《公司理财》斯蒂芬A罗斯英文》PPT课件讲义
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• The rate should be appropriate to the risk presented by the security.
5.1 Definition and Example of a Bond
• A bond is a legally binding agreement between a borrower and a lender: – Specifies the principal amount of the loan. – Specifies the size and timing of the cash flows:
• In dollar terms (fixed-rate borrowing) • As a formula (adjustable-rate borrowing)
5.1 Definition and Example of a Bond
• Consider a U.S. government bond listed as 6 3/8 of December 2009.
N I/Y PV PMT FV
12
5
– 1,070.52
31.875 = 1,000
1,000×0.06375 2
5.3 Bond Concepts
1. Bond prices and market interest rates move in opposite directions.
2. When coupon rate = YTM, price = par value. When coupon rate > YTM, price > par value (premium bond) When coupon rate < YTM, price < par value (discount bond)
PV
F (1 r)T
Pure Discount Bonds: Example
Find the value of a 30-year zero-coupon bond with a $1,000 par value and a YTM of 6%.
$0
0
1
$0
$0
2
29
$1,000
$0$$1,00 1203209
$31.875 $31.875 $31.875
1/1/05 6/30/05 12/31/05 6/30/09
$1,031.875
12/31/09
5.2 How to Value Bonds
• Identify the size and timing of cash flows. • Discount at the correct discount rate.
– The Par Value of the bond is $1,000. – Coupon payments are made semi-annually (June 30 and
December 31 for this particular bond). – Since the coupon rate is 6 3/8 the payment is $31.875. – On January 1, 2005 the size and timing of cash flows are:
3. A bond with longer maturity has higher relative (%) price change than one with shorter maturity when interest rate (YTM) changes. All other features are identical.
The long-maturity bond will have much more volatility with respect to changes in the discount rate
Par
Short Maturity Bond
C
Discount Rate
Long Maturity
Bond
– Zero Growth – Constant Growth – Differential Growth
Case 1: Zero Growth
• Assume that dividends will remain at the same level forever
D1i v D2i vD3i v
Level-Coupon Bonds: Example
Find the present value (as of January 1, 2004), of a 6-3/8 coupon T-bond with semi-annual payments, and a maturity date of December 2009 if the YTM is 5-percent.
Assume that dividends will grow at a constant rate, g, forever. i.e. D1ivD0i(1 vg)
30
PV (1 Fr)T($ 11 .0 ,0)6300 0$17.141
Pure Discount Bonds: Example
Find the value of a 30-year zero-coupon bond with a $1,000 par value and a YTM of 6%.
4. A lower coupon bond has a higher relative price change than a higher coupon bond when YTM changes. All other features are identical.
YTM and Bond Value
(Advanced) 5.8 Price Earnings Ratio 5.9 Stock Market Reporting 5.10 Summary and Conclusions
Valuation of Bonds ales:
– Value of financial securities = PV of expected future cash flows
6 3/8
Discount Rate
When the YTM > coupon, the bond trades at a discount.
Maturity and Bond Price Volatility
Bond Value
Consider two otherwise identical bonds.
$1400
When the YTM < coupon, the bond
1300
trades at a premium.
Bond Value
1200
1100
When the YTM = coupon, the
bond trades at par.
1000
800 0
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
N I/Y PV PMT FV
30 6
174.11
1,000
Level-Coupon Bonds
Information needed to value level-coupon bonds:
– Coupon payment dates and time to maturity (T) – Coupon payment (C) per period and Face value (F) – Discount rate
• To value bonds and stocks we need to:
– Estimate future cash flows:
• Size (how much) and • Timing (when)
– Discount future cash flows at an appropriate rate:
– Time to maturity (T) = Maturity date - today’s date – Face value (F) – Discount rate (r)
$0
$0
$0
$F
0
1
2
T 1
T
Present value of a pure discount bond at time 0:
High Coupon Bond Discount Rate
Low Coupon Bond
5.4 The Present Value of Common Stocks
• Dividends versus Capital Gains • Valuation of Different Types of Stocks
– If you know the price of a bond and the size and timing of cash flows, the yield to maturity is the discount rate.
Pure Discount Bonds
Information needed for valuing pure discount bonds:
• Since future cash flows are constant, the value of a zero growth stock is the present value of a perpetuity:
P0
Div1 (1r)1
(1Dirv2)2
(1Dirv3)3
P0
Div r
Case 2: Constant Growth
$31.875 $31.875 $31.875
1/1/04 6/30/04 12/31/04 6/30/09
$1,031.875
12/31/09
P V $ 3 .0 .8 2 1 5 7 1 ( 5 1 .0 1)2 1 2 5 (1 $ .1 0 ,0)2 10 2 5 $ 0 1 ,0.7 5
$C
$C
$C
$C$F
0
1
2
T 1
T
Value of a Level-coupon bond = PV of coupon payment annuity + PV of face value
PV C r1(11r)T(1Fr)T
Level-Coupon Bonds: Example
Find the present value (as of January 1, 2004), of a 6-3/8 coupon T-bond with semi-annual payments, and a maturity date of December 2009 if the YTM is 5-percent. – On January 1, 2004 the size and timing of cash flows are:
《公司理财》斯蒂芬A罗斯英文
（Suitable for teaching courseware and reports）
Chapter Outline
5.1 Definition and Example of a Bond 5.2 How to Value Bonds 5.3 Bond Concepts 5.4 The Present Value of Common Stocks 5.5 Estimates of Parameters in the Dividend-Discount Model 5.6 Growth Opportunities 5.7 The Dividend Growth Model and the NPVGO Model
Bond Value
Coupon Rate and Bond Price Volatility
Consider two otherwise identical bonds. The low-coupon bond will have much more
volatility with respect to changes in the discount rate
5.1 Definition and Example of a Bond
• A bond is a legally binding agreement between a borrower and a lender: – Specifies the principal amount of the loan. – Specifies the size and timing of the cash flows:
• In dollar terms (fixed-rate borrowing) • As a formula (adjustable-rate borrowing)
5.1 Definition and Example of a Bond
• Consider a U.S. government bond listed as 6 3/8 of December 2009.
N I/Y PV PMT FV
12
5
– 1,070.52
31.875 = 1,000
1,000×0.06375 2
5.3 Bond Concepts
1. Bond prices and market interest rates move in opposite directions.
2. When coupon rate = YTM, price = par value. When coupon rate > YTM, price > par value (premium bond) When coupon rate < YTM, price < par value (discount bond)
PV
F (1 r)T
Pure Discount Bonds: Example
Find the value of a 30-year zero-coupon bond with a $1,000 par value and a YTM of 6%.
$0
0
1
$0
$0
2
29
$1,000
$0$$1,00 1203209
$31.875 $31.875 $31.875
1/1/05 6/30/05 12/31/05 6/30/09
$1,031.875
12/31/09
5.2 How to Value Bonds
• Identify the size and timing of cash flows. • Discount at the correct discount rate.
– The Par Value of the bond is $1,000. – Coupon payments are made semi-annually (June 30 and
December 31 for this particular bond). – Since the coupon rate is 6 3/8 the payment is $31.875. – On January 1, 2005 the size and timing of cash flows are:
3. A bond with longer maturity has higher relative (%) price change than one with shorter maturity when interest rate (YTM) changes. All other features are identical.
The long-maturity bond will have much more volatility with respect to changes in the discount rate
Par
Short Maturity Bond
C
Discount Rate
Long Maturity
Bond
– Zero Growth – Constant Growth – Differential Growth
Case 1: Zero Growth
• Assume that dividends will remain at the same level forever
D1i v D2i vD3i v
Level-Coupon Bonds: Example
Find the present value (as of January 1, 2004), of a 6-3/8 coupon T-bond with semi-annual payments, and a maturity date of December 2009 if the YTM is 5-percent.
Assume that dividends will grow at a constant rate, g, forever. i.e. D1ivD0i(1 vg)
30
PV (1 Fr)T($ 11 .0 ,0)6300 0$17.141
Pure Discount Bonds: Example
Find the value of a 30-year zero-coupon bond with a $1,000 par value and a YTM of 6%.
4. A lower coupon bond has a higher relative price change than a higher coupon bond when YTM changes. All other features are identical.
YTM and Bond Value
(Advanced) 5.8 Price Earnings Ratio 5.9 Stock Market Reporting 5.10 Summary and Conclusions
Valuation of Bonds ales:
– Value of financial securities = PV of expected future cash flows
6 3/8
Discount Rate
When the YTM > coupon, the bond trades at a discount.
Maturity and Bond Price Volatility
Bond Value
Consider two otherwise identical bonds.
$1400
When the YTM < coupon, the bond
1300
trades at a premium.
Bond Value
1200
1100
When the YTM = coupon, the
bond trades at par.
1000
800 0
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
N I/Y PV PMT FV
30 6
174.11
1,000
Level-Coupon Bonds
Information needed to value level-coupon bonds:
– Coupon payment dates and time to maturity (T) – Coupon payment (C) per period and Face value (F) – Discount rate
• To value bonds and stocks we need to:
– Estimate future cash flows:
• Size (how much) and • Timing (when)
– Discount future cash flows at an appropriate rate:
– Time to maturity (T) = Maturity date - today’s date – Face value (F) – Discount rate (r)
$0
$0
$0
$F
0
1
2
T 1
T
Present value of a pure discount bond at time 0:
High Coupon Bond Discount Rate
Low Coupon Bond
5.4 The Present Value of Common Stocks
• Dividends versus Capital Gains • Valuation of Different Types of Stocks
– If you know the price of a bond and the size and timing of cash flows, the yield to maturity is the discount rate.
Pure Discount Bonds
Information needed for valuing pure discount bonds:
• Since future cash flows are constant, the value of a zero growth stock is the present value of a perpetuity:
P0
Div1 (1r)1
(1Dirv2)2
(1Dirv3)3
P0
Div r
Case 2: Constant Growth
$31.875 $31.875 $31.875
1/1/04 6/30/04 12/31/04 6/30/09
$1,031.875
12/31/09
P V $ 3 .0 .8 2 1 5 7 1 ( 5 1 .0 1)2 1 2 5 (1 $ .1 0 ,0)2 10 2 5 $ 0 1 ,0.7 5
$C
$C
$C
$C$F
0
1
2
T 1
T
Value of a Level-coupon bond = PV of coupon payment annuity + PV of face value
PV C r1(11r)T(1Fr)T
Level-Coupon Bonds: Example
Find the present value (as of January 1, 2004), of a 6-3/8 coupon T-bond with semi-annual payments, and a maturity date of December 2009 if the YTM is 5-percent. – On January 1, 2004 the size and timing of cash flows are:
《公司理财》斯蒂芬A罗斯英文
（Suitable for teaching courseware and reports）
Chapter Outline
5.1 Definition and Example of a Bond 5.2 How to Value Bonds 5.3 Bond Concepts 5.4 The Present Value of Common Stocks 5.5 Estimates of Parameters in the Dividend-Discount Model 5.6 Growth Opportunities 5.7 The Dividend Growth Model and the NPVGO Model
Bond Value
Coupon Rate and Bond Price Volatility
Consider two otherwise identical bonds. The low-coupon bond will have much more
volatility with respect to changes in the discount rate