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CHAPTER 7 Bonds and Their Valuation  āļžāļąāļ™āļ˜āļšāļąāļ•āļĢāđāļĨāļ°āļāļēāļĢāļ›āļĢāļ°āđ€āļĄāļīāļ™āļ„āđˆāļēāļžāļąāļ™āļ˜āļšāļąāļ•āļĢ ,[object Object],[object Object],[object Object],[object Object]
What is a bond?  āļžāļąāļ™āļ˜āļšāļąāļ•āļĢāļ„āļ·āļ­āļ­āļ°āđ„āļĢ ,[object Object]
What is a bond?  āļžāļąāļ™āļ˜āļšāļąāļ•āļĢāļ„āļ·āļ­āļ­āļ°āđ„āļĢ ,[object Object],[object Object],[object Object],[object Object],[object Object]
Bond markets āļ•āļĨāļēāļ”āļžāļąāļ™āļ˜āļšāļąāļ•āļĢ ,[object Object],[object Object],[object Object]
Key Features of a Bond āļĨāļąāļāļĐāļ“āļ°āļ—āļĩāđˆāļŠāļģāļ„āļąāļāļ‚āļ­āļ‡āļžāļąāļ™āļ˜āļšāļąāļ•āļĢ ,[object Object],[object Object]
Key Features of a Bond āļĨāļąāļāļĐāļ“āļ°āļ—āļĩāđˆāļŠāļģāļ„āļąāļāļ‚āļ­āļ‡āļžāļąāļ™āļ˜āļšāļąāļ•āļĢ ,[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object],[object Object]
Call Provision  āđ€āļ‡āļ·āđˆāļ­āļ™āđ„āļ‚āļāļēāļĢāđ€āļĢāļĩāļĒāļāļ„āļ·āļ™āļžāļąāļ™āļ˜āļšāļąāļ•āļĢ ,[object Object]
Effect of a call provision ,[object Object],[object Object],[object Object]
What is a sinking fund? āđ€āļ‡āļīāļ™āļ—āļļāļ™āļˆāļĄāļ„āļ·āļ­āļ­āļ°āđ„āļĢ ,[object Object]
What is a sinking fund? āđ€āļ‡āļīāļ™āļ—āļļāļ™āļˆāļĄāļ„āļ·āļ­āļ­āļ°āđ„āļĢ ,[object Object],[object Object]
What is a sinking fund? āđ€āļ‡āļīāļ™āļ—āļļāļ™āļˆāļĄāļ„āļ·āļ­āļ­āļ°āđ„āļĢ ,[object Object],[object Object]
How are sinking funds executed? āđ€āļ‡āļīāļ™āļ—āļļāļ™āļˆāļĄāļĄāļĩāļāļēāļĢāļ”āļģāđ€āļ™āļīāļ™āļāļēāļĢāļ­āļĒāđˆāļēāļ‡āđ„āļĢ ,[object Object],[object Object]
How are sinking funds executed? āđ€āļ‡āļīāļ™āļ—āļļāļ™āļˆāļĄāļĄāļĩāļāļēāļĢāļ”āļģāđ€āļ™āļīāļ™āļāļēāļĢāļ­āļĒāđˆāļēāļ‡āđ„āļĢ ,[object Object],[object Object]
Bond Valuation  āļāļēāļĢāļ›āļĢāļ°āđ€āļĄāļīāļ™āļĄāļđāļĨāļ„āđˆāļēāļžāļąāļ™āļ˜āļšāļąāļ•āļĢ ,[object Object],[object Object]
The value of financial assets 0 1 2 n k CF 1 CF n CF 2 Value ...
Other types (features) of bonds   āļžāļąāļ™āļ˜āļšāļąāļ•āļĢāļ›āļĢāļ°āđ€āļ āļ—āļ•āđˆāļēāļ‡ āđ† ,[object Object],[object Object]
Other types (features) of bonds   āļžāļąāļ™āļ˜āļšāļąāļ•āļĢāļ›āļĢāļ°āđ€āļ āļ—āļ•āđˆāļēāļ‡ āđ† ,[object Object],[object Object],[object Object]
What is the opportunity cost of debt capital?   āļ•āđ‰āļ™āļ—āļļāļ™āđ€āļŠāļĩāļĒāđ‚āļ­āļāļēāļŠāļ‚āļ­āļ‡āđ€āļ‡āļīāļ™āļ—āļļāļ™āļ—āļĩāđˆāđ„āļ”āđ‰āļˆāļēāļāļŦāļ™āļĩāđ‰āļŠāļīāļ™ āļ„āļ·āļ­ āļ­āļ°āđ„āļĢ ,[object Object],[object Object]
What is the value of a 10-year, 10% annual coupon bond, if k d  = 10%? 0 1 2 n k 100 100 + 1,000 100 V B  = ? ...
Using a financial calculator to value a bond ,[object Object],INPUTS OUTPUT N I/YR PMT PV FV 10 10 100 1000 -1000
An example: Increasing inflation and k d ,[object Object],INPUTS OUTPUT N I/YR PMT PV FV 10 13 100 1000 -837.21
An example: Decreasing inflation and k d ,[object Object],INPUTS OUTPUT N I/YR PMT PV FV 10 7 100 1000 -1210.71
The price path of a bond ,[object Object],Years  to Maturity 1,372 1,211 1,000 837 775 30 25   20   15   10   5   0 k d  = 7%. k d  = 13%. k d  = 10%. V B
Bond values over time  āļĄāļđāļĨāļ„āđˆāļēāļ‚āļ­āļ‡āļžāļąāļ™āļ˜āļšāļąāļ•āļĢāļ•āļĨāļ­āļ”āļ­āļēāļĒāļļāļ‚āļ­āļ‡āļžāļąāļ™āļ˜āļšāļąāļ•āļĢ ,[object Object],[object Object]
Bond values over time  āļĄāļđāļĨāļ„āđˆāļēāļ‚āļ­āļ‡āļžāļąāļ™āļ˜āļšāļąāļ•āļĢāļ•āļĨāļ­āļ”āļ­āļēāļĒāļļāļ‚āļ­āļ‡āļžāļąāļ™āļ˜āļšāļąāļ•āļĢ ,[object Object],[object Object],[object Object],[object Object]
āļœāļĨāļ•āļ­āļšāđāļ—āļ™āļˆāļēāļāļžāļąāļ™āļ˜āļšāļąāļ•āļĢ BOND  YIELDS āļ­āļąāļ•āļĢāļēāļ”āļ­āļāđ€āļšāļĩāđ‰āļĒāļ‚āļ­āļ‡āļžāļąāļ™āļ˜āļšāļąāļ•āļĢāļ–āļđāļāļāļģāļŦāļ™āļ”āđ„āļ§āđ‰āļ•āļēāļĒāļ•āļąāļ§ āđāļ•āđˆāļœāļĨāđ„āļ”āđ‰āļŦāļĢāļ·āļ­āļœāļĨāļ•āļ­āļšāđāļ—āļ™āļ—āļĩāđˆāļœāļđāđ‰āļĨāļ‡āļ—āļļāļ™āļˆāļ°āđ„āļ”āđ‰āļĢāļąāļšāļˆāļēāļāļžāļąāļ™āļ˜āļšāļąāļ•āļĢ āļˆāļ°āđ€āļ›āļĨāļĩāđˆāļĒāļ™āđāļ›āļĨāļ‡āļ­āļĒāļđāđˆāļ•āļĨāļ­āļ”āđ€āļ§āļĨāļē āļ‚āļķāđ‰āļ™āļ­āļĒāļđāđˆāļāļąāļšāļŠāļ āļēāļžāļ•āļĨāļēāļ”āļ›āļąāļˆāļˆāļļāļšāļąāļ™ āļœāļĨāļ•āļ­āļšāđāļ—āļ™āļˆāļēāļāļāļēāļĢāļĨāļ‡āļ—āļļāļ™āđƒāļ™āļžāļąāļ™āļ˜āļšāļąāļ•āļĢāļŠāļēāļĄāļēāļĢāļ–āļ„āļģāļ™āļ§āļ“āđ„āļ”āđ‰  3  āļ§āļīāļ˜āļĩ 1. Yield  To  Maturity 2. Yield  To  Call 3. Current  Yield
What’s “yield to maturity”? ,[object Object],YTM  āļ„āļ·āļ­āļ­āļąāļ•āļĢāļēāļœāļĨāļ•āļ­āļšāđāļ—āļ™āļ—āļĩāđˆāļœāļđāđ‰āļĨāļ‡āļ—āļļāļ™āļˆāļ°āđ„āļ”āđ‰āļĢāļąāļš āļ–āđ‰āļēāļ–āļ·āļ­āļžāļąāļ™āļ˜āļšāļąāļ•āļĢāđ„āļ›āļˆāļ™āļ–āļķāļ‡āļ§āļąāļ™āļ„āļĢāļšāļāļģāļŦāļ™āļ”āđ„āļ–āđˆāļ–āļ­āļ™
What is the YTM on a 10-year, 9% annual coupon, $1,000 par value bond, selling for $887? ,[object Object]
Using a financial calculator to find YTM ,[object Object],INPUTS OUTPUT N I/YR PMT PV FV 10 10.91 90 1000 - 887
Find YTM, if the bond price was $1,134.20. ,[object Object],INPUTS OUTPUT N I/YR PMT PV FV 10 7.08 90 1000 -1134.2
Yield  to  Call : YTC YTC  āļ„āļ·āļ­āļ­āļąāļ•āļĢāļēāļœāļĨāļ•āļ­āļšāđāļ—āļ™āļ—āļĩāđˆāđ„āļ”āđ‰āļĢāļąāļšāļˆāļēāļāļžāļąāļ™āļ˜āļšāļąāļ•āļĢ  āļ–āđ‰āļēāļžāļąāļ™āļ˜āļšāļąāļ•āļĢāļ–āļđāļāđ€āļĢāļĩāļĒāļāļĄāļēāđ„āļ–āđˆāļ–āļ­āļ™āļāđˆāļ­āļ™āļ§āļąāļ™āļ—āļĩāđˆāļ„āļĢāļšāļāļģāļŦāļ™āļ” Price of bond =  ÎĢ (INT/(1+k d ) t  + (Call price)/(1+k d ) N t=1 N
āļžāļąāļ™āļ˜āļšāļąāļ•āļĢāļĄāļđāļĨāļ„āđˆāļēāļ—āļĩāđˆāļ•āļĢāļēāđ„āļ§āđ‰   1,000  āļšāļēāļ— āļ­āļąāļ•āļĢāļē āļ”āļ­āļāđ€āļšāļĩāđ‰āļĒ   10 %  āļ āļēāļĒāļŦāļĨāļąāļ‡āļāļēāļĢāļ­āļ­āļāļˆāļģāļŦāļ™āđˆāļēāļĒāļˆāļ°āđ€āļĢāļĩāļĒāļ āđ„āļ–āđˆāļ–āļ­āļ™āļ„āļ·āļ™āđ„āļ”āđ‰āļ āļēāļĒāđƒāļ™  10  āļ›āļĩ āļĢāļēāļ„āļēāđ„āļ–āđˆāļ–āļ­āļ™  1 , 100  āļšāļēāļ—  āđ€āļĄāļ·āđˆāļ­āļ­āļ­āļāļˆāļģāļŦāļ™āđˆāļēāļĒāđāļĨāđ‰āļ§  1  āļ›āļĩ āļ­āļąāļ•āļĢāļēāļ”āļ­āļāđ€āļšāļĩāđ‰āļĒāļ‚āļ­āļ‡āļ•āļĨāļēāļ” āļĨāļ”āļĨāļ‡āđ€āļŦāļĨāļ·āļ­  5  %   āļ—āļģāđƒāļŦāđ‰āļĢāļēāļ„āļēāļ‹āļ·āđ‰āļ­  /  āļ‚āļēāļĒāļžāļąāļ™āļ˜āļšāļąāļ•āļĢāļŠāļđāļ‡āļ‚āļķāđ‰āļ™ āđ€āļ›āđ‡āļ™  1,494.93  āļšāļēāļ—  āļœāļđāđ‰āļĨāļ‡āļ—āļļāļ™āļ—āļĩāđˆāļ‹āļ·āđ‰āļ­āļžāļąāļ™āļ˜āļšāļąāļ•āļĢāđƒāļ™ āļĢāļēāļ„āļē  1 ,494.93  āļšāļēāļ— āļ–āļ·āļ­āđ„āļ§āđ‰  9  āļ›āļĩāļˆāļ™āļāļ§āđˆāļēāļˆāļ°āļ–āļđāļāđ€āļĢāļĩāļĒāļ āđ„āļ–āđˆāļ–āļ­āļ™āļ„āļ·āļ™āļˆāļ°āđ„āļ”āđ‰āļĢāļąāļšāļ­āļąāļ•āļĢāļēāļœāļĨāļ•āļ­āļšāđāļ—āļ™ (YTC)   āļ”āļąāļ‡āļ™āļĩāđ‰  āļ•āļąāļ§āļ­āļĒāđˆāļēāļ‡
V B   =  N   100  +  Call  Price t =  1  ( 1 + k d  )  t   ( 1 + k d  )  N   1,494.93  =  N   100  +  1,100 t =  1  ( 1 + k d  )  t   ( 1 + k d  )  N   1.  āđƒāļŠāđ‰āđ€āļ„āļĢāļ·āđˆāļ­āļ‡āļ„āļģāļ™āļ§āļ“āļ˜āļĢāļĢāļĄāļ”āļē k d  = YTC = 4.21 %
0 1 2 3 - 1,494.93 100 100 100 9 100 1,100 YTC=? YTC = 4.21 %
N PV PMT FV COMP i EXE 4.21 = YTC 9 100 1,100 -1,494.93 2.  āđƒāļŠāđ‰  Financial Calculator :
A 10-year, 10% semiannual coupon bond selling for $1,135.90 can be called in 4 years for $1,050, what is its  yield to call (YTC)  ? ,[object Object],INPUTS OUTPUT N I/YR PMT PV FV 8 3.568 50 1050 - 1135.90
Yield to call ,[object Object],[object Object],[object Object],[object Object]
If you bought these callable bonds, would you be more likely to earn the YTM or YTC? ,[object Object],[object Object],[object Object]
When is a call more likely to occur? ,[object Object],[object Object],[object Object],[object Object]
Current Yield   āļ”āļ­āļāđ€āļšāļĩāđ‰āļĒāļ—āļĩāđˆāđ„āļ”āđ‰āļĢāļąāļš āļĢāļēāļ„āļēāļ•āļĨāļēāļ”āļ›āļąāļˆāļˆāļļāļšāļąāļ™ āļžāļąāļ™āļ˜āļšāļąāļ•āļĢāļˆāđˆāļēāļĒāļ”āļ­āļāđ€āļšāļĩāđ‰āļĒāļ›āļĩāļĨāļ°  100  āļšāļēāļ— āļĢāļēāļ„āļēāļ•āļĨāļēāļ”āļ›āļąāļˆāļˆāļļāļšāļąāļ™  985  āļšāļēāļ— 985 Current  Yield  =  =  10.15 % Current  Yield āļ­āļąāļ•āļĢāļēāļœāļĨāļ•āļ­āļšāđāļ—āļ™āļ›āļąāļˆāļˆāļļāļšāļąāļ™ āļ•āļąāļ§āļ­āļĒāđˆāļēāļ‡  100 =
Definitions
An example:  Current and capital gains yield ,[object Object],[object Object],[object Object]
Calculating capital gains yield ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
āļāļēāļĢāļ›āļĢāļ°āđ€āļĄāļīāļ™āļ„āļ§āļēāļĄāđ€āļŠāļĩāđˆāļĒāļ‡āļ‚āļ­āļ‡āļžāļąāļ™āļ˜āļšāļąāļ•āļĢ ASSESSING  THE  RISKINESS  OF  A  BOND āļ„āļ§āļēāļĄāđ€āļŠāļĩāđˆāļĒāļ‡āļ—āļĩāđˆāļŠāļģāļ„āļąāļāđ„āļ”āđ‰āđāļāđˆ 1.  INTEREST  RATE  RISK āļ„āļ§āļēāļĄāđ€āļŠāļĩāđˆāļĒāļ‡āļˆāļēāļāļ­āļąāļ•āļĢāļēāļ”āļ­āļāđ€āļšāļĩāđ‰āļĒ 2.  REINVESTMENT  RATE  RISK āļ„āļ§āļēāļĄāđ€āļŠāļĩāđˆāļĒāļ‡āđƒāļ™āļāļēāļĢāļāļĨāļąāļšāđ€āļ‚āđ‰āļēāđ„āļ›āļĨāļ‡āļ—āļļāļ™āļ„āļĢāļąāđ‰āļ‡āđƒāļŦāļĄāđˆ
What is interest rate (or price) risk? ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
0 500 1,000 1,500 0% 5% 10% 15% 1-year 10-year k d Value . . . . . .
What is reinvestment rate risk? ,[object Object],[object Object],[object Object],[object Object],[object Object]
Reinvestment rate risk example ,[object Object],[object Object],[object Object],[object Object],[object Object]
Conclusions about interest rate and reinvestment rate risk ,[object Object],Low High Reinvestment rate risk High Low Interest  rate risk Long-term AND/OR Low coupon bonds Short-term AND/OR High coupon bonds
Semiannual bonds   āļžāļąāļ™āļ˜āļšāļąāļ•āļĢāļ—āļĩāđˆāļˆāđˆāļēāļĒāļ”āļ­āļāđ€āļšāļĩāđ‰āļĒāļ—āļļāļāļ„āļĢāļķāđˆāļ‡āļ›āļĩ ,[object Object],[object Object],[object Object],INPUTS OUTPUT N I/YR PMT PV FV 2n k d  / 2 cpn / 2 OK OK
What is the value of a 10-year, 10% semiannual coupon bond, if k d  = 13%? ,[object Object],[object Object],[object Object],INPUTS OUTPUT N I/YR PMT PV FV 20 6.5 50 1000 - 834.72
āļžāļąāļ™āļ˜āļšāļąāļ•āļĢāļ—āļĩāđˆāļˆāđˆāļēāļĒāļ”āļ­āļāđ€āļšāļĩāđ‰āļĒāļ›āļĩāļĨāļ°  2  āļ„āļĢāļąāđ‰āļ‡ āļžāļąāļ™āļ˜āļšāļąāļ•āļĢāļ­āļąāļ•āļĢāļēāļ”āļ­āļāđ€āļšāļĩāđ‰āļĒ   10 %  āļˆāđˆāļēāļĒāļ”āļ­āļāđ€āļšāļĩāđ‰āļĒ āļ›āļĩāļĨāļ°  2  āļ„āļĢāļąāđ‰āļ‡  āļĢāļēāļ„āļēāļ—āļĩāđˆāļ•āļĢāļēāđ„āļ§āđ‰   1,000  āļšāļēāļ—  āļāļģāļŦāļ™āļ” āđ„āļ–āđˆāļ–āļ­āļ™  15  āļ›āļĩ  āļ­āļąāļ•āļĢāļēāļœāļĨāļ•āļ­āļšāđāļ—āļ™āļ—āļĩāđˆāļ•āđ‰āļ­āļ‡āļāļēāļĢ  5  %  āļˆāļ°āļ‹āļ·āđ‰āļ­āļžāļąāļ™āļ˜āļšāļąāļ•āļĢāļ™āļĩāđ‰āđƒāļ™āļĢāļēāļ„āļēāđ€āļ—āđˆāļēāđƒāļ” āļ•āļąāļ§āļ­āļĒāđˆāļēāļ‡ 7 - 38
V B   =  2N   INT / 2  +  M t =  1  ( 1 + k d  /2)  t   ( 1 + k d  /2)  2N   7 - 39
N PV PMT FV COMP i EXE 1 , 523.26  āļšāļēāļ— 30 2.5 50 1,000 7 - 40
Would you prefer to buy a 10-year, 10% annual coupon bond or a 10-year, 10% semiannual coupon bond, all else equal? ,[object Object],[object Object]
If the proper price for this semiannual bond is $1,000, what would be the proper price for the annual coupon bond? ,[object Object],INPUTS OUTPUT N I/YR PMT PV FV 10 10.25 100 1000 - 984.80
Default risk  āļ„āļ§āļēāļĄāđ€āļŠāļĩāđˆāļĒāļ‡āļ—āļĩāđˆāđ„āļĄāđˆāļŠāļēāļĄāļēāļĢāļ–āļŠāļģāļĢāļ°āļŦāļ™āļĩāđ‰āđ„āļ”āđ‰ ,[object Object],[object Object],[object Object]
Types of bonds  āļ›āļĢāļ°āđ€āļ āļ—āļ‚āļ­āļ‡āļžāļąāļ™āļ˜āļšāļąāļ•āļĢ ,[object Object],[object Object],[object Object],[object Object],[object Object]
Evaluating default risk: Bond ratings ,[object Object],BB  B  CCC  D AAA  AA  A  BBB S & P Ba  B  Caa  C Aaa  Aa  A  Baa Moody’s Junk Bonds Investment Grade
Factors affecting default risk and bond ratings ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Other factors affecting default risk ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Bankruptcy  and  Reorganization  āļāļēāļĢāļĨāđ‰āļĄāļĨāļ°āļĨāļēāļĒāđāļĨāļ°āļāļēāļĢāļ›āļĢāļąāļšāļ›āļĢāļļāļ‡āļ­āļ‡āļ„āđŒāļāļēāļĢ āđ€āļĄāļ·āđˆāļ­āļāļīāļˆāļāļēāļĢ āļ‚āļēāļ”āļŠāļ āļēāļžāļ„āļĨāđˆāļ­āļ‡  (Insolvency) āļœāļđāđ‰āļšāļĢāļīāļŦāļēāļĢāļ•āđ‰āļ­āļ‡āļžāļīāļˆāļēāļĢāļ“āļēāļ§āđˆāļēāļ„āļ§āļĢāļ—āļĩāđˆāļˆāļ° āđ€āļĨāļīāļāļāļīāļˆāļāļēāļĢ   (Liquidation) āļŦāļĢāļ·āļ­āļˆāļ° āļ›āļĢāļąāļšāļ›āļĢāļļāļ‡āļ­āļ‡āļ„āđŒāļāļēāļĢāđƒāļŦāļĄāđˆ  (Reorganization) āđ€āļžāļ·āđˆāļ­āđƒāļŦāđ‰āļāļīāļˆāļāļēāļĢāļŠāļēāļĄāļēāļĢāļ–āļ”āļģāļĢāļ‡āļ­āļĒāļđāđˆāđ„āļ”āđ‰

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Ru Fm Chapter07 Updated Plus

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  • 16. The value of financial assets 0 1 2 n k CF 1 CF n CF 2 Value ...
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  • 20. What is the value of a 10-year, 10% annual coupon bond, if k d = 10%? 0 1 2 n k 100 100 + 1,000 100 V B = ? ...
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  • 27. āļœāļĨāļ•āļ­āļšāđāļ—āļ™āļˆāļēāļāļžāļąāļ™āļ˜āļšāļąāļ•āļĢ BOND YIELDS āļ­āļąāļ•āļĢāļēāļ”āļ­āļāđ€āļšāļĩāđ‰āļĒāļ‚āļ­āļ‡āļžāļąāļ™āļ˜āļšāļąāļ•āļĢāļ–āļđāļāļāļģāļŦāļ™āļ”āđ„āļ§āđ‰āļ•āļēāļĒāļ•āļąāļ§ āđāļ•āđˆāļœāļĨāđ„āļ”āđ‰āļŦāļĢāļ·āļ­āļœāļĨāļ•āļ­āļšāđāļ—āļ™āļ—āļĩāđˆāļœāļđāđ‰āļĨāļ‡āļ—āļļāļ™āļˆāļ°āđ„āļ”āđ‰āļĢāļąāļšāļˆāļēāļāļžāļąāļ™āļ˜āļšāļąāļ•āļĢ āļˆāļ°āđ€āļ›āļĨāļĩāđˆāļĒāļ™āđāļ›āļĨāļ‡āļ­āļĒāļđāđˆāļ•āļĨāļ­āļ”āđ€āļ§āļĨāļē āļ‚āļķāđ‰āļ™āļ­āļĒāļđāđˆāļāļąāļšāļŠāļ āļēāļžāļ•āļĨāļēāļ”āļ›āļąāļˆāļˆāļļāļšāļąāļ™ āļœāļĨāļ•āļ­āļšāđāļ—āļ™āļˆāļēāļāļāļēāļĢāļĨāļ‡āļ—āļļāļ™āđƒāļ™āļžāļąāļ™āļ˜āļšāļąāļ•āļĢāļŠāļēāļĄāļēāļĢāļ–āļ„āļģāļ™āļ§āļ“āđ„āļ”āđ‰ 3 āļ§āļīāļ˜āļĩ 1. Yield To Maturity 2. Yield To Call 3. Current Yield
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  • 32. Yield to Call : YTC YTC āļ„āļ·āļ­āļ­āļąāļ•āļĢāļēāļœāļĨāļ•āļ­āļšāđāļ—āļ™āļ—āļĩāđˆāđ„āļ”āđ‰āļĢāļąāļšāļˆāļēāļāļžāļąāļ™āļ˜āļšāļąāļ•āļĢ āļ–āđ‰āļēāļžāļąāļ™āļ˜āļšāļąāļ•āļĢāļ–āļđāļāđ€āļĢāļĩāļĒāļāļĄāļēāđ„āļ–āđˆāļ–āļ­āļ™āļāđˆāļ­āļ™āļ§āļąāļ™āļ—āļĩāđˆāļ„āļĢāļšāļāļģāļŦāļ™āļ” Price of bond = ÎĢ (INT/(1+k d ) t + (Call price)/(1+k d ) N t=1 N
  • 33. āļžāļąāļ™āļ˜āļšāļąāļ•āļĢāļĄāļđāļĨāļ„āđˆāļēāļ—āļĩāđˆāļ•āļĢāļēāđ„āļ§āđ‰ 1,000 āļšāļēāļ— āļ­āļąāļ•āļĢāļē āļ”āļ­āļāđ€āļšāļĩāđ‰āļĒ 10 % āļ āļēāļĒāļŦāļĨāļąāļ‡āļāļēāļĢāļ­āļ­āļāļˆāļģāļŦāļ™āđˆāļēāļĒāļˆāļ°āđ€āļĢāļĩāļĒāļ āđ„āļ–āđˆāļ–āļ­āļ™āļ„āļ·āļ™āđ„āļ”āđ‰āļ āļēāļĒāđƒāļ™ 10 āļ›āļĩ āļĢāļēāļ„āļēāđ„āļ–āđˆāļ–āļ­āļ™ 1 , 100 āļšāļēāļ— āđ€āļĄāļ·āđˆāļ­āļ­āļ­āļāļˆāļģāļŦāļ™āđˆāļēāļĒāđāļĨāđ‰āļ§ 1 āļ›āļĩ āļ­āļąāļ•āļĢāļēāļ”āļ­āļāđ€āļšāļĩāđ‰āļĒāļ‚āļ­āļ‡āļ•āļĨāļēāļ” āļĨāļ”āļĨāļ‡āđ€āļŦāļĨāļ·āļ­ 5 % āļ—āļģāđƒāļŦāđ‰āļĢāļēāļ„āļēāļ‹āļ·āđ‰āļ­ / āļ‚āļēāļĒāļžāļąāļ™āļ˜āļšāļąāļ•āļĢāļŠāļđāļ‡āļ‚āļķāđ‰āļ™ āđ€āļ›āđ‡āļ™ 1,494.93 āļšāļēāļ— āļœāļđāđ‰āļĨāļ‡āļ—āļļāļ™āļ—āļĩāđˆāļ‹āļ·āđ‰āļ­āļžāļąāļ™āļ˜āļšāļąāļ•āļĢāđƒāļ™ āļĢāļēāļ„āļē 1 ,494.93 āļšāļēāļ— āļ–āļ·āļ­āđ„āļ§āđ‰ 9 āļ›āļĩāļˆāļ™āļāļ§āđˆāļēāļˆāļ°āļ–āļđāļāđ€āļĢāļĩāļĒāļ āđ„āļ–āđˆāļ–āļ­āļ™āļ„āļ·āļ™āļˆāļ°āđ„āļ”āđ‰āļĢāļąāļšāļ­āļąāļ•āļĢāļēāļœāļĨāļ•āļ­āļšāđāļ—āļ™ (YTC) āļ”āļąāļ‡āļ™āļĩāđ‰ āļ•āļąāļ§āļ­āļĒāđˆāļēāļ‡
  • 34. V B = N 100 + Call Price t = 1 ( 1 + k d ) t ( 1 + k d ) N 1,494.93 = N 100 + 1,100 t = 1 ( 1 + k d ) t ( 1 + k d ) N 1. āđƒāļŠāđ‰āđ€āļ„āļĢāļ·āđˆāļ­āļ‡āļ„āļģāļ™āļ§āļ“āļ˜āļĢāļĢāļĄāļ”āļē k d = YTC = 4.21 %
  • 35. 0 1 2 3 - 1,494.93 100 100 100 9 100 1,100 YTC=? YTC = 4.21 %
  • 36. N PV PMT FV COMP i EXE 4.21 = YTC 9 100 1,100 -1,494.93 2. āđƒāļŠāđ‰ Financial Calculator :
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  • 41. Current Yield āļ”āļ­āļāđ€āļšāļĩāđ‰āļĒāļ—āļĩāđˆāđ„āļ”āđ‰āļĢāļąāļš āļĢāļēāļ„āļēāļ•āļĨāļēāļ”āļ›āļąāļˆāļˆāļļāļšāļąāļ™ āļžāļąāļ™āļ˜āļšāļąāļ•āļĢāļˆāđˆāļēāļĒāļ”āļ­āļāđ€āļšāļĩāđ‰āļĒāļ›āļĩāļĨāļ° 100 āļšāļēāļ— āļĢāļēāļ„āļēāļ•āļĨāļēāļ”āļ›āļąāļˆāļˆāļļāļšāļąāļ™ 985 āļšāļēāļ— 985 Current Yield = = 10.15 % Current Yield āļ­āļąāļ•āļĢāļēāļœāļĨāļ•āļ­āļšāđāļ—āļ™āļ›āļąāļˆāļˆāļļāļšāļąāļ™ āļ•āļąāļ§āļ­āļĒāđˆāļēāļ‡ 100 =
  • 43.
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  • 45. āļāļēāļĢāļ›āļĢāļ°āđ€āļĄāļīāļ™āļ„āļ§āļēāļĄāđ€āļŠāļĩāđˆāļĒāļ‡āļ‚āļ­āļ‡āļžāļąāļ™āļ˜āļšāļąāļ•āļĢ ASSESSING THE RISKINESS OF A BOND āļ„āļ§āļēāļĄāđ€āļŠāļĩāđˆāļĒāļ‡āļ—āļĩāđˆāļŠāļģāļ„āļąāļāđ„āļ”āđ‰āđāļāđˆ 1. INTEREST RATE RISK āļ„āļ§āļēāļĄāđ€āļŠāļĩāđˆāļĒāļ‡āļˆāļēāļāļ­āļąāļ•āļĢāļēāļ”āļ­āļāđ€āļšāļĩāđ‰āļĒ 2. REINVESTMENT RATE RISK āļ„āļ§āļēāļĄāđ€āļŠāļĩāđˆāļĒāļ‡āđƒāļ™āļāļēāļĢāļāļĨāļąāļšāđ€āļ‚āđ‰āļēāđ„āļ›āļĨāļ‡āļ—āļļāļ™āļ„āļĢāļąāđ‰āļ‡āđƒāļŦāļĄāđˆ
  • 46.
  • 47. 0 500 1,000 1,500 0% 5% 10% 15% 1-year 10-year k d Value . . . . . .
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  • 53. āļžāļąāļ™āļ˜āļšāļąāļ•āļĢāļ—āļĩāđˆāļˆāđˆāļēāļĒāļ”āļ­āļāđ€āļšāļĩāđ‰āļĒāļ›āļĩāļĨāļ° 2 āļ„āļĢāļąāđ‰āļ‡ āļžāļąāļ™āļ˜āļšāļąāļ•āļĢāļ­āļąāļ•āļĢāļēāļ”āļ­āļāđ€āļšāļĩāđ‰āļĒ 10 % āļˆāđˆāļēāļĒāļ”āļ­āļāđ€āļšāļĩāđ‰āļĒ āļ›āļĩāļĨāļ° 2 āļ„āļĢāļąāđ‰āļ‡ āļĢāļēāļ„āļēāļ—āļĩāđˆāļ•āļĢāļēāđ„āļ§āđ‰ 1,000 āļšāļēāļ— āļāļģāļŦāļ™āļ” āđ„āļ–āđˆāļ–āļ­āļ™ 15 āļ›āļĩ āļ­āļąāļ•āļĢāļēāļœāļĨāļ•āļ­āļšāđāļ—āļ™āļ—āļĩāđˆāļ•āđ‰āļ­āļ‡āļāļēāļĢ 5 % āļˆāļ°āļ‹āļ·āđ‰āļ­āļžāļąāļ™āļ˜āļšāļąāļ•āļĢāļ™āļĩāđ‰āđƒāļ™āļĢāļēāļ„āļēāđ€āļ—āđˆāļēāđƒāļ” āļ•āļąāļ§āļ­āļĒāđˆāļēāļ‡ 7 - 38
  • 54. V B = 2N INT / 2 + M t = 1 ( 1 + k d /2) t ( 1 + k d /2) 2N 7 - 39
  • 55. N PV PMT FV COMP i EXE 1 , 523.26 āļšāļēāļ— 30 2.5 50 1,000 7 - 40
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  • 63. Bankruptcy and Reorganization āļāļēāļĢāļĨāđ‰āļĄāļĨāļ°āļĨāļēāļĒāđāļĨāļ°āļāļēāļĢāļ›āļĢāļąāļšāļ›āļĢāļļāļ‡āļ­āļ‡āļ„āđŒāļāļēāļĢ āđ€āļĄāļ·āđˆāļ­āļāļīāļˆāļāļēāļĢ āļ‚āļēāļ”āļŠāļ āļēāļžāļ„āļĨāđˆāļ­āļ‡ (Insolvency) āļœāļđāđ‰āļšāļĢāļīāļŦāļēāļĢāļ•āđ‰āļ­āļ‡āļžāļīāļˆāļēāļĢāļ“āļēāļ§āđˆāļēāļ„āļ§āļĢāļ—āļĩāđˆāļˆāļ° āđ€āļĨāļīāļāļāļīāļˆāļāļēāļĢ (Liquidation) āļŦāļĢāļ·āļ­āļˆāļ° āļ›āļĢāļąāļšāļ›āļĢāļļāļ‡āļ­āļ‡āļ„āđŒāļāļēāļĢāđƒāļŦāļĄāđˆ (Reorganization) āđ€āļžāļ·āđˆāļ­āđƒāļŦāđ‰āļāļīāļˆāļāļēāļĢāļŠāļēāļĄāļēāļĢāļ–āļ”āļģāļĢāļ‡āļ­āļĒāļđāđˆāđ„āļ”āđ‰