taiwan财务管理_lecture4(ch4)
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Yield To Maturity - Interest rate for which the present value of the bond’s payments equal the price.
Irwin/McGraw-Hill
©The McGraw-Hill Companies, Inc.,2001
8
Yield on UK
6
indexed bonds
4 2 0
Irwin/McGraw-Hill
Yield on UK nominal bonds
Year
©The McGraw-Hill Companies, Inc.,2001
4- 19
Default Risk
Credit risk Default premium Investment grade Junk bonds
1,500
1,000
3 yr bond
500
-
0
2
4
6
8
10
Irwin/McGraw-Hill
YTM ©The McGraw-Hill Companies, Inc.,2001
4- 18
Nominal and Real rates
Percent
82 85 88 91 94 97
16 14 12 10
Interest Rate Risk
The Yield Curve
Nominal and Real Rates of Interest
Default Risk
Irwin/McGraw-Hill
©The McGraw-Hill Companies, Inc.,2001
4- 3
Bonds
Terminology Bond - Security that obligates the issuer to
PV
cpn (1 r)1
cpn (1 r)2
....
(cpn par) (1 r)t
Irwin/McGraw-Hill
©The McGraw-Hill Companies, Inc.,2001
4- 13
Bond Yields
Example
What is the YTM of a 6 % annual coupon bond, with a $1,000 face value, which matures in 3 years? The market price of the bond is $1,010.77
PV
30 (1.028 )1
30 (1.028 )2
...
30 (1.028 )5
1,030 (1.028 )6
PV $1,010 .91
Irwin/McGraw-Hill
©The McGraw-Hill Companies, Inc.,2001
4- 10
Bond Pricing
©The McGraw-Hill Companies, Inc.,2001
4- 5
Bond Pricing
The price of a bond is the Present Value of all cash flows generated by the bond (i.e. coupons and face value) discounted at the required rate of return.
percentage of face value.
Irwin/McGraw-Hill
©The McGraw-Hill Companies, Inc.,2001
4- 4
Bonds
WARNING
The coupon rate IS NOT the discount rate used in the Present Value calculations.
Example (continued)
Q: How did the calculation change, given semiannual coupons versus annual coupon payments?
Time Periods
Paying coupons twice a year, instead of once
4-F1 undamentals of Corporate Finance
Third Edition
Chapter 4
Valuing Bonds
Irwin/McGraw-Hill
Brealey Myers Marcus
slides by Matthew Will
©The McGraw-Hill Companies, Inc.,2001
4- 12
Bond Yields
Calculating Yield to Maturity (YTM=r)
If you are given the price of a bond (PV) and the coupon rate, the yield to maturity can be found by solving for r.
4- 15
Bond Yields
Rate of Return - Earnings per period per dollar invested.
Rate of return = total income investment
Rate of return = Coupon income + price change investment
The strongest rating; ability to repay interest and principal is very strong. Very strong likelihood that interest and principal will be repaid Strong ability to repay, but some vulnerability to changes in circumstances Adequate capacity to repay; more vulnerability to changes in economic circumstances Considerable uncertainty about ability to repay. Likelihood of interest and principal payments over sustained periods is questionable. Bonds in the Caa/CCC and Ca/CC classes may already be in default or in danger of imminent default C-rated bonds offer little prospect for interest or principal on the debt ever to be repaid.
changed from the annual rate to the half year rate.
©The McGraw-Hill Companies, Inc.,2001
4- 11
Bond Yields
Current Yield - Annual coupon payments divided by bond price.
PV
cpn (1 r)1
cpn (1 r)2
....
(cpn par) (1 r)t
Irwin/McGraw-Hill
©The McGraw-Hill Companies, Inc.,2001
4- 6
Bond Pricing
Example
What is the price of a 6 % annual coupon bond, with a $1,000 face value, which matures in 3 years? Assume a required return of 5.6%.
PV
60 (1.15)1
60 (1.15)2
1,060 (1.15)3
PV $794 .51
Irwin/McGraw-Hill
©The McGraw-Hill Companies, Inc.,2001
4- 9
Bond Pricing
Example (continued)
What is the price of the bond if the required rate of return is 5.6% AND the coupons are paid semiannually?
Irwin/McGraw-Hill
©The McGraw-Hill Companies, Inc.,2001
4- 16
Interest Rate Risk
Bond Price
1,080 1,060 1,040 1,020 1,000
980 960 940 920 900 880
0
Irwin/McGraw-Hill
doubles the total number of cash flows to be discounted
in the PV formula.
Irwin/McGraw-Hill
Discount Rate
Since the time periods are now half years, the discount rate is also
make specified payments to the bondholder. Coupon - The interest payments made to the
bondholder. Face Value (Par Value or Maturity Value) - Payment
at the maturity of the bond. Coupon Rate - Annual interest payment, as a
PV
60 (1.06)1
60 (1.06)2
1,060 (1.06)3
PV $1,000
Irwin/McGraw-Hill
©The McGraw-Hill Companies, Inc.,2001
4- 8
Bond Pricing
Example (continued)
What is the price of the bond if the required rate of return is 15 %?
PV
60 (1.056 )1
60 (1.056 )2
1,060 (1.056 )3
PV $1,010 .77
Irwin/McGraw-Hill
©The McGraw-Hill Companies, Inc.,2001
4- 7
Bond Pricing
Example (continued)
What is the price of the bond if the required rate of return is 6 %?
4- 2
Topics Covered
Bond Characteristics
reading the financial pages
Bond Prices and Yields
Bond prices and interest rates
YTM vs. current yield
Rate of Return
Irwin/McGraw-Hill
©The McGraw-Hill Companies, Inc.,2001
4- 20
Default Risk
Standard Moody' s & Poor's
Safety
Aaa
AAA
Aa
AA
A
A
Baa
BBB
Ba
BB
B
B
Caa
CCC
Ca
CC
C
C
Irwin/McGraw-Hill
It is highly recommended that you learn to use the “IRR” or “YTM” or “i” functions on a financial calculator.
Irwin/McGraw-Hill
©The McGraw-Hill Companies, Inc.,2001
PV
60 (1 r)1
60 (1 r)2
1,060 (1 r)3
PV $1,010.77
Irwin/McGraw-Hill
©The McGraw-Hill Companies, Inc.,2001
4- 14
Bond Yields
WARNING
Calculating YTM by hand can be very tedious.
Premium Bond
Discount Bond
5
10
15
20
25
30
Time to Maturity
©The McGraw-Hill Companies, Inc.,2001
4- 17
Interest Rate Risk
3,000
2,500
30 yr bond
2,000
$ Bond Price
The coupon rate merely tells us what cash flow the bond will produce.
Since the coupon rate is listed as a %, this misconception is quite common.
Irwin/McGraw-Hill
Irwin/McGraw-Hill
©The McGraw-Hill Companies, Inc.,2001
8
Yield on UK
6
indexed bonds
4 2 0
Irwin/McGraw-Hill
Yield on UK nominal bonds
Year
©The McGraw-Hill Companies, Inc.,2001
4- 19
Default Risk
Credit risk Default premium Investment grade Junk bonds
1,500
1,000
3 yr bond
500
-
0
2
4
6
8
10
Irwin/McGraw-Hill
YTM ©The McGraw-Hill Companies, Inc.,2001
4- 18
Nominal and Real rates
Percent
82 85 88 91 94 97
16 14 12 10
Interest Rate Risk
The Yield Curve
Nominal and Real Rates of Interest
Default Risk
Irwin/McGraw-Hill
©The McGraw-Hill Companies, Inc.,2001
4- 3
Bonds
Terminology Bond - Security that obligates the issuer to
PV
cpn (1 r)1
cpn (1 r)2
....
(cpn par) (1 r)t
Irwin/McGraw-Hill
©The McGraw-Hill Companies, Inc.,2001
4- 13
Bond Yields
Example
What is the YTM of a 6 % annual coupon bond, with a $1,000 face value, which matures in 3 years? The market price of the bond is $1,010.77
PV
30 (1.028 )1
30 (1.028 )2
...
30 (1.028 )5
1,030 (1.028 )6
PV $1,010 .91
Irwin/McGraw-Hill
©The McGraw-Hill Companies, Inc.,2001
4- 10
Bond Pricing
©The McGraw-Hill Companies, Inc.,2001
4- 5
Bond Pricing
The price of a bond is the Present Value of all cash flows generated by the bond (i.e. coupons and face value) discounted at the required rate of return.
percentage of face value.
Irwin/McGraw-Hill
©The McGraw-Hill Companies, Inc.,2001
4- 4
Bonds
WARNING
The coupon rate IS NOT the discount rate used in the Present Value calculations.
Example (continued)
Q: How did the calculation change, given semiannual coupons versus annual coupon payments?
Time Periods
Paying coupons twice a year, instead of once
4-F1 undamentals of Corporate Finance
Third Edition
Chapter 4
Valuing Bonds
Irwin/McGraw-Hill
Brealey Myers Marcus
slides by Matthew Will
©The McGraw-Hill Companies, Inc.,2001
4- 12
Bond Yields
Calculating Yield to Maturity (YTM=r)
If you are given the price of a bond (PV) and the coupon rate, the yield to maturity can be found by solving for r.
4- 15
Bond Yields
Rate of Return - Earnings per period per dollar invested.
Rate of return = total income investment
Rate of return = Coupon income + price change investment
The strongest rating; ability to repay interest and principal is very strong. Very strong likelihood that interest and principal will be repaid Strong ability to repay, but some vulnerability to changes in circumstances Adequate capacity to repay; more vulnerability to changes in economic circumstances Considerable uncertainty about ability to repay. Likelihood of interest and principal payments over sustained periods is questionable. Bonds in the Caa/CCC and Ca/CC classes may already be in default or in danger of imminent default C-rated bonds offer little prospect for interest or principal on the debt ever to be repaid.
changed from the annual rate to the half year rate.
©The McGraw-Hill Companies, Inc.,2001
4- 11
Bond Yields
Current Yield - Annual coupon payments divided by bond price.
PV
cpn (1 r)1
cpn (1 r)2
....
(cpn par) (1 r)t
Irwin/McGraw-Hill
©The McGraw-Hill Companies, Inc.,2001
4- 6
Bond Pricing
Example
What is the price of a 6 % annual coupon bond, with a $1,000 face value, which matures in 3 years? Assume a required return of 5.6%.
PV
60 (1.15)1
60 (1.15)2
1,060 (1.15)3
PV $794 .51
Irwin/McGraw-Hill
©The McGraw-Hill Companies, Inc.,2001
4- 9
Bond Pricing
Example (continued)
What is the price of the bond if the required rate of return is 5.6% AND the coupons are paid semiannually?
Irwin/McGraw-Hill
©The McGraw-Hill Companies, Inc.,2001
4- 16
Interest Rate Risk
Bond Price
1,080 1,060 1,040 1,020 1,000
980 960 940 920 900 880
0
Irwin/McGraw-Hill
doubles the total number of cash flows to be discounted
in the PV formula.
Irwin/McGraw-Hill
Discount Rate
Since the time periods are now half years, the discount rate is also
make specified payments to the bondholder. Coupon - The interest payments made to the
bondholder. Face Value (Par Value or Maturity Value) - Payment
at the maturity of the bond. Coupon Rate - Annual interest payment, as a
PV
60 (1.06)1
60 (1.06)2
1,060 (1.06)3
PV $1,000
Irwin/McGraw-Hill
©The McGraw-Hill Companies, Inc.,2001
4- 8
Bond Pricing
Example (continued)
What is the price of the bond if the required rate of return is 15 %?
PV
60 (1.056 )1
60 (1.056 )2
1,060 (1.056 )3
PV $1,010 .77
Irwin/McGraw-Hill
©The McGraw-Hill Companies, Inc.,2001
4- 7
Bond Pricing
Example (continued)
What is the price of the bond if the required rate of return is 6 %?
4- 2
Topics Covered
Bond Characteristics
reading the financial pages
Bond Prices and Yields
Bond prices and interest rates
YTM vs. current yield
Rate of Return
Irwin/McGraw-Hill
©The McGraw-Hill Companies, Inc.,2001
4- 20
Default Risk
Standard Moody' s & Poor's
Safety
Aaa
AAA
Aa
AA
A
A
Baa
BBB
Ba
BB
B
B
Caa
CCC
Ca
CC
C
C
Irwin/McGraw-Hill
It is highly recommended that you learn to use the “IRR” or “YTM” or “i” functions on a financial calculator.
Irwin/McGraw-Hill
©The McGraw-Hill Companies, Inc.,2001
PV
60 (1 r)1
60 (1 r)2
1,060 (1 r)3
PV $1,010.77
Irwin/McGraw-Hill
©The McGraw-Hill Companies, Inc.,2001
4- 14
Bond Yields
WARNING
Calculating YTM by hand can be very tedious.
Premium Bond
Discount Bond
5
10
15
20
25
30
Time to Maturity
©The McGraw-Hill Companies, Inc.,2001
4- 17
Interest Rate Risk
3,000
2,500
30 yr bond
2,000
$ Bond Price
The coupon rate merely tells us what cash flow the bond will produce.
Since the coupon rate is listed as a %, this misconception is quite common.
Irwin/McGraw-Hill