to fid the values of the table. o get the 5th Coupo Paymet row use P1=5 ad P=5 o get the 6th Coupo Paymet row use P1=6 ad P=6 ime Coupo Iterest Pricipal Book Value 5 th Coupo th Coupo

10 17. (S09) he book value of a bod immediately after the 13th coupo is 9,66.5. he bod has aual coupos of 700. he iterest i the 10th coupo is while the iterest i the 0th coupo is Calculate the book value immediately after the 14th coupo. Solutio: o start we must fid i. We kow that the amout of pricipal i each period is the coupo mius the iterest for the period. So, For the 10th period there is = i pricipal. For the 0th period there is = i pricipal. We also kow that the amout of pricipal i each period is geometric. Meaig, i i i.08 Now that we kow i we ca fid the Book Value after the 14 th paymet. he amout of iterest i the 13 th paymet = (book value)(i) 966.5(.08)=741.3 he amout of pricipal i the 13 th paymet = coupo- iterest =-41.3 Usig this we ca fid the book value after the 14 th paymet. BV 14 =BV 13 priicpal 13 BV 14 =966.5-(-41.3)= (S1HW) Marissa purchases 0 year bod. he bod matures for 100,000. he bod has aual coupos. he first coupo is he secod coupo is 000. he third coupo is he coupos cotiue to icrease util the 0 th coupo is 0,000. Marissa purchase the bod to yield a aual effective rate of 8%. 17 Calculate the pricipal adustmet i the 18 th coupo. Solutio OLB , or OLB v v v v , , 000 0, , , , (.08) 10, , , , 74.7

11 Chapter 6, Sectio (S08) A twety year bod has a redemptio value of 000 ad pays semiaual coupos of 48. he bod was purchased for Complete the followig table if it is ow 4 moths after the 15 th coupo. Solutio: Use your calculator to fid I/Y PV N 40 PM 48 FV 000 CP I / Y 4 wo Methods to fid B 15: Chage to N 5 ad CP PV Or d AMOR P1=15; P=15; BAL= heoretical Practical B 6 15 (1.04) (1.04) B15(1 (.04)) (1 (.04)) D 4 4 Accrued Coupo C 4 6 (1.04) 1 48s / D Accrued Coupo= = D Accrued Coupo= =

12 0. (S09) A bod with coupos of 100 is sold betwee coupo dates. he book value of the bod immediately after the last coupo was paid was 5,000. O the date of sale, usig the practical method, the dirty value was 5,45 ad the clea value was 5,15. Calculate the clea value usig the theoretical method. Solutio: Use the Practical method to fid. C D Fr( f ) f 100 f f 4 D B (1 f) (1.5 ) Now use the heoretical Method: f C B (1 ) Frs f (1.068) (F11HW) A 10 year bod with semi-aual coupos has a Book Value immediately after the 5 th coupo of 90,000. he dirty value 5 moths later usig the theoretical method is 94,591. Calculate the semi-aual yield o the bod. Solutio: , 000(1 i) 94, () 1.30% covertible semi-aually

13 . (F11HW) A bod with semi-aual coupos of 500 has a book value immediately after the 6 th coupo is 95,000. he clea value usig the practical method z moths after the 6 th coupo is 95, Calculate z if the yield rate is 7% covertible semi-aually. Solutio: B (1 f) Fr( f ) z z (0.035) z z 1 Chapter 6, Sectio 9 3. (S08) A 0 year callable bod has a redemptio value of 10,000. he bod pays semi-aual coupos of 500. he bod is callable at the ed of the 1 th, 14 th, ad 16 th years. he call price is listed i the followig table. Solutio: Call Date Call Value 1 th Year 11, th Year 10, th Year 10,650 Calculate the price that Nacy should pay i order to assure a yield of 8% covertible semi-aually. PM 500 I / Y 4 Price= 11, N FV CP PV , , , ,979.8

14 4. (S09) Eric is buyig a 10 year callable bod with semi-aual coupos of 400 ad a maturity value of 5,000. he bod may be called at the ed of 7 years with a call value of 5,500. It may also be called at the ed of 8 years with a call value of 5,00. Determie the price that Eric should pay to assure a yield of 5% covertible semiaually. Solutio: Price= 8, PM 400 I / Y.5 N FV CP PV 14 5,500 8, ,00 8, ,000 9,87.0

15 5. (S103) A twety year bod is callable at the ed of te years or at the ed of fiftee years. he bod pays aual coupos of 100 ad matures for here is o call premium. he cost of the bod is 800. Calculate the miimum yield o this bod. Solutio: N 0 PM 100 FV 1000 PV 800 CP I / Y Yield= N CP I/Y % %

16 Aswers %. 1, covertible semi-aually , a. 101, b. 105, years Discout of % covertible semi-aually 11. Discout of , No Aswer Provided 14. No Aswer Provided ime Coupo Iterest Pricipal Book Value 5 th Coupo th Coupo heoretical Practical D Accrued Coupo C , % covertible semi-aually , %