公司理财 英文版 第八章
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8-12
Reinvestment Rate Risk
Maturity and Bond Price Volatility
Bond Value
Consider two otherwise identical bonds. The long-maturity bond will have much more volatility with respect to changes in the discount rate.
N I/Y PV PMT FV 10 2.5 – 1,060.17 31.875 = 1,000
8-8
1,000×0.0637 5 2
Bond Example
Now assume that the required yield is 11%. How does this change the bond’s price?
Chapter 8
Interest Rates and Bond Valuation
McGraw-Hill/IBiblioteka Baiduwin
Copyright © 2010 by the McGraw-Hill Companies, Inc. All rights reserved.
Key Concepts and Skills
Know the important bond features and bond types Understand bond values and why they fluctuate Understand bond ratings and what they mean Understand the impact of inflation on interest rates Understand the term structure of interest rates and the determinants of bond yields
Bond Concepts
Bond prices and market interest rates move in opposite directions. 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)
$1,000 $31.875 1 PV 1 $1,060.17 10 10 .05 2 (1.025) (1.025)
8-7
Bond Example: Calculator
Find the present value (as of January 1, 2009), of a 6 3/8% coupon bond with semi-annual payments, and a maturity date of December 2013 if the YTM is 5%.
Current yield = 100 / 1197.93 = .0835 = 8.35% Price in one year, assuming no change in YTM = 1,193.68 Capital gain yield = (1193.68 – 1197.93) / 1197.93 = -.0035 = -.35% YTM = 8.35 - .35 = 8%, which is the same YTM computed earlier
8-4
The Bond-Pricing Equation
1 1 (1 r) T Bond Value C r F T (1 r)
8-5
Bond Example
Consider a U.S. government bond with as 6 3/8% coupon that expires in December 2013.
Uncertainty concerning rates at which cash flows can be reinvested Short-term bonds have more reinvestment rate risk than long-term bonds. High coupon rate bonds have more reinvestment rate risk than low coupon rate bonds.
$1,000 $31.875 1 PV 1 $825.69 10 10 .11 2 (1.055) (1.055)
8-9
YTM and Bond Value
1300
When the YTM < coupon, the bond trades at a premium.
The yield to maturity is the required market interest rate on the bond.
8-3
Bond Valuation
Primary Principle:
Value of financial securities = PV of expected future cash flows
$31.875 $31.875
$31.875
$1,031.875
12 / 31 / 13
8-6
1 / 1 / 09 6 / 30 / 09
12 / 31 / 09
6 / 30 / 13
Bond Example
On January 1, 2009, the required yield is 5%. The current value is:
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 6 3/8 0.08 0.09 0.1
Discount Rate
8-10
When the YTM > coupon, the bond trades at a discount.
The Par Value of the bond is $1,000. Coupon payments are made semiannually (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, 2009 the size and timing of cash flows are:
Par
Short Maturity Bond
C
Discount Rate Long Maturity Bond
8-13
Coupon Rates and Bond Prices
Bond Value
Consider two otherwise identical bonds. The low-coupon bond will have much more volatility with respect to changes in the discount rate.
8-15
YTM with Annual Coupons
Consider a bond with a 10% annual coupon rate, 15 years to maturity, and a par value of $1,000. The current price is $928.09.
8-11
Interest Rate Risk
Price Risk
Change in price due to changes in interest rates Long-term bonds have more price risk than short-term bonds Low coupon rate bonds have more price risk than high coupon rate bonds.
8-1
Chapter Outline
8.1 8.2 8.3 8.4 8.5 Bonds and Bond Valuation Government and Corporate Bonds Bond Markets Inflation and Interest Rates Determinants of Bond Yields
8-17
Current Yield vs. Yield to Maturity
Current Yield = annual coupon / price Yield to maturity = current yield + capital gains yield Example: 10% coupon bond, with semi-annual coupons, face value of 1,000, 20 years to maturity, $1,197.93 price
8-2
8.1 Bonds and Bond Valuation
A bond is a legally binding agreement between a borrower and a lender that specifies the:
Par (face) value Coupon rate Coupon payment Maturity Date
Is the YTM more or less than 10%? What is the semi-annual coupon payment? How many periods are there? N = 40; PV = -1,197.93; PMT = 50; FV = 1,000; CPT I/Y = 4% (Is this the YTM?) YTM = 4%*2 = 8%
Bond value is, therefore, determined by the present value of the coupon payments and par value. Interest rates are inversely related to present (i.e., bond) values.
Will the yield be more or less than 10%? N = 15; PV = -928.09; FV = 1,000; PMT = 100 CPT I/Y = 11%
8-16
YTM with Semiannual Coupons
Suppose a bond with a 10% coupon rate and semiannual coupons has a face value of $1,000, 20 years to maturity, and is selling for $1,197.93.
Par
High Coupon Bond
C
Low Coupon Bond Discount Rate
8-14
Computing Yield to Maturity
Yield to maturity is the rate implied by the current bond price. Finding the YTM requires trial and error if you do not have a financial calculator and is similar to the process for finding r with an annuity. If you have a financial calculator, enter N, PV, PMT, and FV, remembering the sign convention (PMT and FV need to have the same sign, PV the opposite sign).
Reinvestment Rate Risk
Maturity and Bond Price Volatility
Bond Value
Consider two otherwise identical bonds. The long-maturity bond will have much more volatility with respect to changes in the discount rate.
N I/Y PV PMT FV 10 2.5 – 1,060.17 31.875 = 1,000
8-8
1,000×0.0637 5 2
Bond Example
Now assume that the required yield is 11%. How does this change the bond’s price?
Chapter 8
Interest Rates and Bond Valuation
McGraw-Hill/IBiblioteka Baiduwin
Copyright © 2010 by the McGraw-Hill Companies, Inc. All rights reserved.
Key Concepts and Skills
Know the important bond features and bond types Understand bond values and why they fluctuate Understand bond ratings and what they mean Understand the impact of inflation on interest rates Understand the term structure of interest rates and the determinants of bond yields
Bond Concepts
Bond prices and market interest rates move in opposite directions. 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)
$1,000 $31.875 1 PV 1 $1,060.17 10 10 .05 2 (1.025) (1.025)
8-7
Bond Example: Calculator
Find the present value (as of January 1, 2009), of a 6 3/8% coupon bond with semi-annual payments, and a maturity date of December 2013 if the YTM is 5%.
Current yield = 100 / 1197.93 = .0835 = 8.35% Price in one year, assuming no change in YTM = 1,193.68 Capital gain yield = (1193.68 – 1197.93) / 1197.93 = -.0035 = -.35% YTM = 8.35 - .35 = 8%, which is the same YTM computed earlier
8-4
The Bond-Pricing Equation
1 1 (1 r) T Bond Value C r F T (1 r)
8-5
Bond Example
Consider a U.S. government bond with as 6 3/8% coupon that expires in December 2013.
Uncertainty concerning rates at which cash flows can be reinvested Short-term bonds have more reinvestment rate risk than long-term bonds. High coupon rate bonds have more reinvestment rate risk than low coupon rate bonds.
$1,000 $31.875 1 PV 1 $825.69 10 10 .11 2 (1.055) (1.055)
8-9
YTM and Bond Value
1300
When the YTM < coupon, the bond trades at a premium.
The yield to maturity is the required market interest rate on the bond.
8-3
Bond Valuation
Primary Principle:
Value of financial securities = PV of expected future cash flows
$31.875 $31.875
$31.875
$1,031.875
12 / 31 / 13
8-6
1 / 1 / 09 6 / 30 / 09
12 / 31 / 09
6 / 30 / 13
Bond Example
On January 1, 2009, the required yield is 5%. The current value is:
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 6 3/8 0.08 0.09 0.1
Discount Rate
8-10
When the YTM > coupon, the bond trades at a discount.
The Par Value of the bond is $1,000. Coupon payments are made semiannually (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, 2009 the size and timing of cash flows are:
Par
Short Maturity Bond
C
Discount Rate Long Maturity Bond
8-13
Coupon Rates and Bond Prices
Bond Value
Consider two otherwise identical bonds. The low-coupon bond will have much more volatility with respect to changes in the discount rate.
8-15
YTM with Annual Coupons
Consider a bond with a 10% annual coupon rate, 15 years to maturity, and a par value of $1,000. The current price is $928.09.
8-11
Interest Rate Risk
Price Risk
Change in price due to changes in interest rates Long-term bonds have more price risk than short-term bonds Low coupon rate bonds have more price risk than high coupon rate bonds.
8-1
Chapter Outline
8.1 8.2 8.3 8.4 8.5 Bonds and Bond Valuation Government and Corporate Bonds Bond Markets Inflation and Interest Rates Determinants of Bond Yields
8-17
Current Yield vs. Yield to Maturity
Current Yield = annual coupon / price Yield to maturity = current yield + capital gains yield Example: 10% coupon bond, with semi-annual coupons, face value of 1,000, 20 years to maturity, $1,197.93 price
8-2
8.1 Bonds and Bond Valuation
A bond is a legally binding agreement between a borrower and a lender that specifies the:
Par (face) value Coupon rate Coupon payment Maturity Date
Is the YTM more or less than 10%? What is the semi-annual coupon payment? How many periods are there? N = 40; PV = -1,197.93; PMT = 50; FV = 1,000; CPT I/Y = 4% (Is this the YTM?) YTM = 4%*2 = 8%
Bond value is, therefore, determined by the present value of the coupon payments and par value. Interest rates are inversely related to present (i.e., bond) values.
Will the yield be more or less than 10%? N = 15; PV = -928.09; FV = 1,000; PMT = 100 CPT I/Y = 11%
8-16
YTM with Semiannual Coupons
Suppose a bond with a 10% coupon rate and semiannual coupons has a face value of $1,000, 20 years to maturity, and is selling for $1,197.93.
Par
High Coupon Bond
C
Low Coupon Bond Discount Rate
8-14
Computing Yield to Maturity
Yield to maturity is the rate implied by the current bond price. Finding the YTM requires trial and error if you do not have a financial calculator and is similar to the process for finding r with an annuity. If you have a financial calculator, enter N, PV, PMT, and FV, remembering the sign convention (PMT and FV need to have the same sign, PV the opposite sign).