Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

93
Chapter 6 – Bond Valuation and Interest Rates INTRODUCTION TO CORPORATE FINANCE Second Edition Laurence Booth • W. Sean Cleary Prepared by Ken Hartviksen

Transcript of Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Page 1: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Chapter 6 – Bond Valuation and Interest Rates

INTRODUCTION TO CORPORATE FINANCE

Second Edition

Laurence Booth • W. Sean Cleary

Prepared by

Ken Hartviksen

Page 2: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Lecture Agenda

1. Basic Structure of Bonds1. Basic Structure of Bonds

2. Bond Valuation 2. Bond Valuation

3. Bond Yields3. Bond Yields

4. Interest Rate Determinants4. Interest Rate Determinants

5. Other Debt Instruments5. Other Debt Instruments

Bond Basics Bond Basics Valuation Valuation YieldsYields DeterminantsDeterminants Other DebtOther Debt

Page 3: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Learning Objectives

The basic features of different types of bonds How to value bonds given an appropriate discount rate How to determine the discount rate or yield given the

market value of a bond How market interest rates or yields affect bond investors How bond prices change over time The factors (both domestic and global) that affect interest

rates

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Page 4: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Basic Structure of Bonds

Page 5: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

The Basic Structure of Bonds

What is a bond? In its broadest sense, a bond is any debt

instrument that promises a fixed income stream to the holder

Fixed income securities are often classified according to maturity, as follows:

Less than one year – Bills or “Paper” 1 year < Maturity < 7 years – Notes < 7 years – Bonds

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Page 6: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

The Basic Structure of Bonds

A typical bond has the following characteristics: A fixed face or par value, paid to the holder of the

bond, at maturity A fixed coupon, which specifies the interest payable

over the life of the bond Coupons are usually paid either annually or semi-

annually A fixed maturity date

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Page 7: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Bonds may be either: Bearer bonds Registered bonds

Bond indenture - the contract between the issuer of the bond and the investors who hold it

The market price of a bond is equal to the present value of the payments promised by the bond

(See the basic pattern of cash flows from a traditional bond on the next slide)

The Basic Structure of Bonds

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Page 8: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

The Basic Structure of BondsCash Flow Pattern for a Traditional Coupon-Paying Bond

0 1 2 3 … n

I I I I I

F

0 1 2 3 … n

I I I I I

F

FIGURE 6-1

I = interest payments, and F = principal repayment

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Page 9: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Cash Flow Pattern of a Bond

The Purchase Price or Market Price of a bond is simply the present value of the cash inflows, discounted at the bond’s yield-to-maturity

0 2 3 4 n1

Coupon Coupon Coupon Coupon Coupon +Face Value

Purchase Price

Cash Inflows to the Investor

Cash Outflows to the Investor

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Page 10: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Bond indenture is the contract between the issuer and the holder. It specifies:

Details regarding payment terms Collateral Positive and negative covenants Par or face value (usually increments of $1,000) Bond pricing – usually shown as the price per $100

of par value, which is equal to the percentage of the bond’s face value

The Basic Structure of Bonds

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Page 11: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Term-to-maturity – the time remaining to the bond’s maturity date

Coupon rate – the annual percentage interest paid on the bond’s face value; to calculate the dollar value of the annual coupon, multiply the coupon rate by the face value

If the coupon is paid twice a year, divide the annual coupon by two

Example: A $1,000 bond with an 8% coupon rate will have an $80 coupon if paid annually or a $40 coupon if paid semi-annually

The Basic Structure of Bonds

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Page 12: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Security and Protective Provisions

Mortgage bonds – secured by real assets Debentures – either unsecured or secured with

a floating charge over the firm’s assets Collateral trust bonds – secured by a pledge of

financial assets, such as common stock, other bonds or treasury bills

Equipment trust certificates – secured by a pledge of equipment, such as railway rolling stock

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Page 13: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Security and Protective Provisions

Covenants Positive covenants – things the firm agrees to do

Supply periodic financial statements Maintain certain ratios

Negative covenants – things the firm agrees not to do Restricts the amount of debt the firm can take on Prevents the firm from acquiring or disposing of

assets

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Page 14: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

More Bond Features

Call feature – allows the issuer to redeem or pay off the bond prior to maturity, usually at a premium

Retractable bonds – allows the holder to sell the bonds back to the issuer before maturity

Extendible bonds – allows the holder to extend the maturity of the bond

Sinking funds – funds set aside by the issuer to ensure the firm is able to redeem the bond at maturity

Convertible bonds – can be converted into common stock at a pre-determined conversion price

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Page 15: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Bond Valuation

Page 16: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Bond Valuation

The value of a bond is a function of: Par value Term to maturity Coupon rate Investor’s required rate of return (discount rate is

also known as the bond’s yield to maturity)

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Page 17: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Bond ValueGeneral Formula

)k(

Fk

)k(IB

nbb

nb

1

111

1

[ 6-1]

Where:I = interest (or coupon ) paymentskb = the bond discount rate (or market rate)n = the term to maturityF = Face (or par) value of the bond

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Page 18: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Bond Valuation: Example

What is the market price of a ten-year, $1,000 bond with a 5% coupon, if the bond’s yield-to-maturity is 6%?

10

10

1 1

1

1 1.06 1,00050

0.06 1.06

$926.40

n

bn

b b

k FB I

k k

Calculator Approach:1,000 FV50PMT10NI/Y 6CPT PV 926.40

Bond Basics Bond Basics Valuation Valuation YieldsYields DeterminantsDeterminants Other DebtOther Debt

ExampleExample

Page 19: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Factors Affecting Bond PricesBond Price-Yield Curve

Market Yield (%)

FIGURE 6-2

Price ($)

When interest rates increase, bond prices fallWhen interest rates increase, bond prices fall

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Page 20: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

The relationship between the coupon rate and the bond’s yield-to-maturity (YTM) determines if the bond will sell at a premium, at a discount, or at par

If Then Bond Sells at a:

Coupon < YTM Market < Face Discount

Coupon = YTM Market = Face Par

Coupon > YTM Market > Face Premium

Factors Affecting Bond Prices

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Page 21: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Bond Valuation: Semi-Annual Coupons

So far, we have assumed that all bonds have annual pay coupons. While this is true for many Eurobonds, it is not true for most domestic bond issues, which have coupons that are paid semi-annually

To adjust for semi-annual coupons, we must make three changes:

Size of the coupon payment (divide by 2) Number of periods (multiply by 2) Yield-to-maturity (divide by 2)

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Page 22: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Bond Valuation: Semi-Annual Coupons

For example, suppose you want to value a five-year, $10,000 Government of Canada bond with a 4% coupon, paid twice a year, given a YTM of 6%.

2

2

2 5

2 5

1 12

212 2

.061 1

400 10,00020.062 .06

12 2

$9,146.98

n

b

nb b

x

x

kI F

Bk k

Calculator Approach:10,000 FV400 ÷ 2 = PMT5 x 2 = N6 ÷ 2 = I/YCPT PV 926.40

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Page 23: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Factors Affecting Bond Prices

There are three factors that affect the price volatility of a bond

Yield to maturity Time to maturity Size of coupon

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Page 24: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Factors Affecting Bond Prices

Yield to maturity Bond prices go down when the YTM goes up Bond prices go up when the YTM goes down

Look at the graph on the next slide. It shows how the price of a 25 year, 10% coupon bond changes as the bond’s YTM varies from 1% to 30%

Note that the graph is not linear – instead it is said to be convex to the origin

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Page 25: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Factors Affecting Bond Prices Price and Yield: 25 Year Bond, 10% Coupon

Price/Yield Relationship

0

50

100

150

200

250

300

350

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29

Percent YTM

Pri

ce p

er $

100

of F

ace

Val

ue

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Page 26: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

The convexity of the price/YTM graph reveals two important insights:

The price rise due to a fall in YTM is greater than the price decline due to a rise in YTM, given an identical change in the YTM

For a given change in YTM, bond prices will change more when interest rates are low than when they are high

Factors Affecting Bond Prices Bond Convexity

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Page 27: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Factors Affecting Bond Prices

Time to maturity Long bonds have greater price volatility than

short bonds The longer the bond, the longer the period for

which the cash flows are fixed

Size of coupon Low coupon bonds have greater price volatility

than high coupon bonds High coupons act like a stabilizing device, since a

greater proportion of the bond’s total cash flows occur closer to today & are therefore less affected by a change in YTM

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Page 28: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Interest Rate Risk & Duration

The sensitivity of bond prices to changes in interest rates is a measure of the bond’s interest rate risk

A bond’s interest rate risk is affected by: Yield to maturity Term to maturity Size of coupon

These three factors are all captured in one number called duration

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Page 29: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Duration

Duration is a measure of interest rate risk The higher the duration, the more sensitive the

bond is to changes in interest rates A bond’s duration will be higher if its:

YTM is lower Term to maturity is longer Coupon is lower

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Page 30: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Bond Quotations

Issuer Coupon Maturity Price Yield

Canada 5.500 2009-Jun-01 103.79 4.16

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Page 31: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Cash Versus Quoted Prices

The quoted price is the price reported by the media

The cash price is the price paid by an investor The cash price includes both the quoted price

plus any interest that has accrued since the last coupon payment date

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Page 32: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Cash Versus Quoted Price: Example

Assume you want to purchase a $1,000 bond with a 5% coupon, paid semi-annually. Today is July 15th. The last coupon was paid June 30th. If the quoted price is $902, how much is the cash price?

Solution: The cash price is equal to: Quoted price of $902 Plus 15 days of interest

15902 1,000 0.05

365

902 2.05

$904.05

Cash price = Quoted Price+ Accrued Interest

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Page 33: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Bond Yields

Page 34: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Bond Yields

Yield-to-maturity (YTM) – the discount rate used to evaluate bonds

The yield earned by a bond investor who: Purchases the bond at the current market price Held the bond to maturity Reinvested all of the coupons at the YTM

Is the bond’s Internal Rate of Return (IRR)

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Page 35: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Bond Yield to Maturity

The yield to maturity is that discount rate that causes the sum of the present value of promised cash flows to equal the current bond price.

YTM)(

FYTM

YTM)(IB

n

n

1

111

1

[ 6-2]

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Page 36: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Solving for YTM

To solve for YTM, solve for YTM in the following formula:

Problem: can’t solve for YTM algebraically; therefore, must either use a financial calculator, spreadsheet, trial and error, or approximation formula.

1 1

1

n

n

YTM FB I

YTM YTM

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Page 37: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Solving for YTM

Example: What is the YTM on a 10 year, 5% coupon bond (annual pay coupons) that is selling for $980?

10

10

1 1

1

1 1 1,000980 50

1

5.26%

n

n

YTM FB I

YTM YTM

YTM

YTM YTM

YTM

Financial Calculator1,000 FV980 +/- PV50 PMT51 NI/Y 5.26%

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Page 38: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Solving for YTM: Semi-annual Coupons

When solving for YTM with a semi-annual pay coupon, the yield obtained must be multiplied by two to obtain the annual YTM

Example: What is the YTM for a 20 year, $1,000 bond with a 6% coupon, paid semi-annually, given a current market price of $1,030?

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Page 39: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Solving for YTM: Semi-annual Coupons

40

40

1 1

1

1 1 1,0001,030 30

1

2.87 2 5.74%

n

n

YTM FB I

YTM YTM

YTM

YTM YTM

YTM x

Financial Calculator1,000 FV1,030 +/- PV30 PMT40 NI/Y 2.87 x

2 =

5.746%

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Page 40: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

The Approximation Formula

Where

F = Face Value = Par Value = $1,000

B = Bond Price

I = the semi annual coupon interest

N = number of semi-annual periods left to maturity

1YTM) annual-semi (1YTM

YTM annual-semi 2YTM2

nB-F

Maturity toYield annual-Semi

2

BF

I

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Page 41: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Example

Find the yield-to-maturity of a 5 year 6% coupon bond that is currently priced at $850. (Always assume the coupon interest is paid semi-annually.)

Therefore there is coupon interest of $30 paid semi-annually

There are 10 semi-annual periods left until maturity

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Page 42: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Solution

The actual answer is 9.87%...so of course, the approximation approach only gives us an approximate answer…but that is just fine for tests and exams.

The actual answer is 9.87%...so of course, the approximation approach only gives us an approximate answer…but that is just fine for tests and exams.

%97.91)0486.1(1YTM) annual-semi (1YTM

9.3%0.0927320.0486YTM annual-semi 2YTM

0486.0925$

30$15$

2850,1$

30$10

850$000,1$

2

nB-F

Maturity toYield annual-Semi

22

BF

I

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Page 43: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

The Logic of the EquationApproximation Formula for YTM

The numerator simply represents the average semi-annual returns on the investment; it is made up of two components: The first component is the average capital gain (if it is a

discount bond) or capital loss (if it is a premium priced bond) per semi-annual period.

The second component is the semi-annual coupon interest received.

The denominator represents the average price of the bond. Therefore the formula is basically, average semi-annual

return on average investment. Of course, we annualize the semi-annual return so that we

can compare this return to other returns on other investments for comparison purposes.

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Page 44: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Yield to Call

If a bond has a call feature, the issuer can call the bond prior to its stated maturity

To calculate the yield to call, replace the maturity date with the first call date

Page 45: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Yield to Call

The yield to call is that discount rate that causes the present value of all promised cash flows including the call price (CP) to equal the current bond price.

YTC)(

CPYTC

YTC)(IB

n

n

1

111

1

[ 6-3]

Bond Basics Bond Basics Valuation Valuation YieldsYields DeterminantsDeterminants Other DebtOther Debt

Page 46: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Solving for YTC: Semi-Annual Coupons

Financial Calculator1,050 FV1,030 +/- PV30 PMT10 NI/Y 3.081 x

2 =

6.16%

YTC on a 20-year 6 percent bond that is callable in five years at a call price of $1,050. The bond pays semi-annual coupons and is selling for $1,030.

%16.62%081.3

%081.3

1

050,1$11

130$030,1$

1

111

1

10

10

YTC

annuallysemiYTC

YTC)(YTCYTC)(

YTC)(

CPYTC

YTC)(IB

n

n

Bond Basics Bond Basics Valuation Valuation YieldsYields DeterminantsDeterminants Other DebtOther Debt

Page 47: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Current Yield

The current yield is the yield on the bond’s current market price provided by the annual coupon

It is not a true measure of the return to the bondholder because it does not consider potential capital gain or capital losses based on the relationship between the purchase price of the bond and it’s par value.

B

interestAnnualCY [ 6-4]

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Page 48: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Current YieldExample

The current yield is the yield on the bond’s current market price provided by the annual coupon

Example: If a bond has a 5.5% annual pay coupon and the current market price of the bond is $1,050, the current yield is:

55

1,050

5.24%

Annual CouponCurrent Yield =

Current Market Price

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Page 49: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Interest Rate Determinants

Page 50: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Interest Rate Determinants

Interest is the “price” of money Basis points – 1/100 of 1% Interest rates go:

Up – when the demand for loanable funds rises Down – when the demand for loanable funds falls

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Page 51: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Risk-free Interest Rate

Usually use the yield on short federal government treasury bills as a proxy for the risk-free rate (RF)

The risk-free rate is comprised of two components: Real rate – compensation for deferring consumption Expected inflation – compensation for the expected loss in

purchasing power

(See Figure 6-3 to see rates of inflation and yields on long Canada bonds since 1961)

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Page 52: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Inflation and Yields over Time

FIGURE 6-3

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Page 53: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Fisher Equation

If we call the risk-free rate the nominal rate, then the relationship between the real rate, the nominal rate and expected inflation is usually referred to as the Fisher Equation (after Irving Fisher)

inflation Expectedrate RealRF [ 6-5]

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Page 54: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Fisher Equation

When inflation is low, can safely use the approximation formula:

When inflation is high, use the exact form of the Fisher Equation:

Nominal RealR = R + Expected Inflation

1 1 1Nominal RealR = R Expected Inflation

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Page 55: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Fisher Equation Example

If the real rate is 3% and the nominal rate is 5.5%, what is the approximate expected future inflation rate?

5.5 3

2.5%

Nominal RealR = R + Expected Inflation

Expected Inflation

Expected Inflation

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Page 56: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Global Influences on Interest Rates

Canadian domestic interest rates are heavily influenced by global interest rates

Interest rate parity (IRP) theory states that FX forward rates will be established that equalize the yield an investor can earn, whether investing domestically or in a foreign jurisdiction

A country with high inflation and high interest rates will have a depreciating currency

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Page 57: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Term Structure of Interest Rates

Is that set of rates (YTM) for a given risk-class of debt securities (for example, Government of Canada Bonds) at a given point in time.

When plotted on a graph, the line is called a Yield Curve

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Page 58: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Term Structure of Interest Rates

The Yield Curve is the graph created by putting term to maturity on the X axis, YTM on the Y axis and then plotting the yield at each maturity.

The four typical shapes of yield curves: Upward sloping (the most common shape) Downward sloping Flat Humped

(See Figure 6-4 for Yield curves that existed at various times in Canada)

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Page 59: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Historical Yield Curves1990, 1994, 1998, 2004

Pe

rce

nt

Term Left to Maturity

16

14

12

10

8

6

4

2

0

1 mth 3 mths 6 mths 1 yr 2yrs 5 yrs 7 yrs 10 yrs 30 yrs

FIGURE 6-4

1990 1994 1998 2004

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Page 60: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Theories of the Term Structure

Three theories are used to explain the shape of the term structure

Liquidity preference theory Investors must be paid a “liquidity premium” to hold

less liquid, long-term debt Expectations theory

The long rate is the average of expected future short interest rates

Market segmentation theory Distinct markets exist for securities of different

maturities

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Page 61: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Term Structure of Interest RatesRisk Premiums

More risky bonds (i.e.. BBB rated Corporate Bonds) will have their own yield curve and it will plot at higher YTM at every term to maturity because of the default risk that BBBs carry

The difference between the YTM on a 10-year BBB corporate bond and a 10-year Government of Canada bond is called a yield spread and represents a default-risk premium investors demand for investing in more risky securities.

Spreads will increase when pessimism increases in the economy

Spreads will narrow during times of economic expansion (confidence)

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Page 62: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Yield Curves for Different Risk ClassesRisk Premiums (Yield Spreads)

Pe

rce

nt

Term Left to Maturity

16

14

12

10

8

6

4

2

0

1 mth 3 mths 6 mths 1 yr 2yrs 5 yrs 7 yrs 10 yrs 30 yrs

BBB Corporates Government of Canada Bonds

Yield Spread

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Page 63: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Risk Premiums

The YTM on a corporate bond is comprised of:

The maturity yield differential is explained by the term structure

Spread is the additional yield due to default risk

Spread aldifferenti yieldMaturity -/ RFkb YTM[ 6-6]

Bond Basics Bond Basics Valuation Valuation YieldsYields DeterminantsDeterminants Other DebtOther Debt

Page 64: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Debt Ratings

All publicly traded bonds are assigned a “risk rating” by a rating agency, such as Dominion Bond Rating Service (DBRS), Standard & Poors (S&P), Moodys, Fitch, etc.

Bonds are categorized as Investment grade – top four rating categories (AAA,

AA, A & BBB) Junk or high yield – everything below investment

grade (BB, B, CCC, CC, D, Suspended)

Bond Basics Bond Basics Valuation Valuation YieldsYields DeterminantsDeterminants Other DebtOther Debt

Page 65: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Why Do Bonds Have Different Yields?

Default risk – the higher the default risk, the higher the required YTM

Liquidity – the less liquid the bond, the higher the required YTM

Call features – increase required YTM Extendible feature – reduce required YTM Retractable feature – reduce required YTM

Bond Basics Bond Basics Valuation Valuation YieldsYields DeterminantsDeterminants Other DebtOther Debt

Page 66: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Other Types of Bonds/Debt Instruments

Page 67: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Treasury Bills

Treasury bills are short-term obligations of government with an initial term to maturity of one year or less

Issued at a discount and mature at face value The difference between the issue price and the face

value is treated as interest income To calculate the price of a T-bill, use the following

formula

1T Bill

FP

nBEY

B

Where:P = market price of the T BillF = face value of the T BillBEY = the bond equivalent yieldn = the number of days until maturityB = the annual basis (365 days in Canada)

Bond Basics Bond Basics Valuation Valuation YieldsYields DeterminantsDeterminants Other DebtOther Debt

Page 68: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Treasury Bills: Example

What is the price of a $1,000,000 Canadian T bill with 80 days to maturity and a BEY of 4.5%?

1

1,000,00080

1 .045365

$990,233.32

T Bill

FP

nBEY

B

Bond Basics Bond Basics Valuation Valuation YieldsYields DeterminantsDeterminants Other DebtOther Debt

Page 69: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Solving for Yield on a T Bill

To solve for the yield on a T bill, rearrange the previous formula and solve for BEY.

Example: What is the yield on a $100,000 T bill with 180 days to maturity and a market price of $98,200?

100,000 98,200 365

98,200 180

3.72%

F P BBEY

P n

Bond Basics Bond Basics Valuation Valuation YieldsYields DeterminantsDeterminants Other DebtOther Debt

Page 70: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Zero Coupon Bonds

A zero coupon bond is a bond issued at a discount that matures at par or face value

A zero coupon bond has no reinvestment rate risk, since there are no coupons to be reinvested

To calculate the price of a zero coupon bond, solve for the PV of the face amount

Bond Basics Bond Basics Valuation Valuation YieldsYields DeterminantsDeterminants Other DebtOther Debt

Page 71: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Zero Coupon Bonds

Example: What is the market price of a $50,000 zero coupon bond with 25 years to maturity that is currently yielding 6%?

25

F

1

50,000

1.06

$11,649.93

n

b

Bk

Bond Basics Bond Basics Valuation Valuation YieldsYields DeterminantsDeterminants Other DebtOther Debt

Page 72: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Floating Rate & Real Return Bonds

Floating rate bonds have a coupon that floats with some reference rate, such as the yield on T bills

Because the coupon floats, the market price will typically be close to the bond’s face value

Real return bonds are issued by the Government of Canada to protect investors against unexpected inflation

Each period, the face value of the bond is grossed up by the inflation rate. The coupon is then paid on the grossed up face value.

Bond Basics Bond Basics Valuation Valuation YieldsYields DeterminantsDeterminants Other DebtOther Debt

Page 73: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Canada Savings Bonds

A Canada Savings Bond (CSB) is a special type of bond issued by the Government of Canada

It is issued in two forms: Regular interest – interest is paid annually Compound interest – interest compounds over the

life of the bond

CSBs are redeemable at any chartered bank in Canada at their face value

There is no secondary market for CSBs

Bond Basics Bond Basics Valuation Valuation YieldsYields DeterminantsDeterminants Other DebtOther Debt

Page 74: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Summary and Conclusions

In this chapter you have learned: About the nature of bonds as an investment How to value a bond using discounted cash flow

concepts About the determinants of interest rates and

theories used to explain the term structure of interest rates

Bond Basics Bond Basics Valuation Valuation YieldsYields DeterminantsDeterminants Other DebtOther Debt

Page 75: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Interesting Web Links

1. Bond Characteristics

2. Bond Valuation

3. Bond Yields

4. Bond Ratings and Agencies

Bond Basics Bond Basics Valuation Valuation YieldsYields DeterminantsDeterminants Other DebtOther Debt

Page 76: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

End of Chapter Problems

Chapter 6 – Bond Valuation and Interest Rates

Page 77: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Question 6 - 1

Which of the following statements concerning bonds is incorrect?

A. They involve blended payments of principal and interest.B. They have a fixed maturity date at which time the issuer

repays the full principal amount.C. Bondholders are paid a series of fixed periodic amounts

before the maturity date.D. The bond indenture is a legal document, specifying

payment requirements and so on.Solution: A

Mortgages have “blended” payments including interest and principal payment, not bonds.

End-of-Chapter Problems

Page 78: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Question 6 - 2

Which of the following statements is incorrect?A. Callable bonds give the bond issuer an option to call the

bond at a predetermined price.B. All debentures are secured bonds.C. Extendible bonds allow bondholders to extend the

maturity date.D. Convertible bonds give the bondholders an option to

convert into common shares at a predetermined conversion ratio.

Solution: B

Debentures are generally unsecured.

End-of-Chapter Problems

Page 79: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Question 6 - 3

Determine the price of a five-year 7 percent annual coupon bond when the market rate is 8 percent. The face value is $100.

A. $100

B. $102.50

C. $96.01

D. $104.10

Solution: C

Or, by financial calculator:

N = 5; I/Y= 8; PMT = 7; FV = 100; CPT PV = –96.01

$96.0168.058327.9490

)08.1(

1100

08.)08.1(

11

75

5

B

End-of-Chapter Problems

Page 80: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Question 6 - 4

Which of the following bond prices is most sensitive to market rate changes? The par value = $100 for all.

A. 5-year, 5 percent coupon rate, yield = 5.5 percent

B. 3-year, 8 percent coupon rate, yield = 5.6 percent

C. 7.5-year, 4.5 percent coupon rate, yield = 5.5 percent

D. 10-year, 4.5 percent coupon rate, yield = 5.5 percent

Solution: DAll else being equal, interest rate risk is positively related to term to

maturity, but negatively related to coupon rate and market yields. The bond in choice D has the lowest yield, lowest coupon rate and the longest term to maturity relative to other bonds. Therefore it has the highest interest rate risk.

End-of-Chapter Problems

Page 81: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Question 6 - 5

Determine the yield to maturity on a six-year, 7 percent, semi-annual-pay bond, which is now priced at $993. Use a financial calculator.

A. 7.05 percentB. 6.98 percentC. 3.57 percentD. 7.15 percent

Solution: DCoupon = ($1,000)(7%)/2=$35, N=6×2=12, FV=1,000, PV= –993

Using a financial calculator, N=12, PV= –993, PMT=35, FV=1,000 CPT I/Y=3.5727Therefore, YTM=3.5727%×2=7.15%

End-of-Chapter Problems

Page 82: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Question 6 - 6

Which of the following statements is correct?A. Current yield is the ratio of annual coupon payment divided by

the par value.

B. When the coupon rate is higher than the market rate, the bond is priced at discount.

C. When the market rate is higher than the coupon rate, the bond is priced at premium.

D. If a bond is at discount, the coupon rate < current yield < YTM.

Solution: DCurrent yield is the ratio of annual coupon divided by the current market price. When coupon rate is higher than the market rate, bond is at premium and when the market rate is higher, bond is at discount.

End-of-Chapter Problems

Page 83: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Question 6 - 7

According to interest rate parity (IRP) theory,A. differences in interest rates across countries cannot be totally offset by

expected changes in exchange rates.B. forward exchange rates may be locked in today to eliminate foreign

exchange risk and ensure investors can profit from moving capital to countries with higher interest rates.

C. the inflation differentials between countries affect both interest rates and currency exchange rates.

D. the country with a higher inflation rate will see its currency appreciate against another country with a lower inflation rate.

Solution: CDifference in interest rates across countries can be offset by expected changes in exchange rates. If a country has a higher expected inflation rate, its currency will depreciate.

IRP states that forward exchange rates locked-in today to eliminate foreign exchange risk ensure investors earn the same amount no matter where they invest.

End-of-Chapter Problems

Page 84: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Question 6 - 8

Which statement is incorrect?A. The liquidity preference theory states that investors prefer

short-term debt.

B. According to the expectations theory, a downward-sloping yield curve implies that interest rates are expected to decline in the future.

C. The risk premium in the bond yield reflects default risk, liquidity risk, and issue-specific features.

D. A debt rating of AAA is a worse rating than BB for S&P.

Solution: DAAA is rated higher than BB.

End-of-Chapter Problems

Page 85: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Question 6 - 9

Calculate the quoted price of a 182-day Canadian T-bill that has a face value of $10,000 and a quoted yield of 5.5 percent.

A. $9,733.07

B. $9,478.67

C. $97.3307

D. $94.7867

Solution: C

Because it is quoted on a basis of $100, therefore quoted price is $97.3307.

07.733,9$02742466.1

000,10

)365182

055.01(

000,10

P

End-of-Chapter Problems

Page 86: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Question 6 - 10

Which of the following statements is false?A. Zero coupon bonds are deep-discount bonds.

B. Zero coupon bonds are often created when cash flows are stripped from traditional bonds.

C. Floating rate bonds provide protection against decreasing interest rates.

D. There are two forms of return available for Canadian Savings Bond buyers.

Solution: C

Floating rate bonds provide protection against increasing interest rates compared to fixed rate bonds.

End-of-Chapter Problems

Page 87: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Question 6 - 11

State the relationship between the market rates and bond prices.

Solution:

When market interest rates increase, prices of bonds decrease. When market interest rates decrease, prices of bonds increase.

End-of-Chapter Problems

Page 88: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Question 6 - 12

Find the price of a bond with FV = $1,000, a coupon rate of 6 percent (paid semi-annually), and three years to maturity when

A. kb = 7 percent.B. kb = 6 percent.C. kb = 5 percent.

Solution:

Using a financial calculator:A. N = 6; I/Y= 3.5; PMT = 30; FV = 1,000; CPT PV = –973.36B. N = 6; I/Y= 3; PMT = 30; FV = 1,000; CPT PV = –1,000C. N = 6; I/Y= 2.5; PMT = 30; FV = 1,000; CPT PV = –1,027.54Clearly, the price of bonds is inversely related to the market yield.

End-of-Chapter Problems

Page 89: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Question 6 - 13

At maturity, each of the following zero-coupon bonds (pure discount bonds) will be worth $1,000. For each bond, find the missing quantity in the table below.

Solution:

Using a financial calculator:A. N = 30; PMT = 0; FV = 1,000; PV = - 400; CPT I/Y = 3.10%B. I/Y = 8; PMT = 0; FV = 1,000; PV = - 400; CPT N = 11.9 yearsC. N = 10; I/Y = 12; PMT = 0; FV = 1,000; CPT PV = $321.97

Price Maturity (years)

Yield to Maturity

A. $400 30

B. $400 8%

C. 10 12%

End-of-Chapter Problems

Page 90: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Question 6 - 14

Suppose that a government of Canada 9 percent annual-pay bond that matures in two years has a yield to maturity of 9.80 percent. If inflation is expected to be 3 percent per year over the next two years, what coupon rate would you expect to find on a Real Return Bond that is otherwise identical?

Solution:

Using the approximate relationship: 9.80% = Real Rate + 3%, so the Real Rate = 6.8%.

Using the exact relationship:Real Rate = (1+0.098)/(1+0.03) – 1 = 6.60%

End-of-Chapter Problems

Page 91: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Question 6 - 15

Suppose the inflation rate in Canada, as measured by the CPI, has been averaging 2.5 percent in recent years. The most recent Bank of Canada announcement indicates that it expects 4 percent inflation over the next year. If the real rate of return on Canadian T-bills is 1.75 percent, what is the nominal risk-free rate?

Solution:

The Fisher relationship uses expected inflation figures, not the actual rate of inflation experienced in the past. Therefore:

RF = 1.75% + 4% = 5.75%

Using the exact relationship:

RF = (1+0.0175)(1.04)–1=5.82%

End-of-Chapter Problems

Page 92: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Question 6 - 16

The following values are the spread for corporate bond yields:

A. One-year T-bills are trading with a YTM of 6 percent. What yield would you expect to find on A rated corporate bonds maturing in one year?

B. Five-year government bonds have a maturity yield differential of 50 basis points. What yield would you expect to observe on non-investment grade (BB rated) corporate bonds with a five-year maturity?

Solution: A. We can assume that T-bills (short-term, federal government bonds) have the highest possible credit rating,

“AAA”, because they have virtually no default risk. We expect lower rated (riskier) bonds to have a higher yield. For “A” rated bonds, we should expect kb = 6% + 0.45% = 6.45%

B. Adding the maturity yield and the “spread” for this bond rating, we find: kb = 6% + 0.50% + 1.10% = 7.60%

Bond Rating Spread over AAA

AA 30 basis points

A 45 basis points

BBB 70 basis points

BB 110 basis points

End-of-Chapter Problems

Page 93: Booth Cleary 2nd Edition Chapter 6 - Bond Valuation and Interest Rates

Copyright

Copyright © 2010 John Wiley & Sons Canada, Ltd. All rights reserved. Reproduction or translation of this work beyond that permitted by Access Copyright (the Canadian copyright licensing agency) is unlawful. Requests for further information should be addressed to the Permissions Department, John Wiley & Sons Canada, Ltd. The purchaser may make back-up copies for his or her own use only and not for distribution or resale. The author and the publisher assume no responsibility for errors, omissions, or damages caused by the use of these files or programs or from the use of the information contained herein.