chapter mcgraw-hill ryerson © 2013 mcgraw-hill ryerson limited interest rates and bond valuation...
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Chapter
McGraw-Hill Ryerson © 2013 McGraw-Hill Ryerson Limited
Interest Rates and Bond Valuation
Prepared by Anne Inglis
7
7-2
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
• Know how bond prices are quoted• Understand the impact of inflation on interest
rates• Understand the term structure of interest
rates and the determinants of bond yields© 2013 McGraw-Hill Ryerson Limited
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Chapter Outline
• Bonds and Bond Valuation
• More on Bond Features
• Bond Ratings
• Some Different Types of Bonds
• Bond Markets
• Inflation and Interest Rates
• Determinants of Bond Yields
• Summary and Conclusions© 2013 McGraw-Hill Ryerson Limited
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Bond Definitions 7.1
• Bond
• Par value (face value)
• Coupon rate
• Coupon payment
• Maturity date
• Yield or Yield to maturity
LO1
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Present Value of Cash Flows as Rates Change
• Bond Value = PV of coupons + PV of face
• Bond Value = PV annuity + PV of lump sum
• Remember, as interest rates increase the PV’s decrease and vice versa
• So, as interest rates increase, bond prices decrease and vice versa
LO2
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Valuing a Discount Bond with Annual Coupons
• Consider a bond with a coupon rate of 10% and coupons paid annually. The par value is $1000 and the bond has 5 years to maturity. The yield to maturity is 11%. What is the value of the bond?• Using the formula:
• B = PV of annuity + PV of lump sum• B = 100[1 – 1/(1.11)5] / .11 + 1000 / (1.11)5
• B = 369.59 + 593.45 = 963.04• Using the calculator:
• N = 5; I/Y = 11; PMT = 100; FV = 1000• CPT PV = -963.04
LO2
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Valuing a Premium Bond with Annual Coupons
• Suppose you are looking at a bond that has a 10% annual coupon and a face value of $1000. There are 20 years to maturity and the yield to maturity is 8%. What is the price of this bond?• Using the formula:
• B = PV of annuity + PV of lump sum• B = 100[1 – 1/(1.08)20] / .08 + 1000 / (1.08)20
• B = 981.81 + 214.55 = 1196.36• Using the calculator:
• N = 20; I/Y = 8; PMT = 100; FV = 1000• CPT PV = -1196.36
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Graphical Relationship Between Price andYield-to-Maturity
600
700
800
900
1000
1100
1200
1300
1400
1500
0% 2% 4% 6% 8% 10% 12% 14%
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Bond Prices: Relationship Between Couponand Yield
• If YTM = coupon rate, then par value = bond price
• If YTM > coupon rate, then par value > bond price• Why?
• Selling at a discount, called a discount bond
• If YTM < coupon rate, then par value < bond price• Why?
• Selling at a premium, called a premium bond
LO2
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The Bond-Pricing Equation
t
t
r)(1
F
rr)(1
1-1
C Value Bond
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Example – Semiannual Coupons
• Most bonds in Canada make coupon payments semiannually.
• Suppose you have an 8% semiannual-pay bond with a face value of $1,000 that matures in 7 years. If the yield is 10%, what is the price of this bond?• The bondholder receives a payment of $40
every six months (a total of $80 per year)• The market automatically assumes that the
yield is compounded semiannually• The number of semiannual periods is 14
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Example – Semiannual Coupons continued
• Or PMT = 40; N = 14; I/Y = 5; FV = 1000; CPT PV = -901.01
01.90105.1
000,1
05.01.05
1-1
40 Price Bond14
14
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Interest Rate Risk
• Arises from fluctuating interest rates
• Two things determine how sensitive a bond will be to interest rate risk:
1. Time to Maturity – All other things being equal, the longer the time to maturity, the greater the interest rate.
2. Coupon rate – All other things being equal, the lower the coupon rate, the greater the interest rate risk.
LO2
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Figure 7.2 – Interest Rate Risk and Time to Maturity
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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)
LO2
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Example – Finding the YTM
• Consider a bond with a 10% annual coupon rate, 15 years to maturity and a par value of $1000. The current price is $928.09.• Will the yield be more or less than 10%?• N = 15; PV = -928.09; FV = 1000; PMT = 100• CPT I/Y = 11%
LO2
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YTM with Semiannual Coupons
• Suppose a bond with a 10% coupon rate and semiannual coupons has a face value of $1000, 20 years to maturity and is selling for $1197.93.• Is the YTM more or less than 10%?• What is the semiannual coupon payment?• How many periods are there?• N = 40; PV = -1197.93; PMT = 50; FV = 1000;
CPT I/Y = 4% (Is this the YTM?)• YTM = 4%*2 = 8%
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Table 7.1 – Summary of Bond Valuation
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Bond Pricing Theorems
• Bonds of similar risk (and maturity) will be priced to yield about the same return, regardless of the coupon rate
• If you know the price of one bond, you can estimate its YTM and use that to find the price of the second bond
• This is a useful concept that can be transferred to valuing assets other than bonds
LO3
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Bond Prices with a Spreadsheet
• There is a specific formula for finding bond prices on a spreadsheet• PRICE (Settlement, Maturity, Rate, Yield,
Redemption, Frequency, Basis)
• YIELD(Settlement,Maturity,Rate,Pr,Redemption, Frequency,Basis)
• Settlement and maturity need to be actual dates
• The redemption and Pr need to given as % of par value
• Click on the Excel icon for an example
LO2
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Differences Between Debt and Equity 7.2
• Debt• Not an ownership interest• Bondholders do not have voting rights• Interest is considered a cost of doing
business and is tax deductible• Bondholders have legal recourse if
interest or principal payments are missed
• Excess debt can lead to financial distress and bankruptcy
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Differences Between Debt and Equity Continued
• Equity• Ownership interest• Common shareholders vote for the board of
directors and other issues• Dividends are not considered a cost of doing
business and are not tax deductible• Dividends are not a liability of the firm and
shareholders have no legal recourse if dividends are not paid
• An all equity firm can not go bankrupt
LO3
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The Bond Indenture
• Contract between the company and the bondholders; includes:• The basic terms of the bonds• The total amount of bonds issued• A description of property used as security, if
applicable• Sinking fund provisions• Call provisions• Details of protective covenants
LO1
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Bond Classifications• Registered vs. Bearer Forms• Security
• Collateral – secured by financial securities• Mortgage – secured by real property, normally land or
buildings• Debentures – unsecured debt with original maturity of
10 years or more• Notes – unsecured debt with original maturity less
than 10 years
• Seniority• Sinking Fund – Account managed by the bond
trustee for early bond redemption
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Bond Classifications Continued
• Call Provision• Call premium• Deferred call• Call protected• Canada plus call
• Protective Covenants• Negative covenants• Positive covenants
LO3
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Bond Characteristics and Required Returns
• The coupon rate depends on the risk characteristics of the bond when issued
• Which bonds will have the higher coupon, all else equal?• Secured debt versus a debenture• Subordinated debenture versus senior debt• A bond with a sinking fund versus one without• A callable bond versus a non-callable bond
LO3
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Bond Ratings – Investment Quality 7.3
• High Grade• DBRS’s AAA – capacity to pay is
exceptionally strong• DBRS’s AA – capacity to pay is very strong
• Medium Grade• DBRS’s A – capacity to pay is strong, but
more susceptible to changes in circumstances
• DBRS’s BBB – capacity to pay is adequate, adverse conditions will have more impact on the firm’s ability to pay
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Bond Ratings - Speculative
• Low Grade• DBRS’s BB, B, CCC, CC
• Considered speculative with respect to capacity to pay.
• Very Low Grade• DBRS’s C – bonds are in immediate
danger of default
• DBRS’s D – in default, with principal and/or interest in arrears
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Stripped or Zero-Coupon Bonds 7.4
• Make no periodic interest payments (coupon rate = 0%)
• The entire yield-to-maturity comes from the difference between the purchase price and the par value
• Cannot sell for more than par value• Sometimes called zeroes, or deep discount
bonds• Bondholder must pay taxes on accrued
interest every year, even though no interest is received
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Floating Rate Bonds
• Coupon rate floats depending on some index value
• There is less price risk with floating rate bonds• The coupon floats, so it is less likely to differ
substantially from the yield-to-maturity
• Coupons may have a “collar” – the rate cannot go above a specified “ceiling” or below a specified “floor”
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Other Bond Types
• Catastrophe bonds
• Income bonds
• Convertible bonds
• Put bond (retractable bond)
• There are many other types of provisions that can be added to a bond and many bonds have several provisions – it is important to recognize how these provisions affect required returns
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Bond Markets 7.5
• Primarily over-the-counter transactions with dealers connected electronically
• Extremely large number of bond issues, but generally low daily volume in single issues
• Makes getting up-to-date prices difficult, particularly on small corporate issues
• Treasury securities are an exception
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Bond Quotations
• From Figure 7.4
Canada 9.75 Jun 1/21 167.09 1.91
• Issue is a Government of Canada bond
• Coupon rate is 9.75% (assumed to be semiannual)
• Maturity date is June 1, 2021
• Price that a bondholder can sell for is $1,670.90
• Yield to maturity is 1.91% compounded semiannually
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Inflation and Interest Rates 7.6
• Real rate of interest – compensation for change in purchasing power
• Nominal rate of interest – quoted rate of interest, includes compensation for change in purchasing power and inflation
LO5
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The Fisher Effect
• The Fisher Effect defines the relationship between real rates, nominal rates and inflation
• Exact relationship is (1 + R) = (1 + r)(1 + h), where:• R = nominal rate• r = real rate• h = expected inflation rate
• Approximation of the above relationship is:• R = r + h
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Example – Fisher Effect
• If we require a 10% real return and we expect inflation to be 8%, what is the nominal rate?
• R = (1.1)(1.08) – 1 = .188 = 18.8%
• Approximation: R = 10% + 8% = 18%
• Since the real return and expected inflation are relatively high, there is significant difference between the actual Fisher Effect and the approximation.
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Term Structure of Interest Rates 7.7
• Term structure is the relationship between time to maturity and yields, all else equal
• It is important to recognize that we pull out the effect of default risk, different coupons, etc.
• Yield curve – graphical representation of the term structure• Normal – upward-sloping, long-term yields
are higher than short-term yields• Inverted – downward-sloping, long-term
yields are lower than short-term yields
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Figure 7.4 – Upward-Sloping Yield Curve
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Figure 7.4 – Downward-Sloping Yield Curve
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Figure 7.6 – Government of Canada Yield Curve
January 5, 2012LO6
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Factors Affecting Required Return
• Default risk premium – remember bond ratings
• Liquidity premium – bonds that have more frequent trading will generally have lower required returns
• Anything else that affects the risk of the cash flows to the bondholders, will affect the required returns
LO6
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Quick Quiz
• How do you find the value of a bond and why do bond prices change?
• What is a bond indenture and what are some of the important features?
• What are bond ratings and why are they important?
• How does inflation affect interest rates?• What is the term structure of interest rates?• What factors determine the required return on
bonds?
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Summary 7.8
• You should know:
• How to price a bond or find the yield
• Bond prices move inversely with interest rates
• Bonds have a variety of features that are spelled out in the indenture
• Bonds are rated based on their default risk
• Most bonds trade OTC
• Fisher effect links interest rates and inflation
• Term structure of interest rates shows the relationship between interest rates and maturity
© 2013 McGraw-Hill Ryerson Limited
Homework
• 2, 3, 5, 16, 17
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