MATH 373 Quiz 5 Fall 2018 November 20, 2018

Transcription

1 MATH 373 Quz 5 Fall 218 November 2, A callable bond matures at the end of 2 years for 1,. The bond pays coupons at a rate of 7% convertble sem-annually. The bond can be called at the end of 14 year for a call value of 1,5. The bond can be called at the end of 16 years for a call value of 1,35. Fnally, the bond can be called at the end of 18 years for a call value of 1,2. Determne the prce of ths callable bond to yeld a return of 7% convertble sem-annually. Soluton: I/Y N FV PMT CPT 7/2=3.5 14*2=28 1,5 (1,)(.7/2)=35 1, , , ,2 35 1, , 35 1,. Prce s 1, snce that s the lowest prce.

2 2. The stock of Bray Industres pays a quarterly dvdend wth the next dvdend payable n 2 months. The frst dvdend wll be 1. The second dvdend wll be 11. The thrd dvdend wll be 12. Each dvdend wll follow the same pattern wth each dvdend beng 1 greater than the pror dvdend. Usng the dvdend dscount method, determne the prce to yeld 1% compounded quarterly. Soluton: (4) We need. We are gven that.1 so (1.25) We multply by (1.25) because the frst dvdend s pad at the end of two months.

3 3. The stock of Crouthamel Company pays quarterly dvdends wth the next dvdend of 4 beng pad later today. Each dvdend thereafter ncreases 1.5% of the pror dvdend. In other words, the second dvdend at the end of three months wll be 4(1.15). The thrd dvdend pad at the end of sx months wll be 2 4(1.15), etc. Usng the dvdend dscount method, determne the prce of Crouthamel stock at an annual effectve dscount rate of 12%. Soluton: We need. We are gven that.12 so (1.12) (1.15)( ) 4(1.15) ( ) (1.15)( ) Because of poor wordng, some students nterpreted the queston to say that d.12. Then d.12 1 d (4) ( ) (1.15)( ) 4(1.15) ( ) (1.15)( )

4 MATH 373 Quz 5 Fall 218 November 2, The stock of Bray Industres pays a quarterly dvdend wth the next dvdend payable n 2 months. The frst dvdend wll be 12. The second dvdend wll be 13. The thrd dvdend wll be 14. Each dvdend wll follow the same pattern wth each dvdend beng 1 greater than the pror dvdend. Usng the dvdend dscount method, determne the prce to yeld 16% compounded quarterly. Soluton: (4) We need. We are gven that.16 so (1.4) We multply by (1.4) because the frst dvdend s pad at the end of two months.

5 2. The stock of Crouthamel Company pays quarterly dvdends wth the next dvdend of 8 beng pad later today. Each dvdend thereafter ncreases 1.% of the pror dvdend. In other words, the second dvdend at the end of three months wll be 8(1.1). The thrd dvdend pad at the end of sx months wll be 2 8(1.1), etc. Usng the dvdend dscount method, determne the prce of Crouthamel stock at an annual effectve dscount rate of 1%. Soluton: We need. We are gven that.1 so (1.1) (1.1)( ) 8(1.1) ( ) (1.1)( ) Because of poor wordng, some students nterpreted the queston to say that d.1. Then d.1 1 d (4) ( ) (1.15)( ) 8(1.15) ( ) (1.15)( )

6 3. A callable bond matures at the end of 2 years for 1,. The bond pays coupons at a rate of 7% convertble sem-annually. The bond can be called at the end of 14 year for a call value of 1,5. The bond can be called at the end of 16 years for a call value of 1,35. Fnally, the bond can be called at the end of 18 years for a call value of 1,2. Determne the prce of ths callable bond to yeld a return of 7% convertble sem-annually. Soluton: I/Y N FV PMT CPT 7/2=3.5 14*2=28 1,5 (1,)(.7/2)=35 1, , , ,2 35 1, , 35 1,. Prce s 1, snce that s the lowest prce.

7 MATH 373 Quz 5 Fall 218 November 2, The stock of Crouthamel Company pays quarterly dvdends wth the next dvdend of 6 beng pad later today. Each dvdend thereafter ncreases 2.5% of the pror dvdend. In other words, the second dvdend at the end of three months wll be 6(1.25). The thrd dvdend pad at the end of sx months wll be 2 6(1.25), etc. Usng the dvdend dscount method, determne the prce of Crouthamel stock at an annual effectve dscount rate of 15%. Soluton: We need. We are gven that.15 so (1.15) (1.25)( ) 6(1.25) ( ) (1.25)( ) Because of poor wordng, some students nterpreted the queston to say that d.15. Then d.15 1 d (4) ( ) (1.25)( ) 6(1.25) ( ) (1.25)( )

8 2. A callable bond matures at the end of 2 years for 1,. The bond pays coupons at a rate of 7% convertble sem-annually. The bond can be called at the end of 14 year for a call value of 1,5. The bond can be called at the end of 16 years for a call value of 1,35. Fnally, the bond can be called at the end of 18 years for a call value of 1,2. Determne the prce of ths callable bond to yeld a return of 7% convertble sem-annually. Soluton: I/Y N FV PMT CPT 7/2=3.5 14*2=28 1,5 (1,)(.7/2)=35 1, , , ,2 35 1, , 35 1,. Prce s 1, snce that s the lowest prce.

9 3. The stock of Bray Industres pays a quarterly dvdend wth the next dvdend payable n 2 months. The frst dvdend wll be 12. The second dvdend wll be 14. The thrd dvdend wll be 16. Each dvdend wll follow the same pattern wth each dvdend beng 2 greater than the pror dvdend. Usng the dvdend dscount method, determne the prce to yeld 2% compounded quarterly. Soluton: (4) We need. We are gven that.2 so (1.5) We multply by (1.5) because the frst dvdend s pad at the end of two months.