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. Haie 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 Haie. 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 CPT I / Y P Cv.We are give. A 0 year bod with a par value of 10,000 will mature i 0 years for 10,500. The coupo rate is 8% covertible semi-aually. Calculate the price that Abhiit 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 PMT 400 FV CPT 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. Jaiyi purchases the bod for 1,000. Calculate Jaiyi s semi-aual yield to maturity o the bod. Solutio: P Fra Cv We kow Fr 500; C 0,000; P 1,000. This gives us We caot solve this algebraically so we will solve it usig our calculator. N 40 PV 1000 PMT 500 FV 0000 CPT I / Y.307 i This give us semi-aually. () Our aswer is * 4.614% covertible 4. Marissa purchases 0 year bod. The bod matures for 100,000. The bod has aual coupos. The first coupo is The secod coupo is 000. The third coupo is The 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, , , Jie bought a 10 year bod four years ago. The bod matures for 100,000 which is the par value. The bod has a coupo rate of 9.% covertible semi-aually. Jie paid 10,000 for the bod.

3 Today the bod has exactly six years util maturity. Calculate the price at which Jie could sell the bod if: a. The bod is sold to yield the same yield that was used to whe Jie bought the bod. b. The 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 PMT 4600 FV CPT 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 This value ca easily be obtaied usig your calculator. 1 ND AMORT P1 8 P 8 BAL 101, or N 1 I / Y PMT 4600 FV CPT 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 PMT 4600 FV CPT PV Chloe buys a bod to yield 8% covertible semi-aually for a price of 19, The bod has a coupo rate of 7% covertible semi-aually. The 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 PMT 700 FV 0000 CPT N semiaual periods is equal to 6.5 years.

4 7. Charles buys a 50 year bod with semi-aual coupos. The bod matures for Each semi-aual coupo is 5 durig the first year. Each semi-aual coupo is 10 durig the secod year. The 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 The 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 (S09T) A 8 year bod has a par value of X. The redemptio value is X+500. The 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. A five year bod with a par value of 1000 pays aual coupos of 10%. The 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 This shows that we are buyig it for less that maturity value which meas we are buyig this at a discout. The amout of discout= C P Justi buys a bod at a discout of 500. The bod is a 15 year bod with a par value of 8,000 ad a coupo rate of 6% covertible semi-aually. The bod matures for its par value. Calculate the yield covertible twice a year o this bod. Solutio: Usig your calculator: PV 7500 N 30 PMT 40 FV 8000 CPT I / Y ( ) % covertible semiaually.

6 11. Haah is cosiderig buyig two bods both priced to produce the same yield rate. The first bod is a 0 year bod with aual coupos of 500. The bod matures for 10,500. The purchase price of this bod is 7,000. The 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 PMT 40 FV 8000 CPT 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. A 0 year bod with a par value of 10,000 will mature i 0 years for 10,500. The coupo rate is 8% covertible semi-aually. The 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 PMT 400 FV CPT PV Do ot clear your calculator but chage to N 10 ad the CPT FV Now, fid P P a v Now we ca solve for the face value after the 10 th coupo paymet a Cv C 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 PMT 60 FV 1000 CPT PV Use the AMORT fuctio o the calculator. For example, year 1 is P1 1ad P 1. Year PRN INT Book Value

8 14. Calculate the Bod Amortizatio Schedule if the bod i Problem 13 is bought to yield 5%. Solutio: I / Y 5 N 5 PMT 60 FV 1000 CPT PV Use the AMORT fuctio o the calculator. Year PRN INT Book Value A 40 year bod with a par value of 5000 is redeemable at par ad pays semiaual coupos at a rate of 7% covertible semi-aually. The 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 PMT 175 FV 5000 CPT PV Use the AMORT fuctio with P 1 =61 ad P =61 PRN=13.84

9 16. A bod with a par value of 1000 is bought to yield 8% covertible semi-aually. The bod pays semi-aual coupos at a rate of 6% compouded semi-aually. The 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. Time Coupo Iterest Pricipal Book Value 14 / It = th Coupo 1000(.03) 30 Sice Pricipal is 1100 (Give) =>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 PMT 30 FV 1100 CPT PV Use the AMORT fuctio to fid the values of the table. To get the 5th Coupo Paymet row use P1=5 ad P=5 To get the 6th Coupo Paymet row use P1=6 ad P=6 Time Coupo Iterest Pricipal Book Value 5 th Coupo th Coupo

10 17. The book value of a bod immediately after the 13th coupo is 9,66.5. The bod has aual coupos of 700. The iterest i the 10th coupo is while the iterest i the 0th coupo is Calculate the book value immediately after the 14th coupo. Solutio: To 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. The amout of iterest i the 13 th paymet = (book value)(i) 966.5(.08)=741.3 The 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)= Yifa purchases 0 year bod. The bod matures for 100,000. The bod has aual coupos. The first coupo is The secod coupo is 000. The third coupo is The coupos cotiue to icrease util the 0 th coupo is 0,000. Yifa 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 A 0 year callable bod has a redemptio value of 10,000. The bod pays semiaual coupos of 500. The bod is callable at the ed of the 1 th, 14 th, ad 16 th years. The call price is listed i the followig table. 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. Solutio: PMT 500 I / Y 4 N FV CPT PV , , , ,979.8 Price= 11,966.44

12 0. Eric is buyig a 10 year callable bod with semi-aual coupos of 400 ad a maturity value of 5,000. The 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, PMT 400 I / Y.5 N FV CPT PV 14 5,500 8, ,00 8, ,000 9,87.0

13 1. A twety year bod is callable at the ed of te years or at the ed of fiftee years. The bod pays aual coupos of 100 ad matures for There is o call premium. The cost of the bod is 800. Calculate the miimum yield o this bod. Solutio: N 0 PMT 100 FV 1000 PV 800 CPT I / Y Yield= N CPT I/Y % % %

14 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 Time Coupo Iterest Pricipal Book Value 5 th Coupo th Coupo , %