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Interest Rates and Bond Valuation

- Chapter 6

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

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

Issuer (Seller) of Bonds (Borrower) Bond

Issuer

- Bonds Debt Liability Long-term debt
- 1 Bond usually means the corporation borrows

1000 (face value) - Corporations usually issue many Bonds
- Bond Issue
- The total number of bonds that a corporation

issues at the same time, in denominations of

1,000 or 5,000 each - Like any contractual debt
- Bond issuer pays periodic interest to the

bondholder - Bond issuer pays the face value back at the end

of the bond term

Issuer (Seller) of Bonds (Borrower) Bond

Issuer

- When you issue a bond, you borrow the money, then

use the money to buy assets that earn more cash

than the cash you have to pay out to the

bondholder - Leverage
- Example
- Borrow money at 8 interest and buy a machine

that earns the corporation 13 - The difference between 13 and 8, or 5, is left

for the stockholders

Buyer of Bonds (Lender) Bondholder

- Bonds Asset
- 1 Bond usually means the borrow lends money to

the corporation or government - Like any contractual debt
- Bondholders are paid periodic interest for

loaning money to the corporation and are paid

back the face value at the end of the bond term - When you buy a bond you are paying for a future

steam of cash flow

Bond Vocabulary

- Face value par value loan repayment at

maturity FV - Annual interest payments annual coupon
- Coupon is from the days when you presented coupon

to get paid interest - Annual interest rate (not discount rate) coupon

rate annual interest rate for calculating

interest payments annual coupon/face value - Number of interest payments per year n
- Periodic rate (not discount rate) periodic

coupon rate (annual coupon rate)/n - The book is inconsistent with the use of coupon

(sometimes annual, sometimes semi-annual) - Periodic interest payment periodic rateface

PMT - Years until maturity term of bond years until

paying back face value and last periodic interest

payment x - Maturity specified date on which principal is

repaid

Bond Vocabulary

- Yield To Maturity (YTM) discount rate used to

value bond i YTM - YTM Bond Yield Required Return Market Rate

Rate required in the market on a bond - YTMs are quoted like APRs
- YTM (Period Discount Rate) n
- Example YTM 10 and bond pays semiannual

interest payments, then period discount rate

YTM/n .10/2 .05 - Effective Annual Yield on the Bond (1.10/2)2

.1025

Bonds

- Bonds are interest only loans
- Corporations/Governments borrow money, pay

interest each period, then pay back face amount

at end of bond term - Corporations/Governments plan to issue bonds and

then set the coupon rate, but by the time they

actually issue the bond the financial markets

have already calculated a discount rate for the

future values that is often different than the

coupon rate - Corporations/Governments issue bonds and get the

cash in (Bonds sold in primary market) - Many Bonds from Corporations/Governments can be

traded in the financial markets (Bonds sold in

the secondary market)

Bonds

- Each bond has a price expressed as a percentage

of the face value - For example, 103 means 1.03 times the face value

of the bond - When the corporation issues the 1,000 face-value

bond, it receives 1,030 - At maturity, the corporation pays back only the

face value of 1,000 - 103 and 103 and 1.03 all convey the same meaning

? The bond is selling for 3 above the face value

Example 1

- On January 1, Cox Construction Corp. issues 750

10-year bonds with a face of 1000 with a coupon

rate of 9 at 103, with interest payable

semiannually, on June 30 and December 31

This Bond with its 9 coupon, is priced to yield

8.74 at 1,030

But If The Loan Has A Face Value Of 750,000, Why

Did The Bondholder Pay 772,500?

- If a corporation offers a rate of interest that

is higher than the market rate for similar

securities, investors may be willing to pay a

premium for the bond - If a corporation offers a rate of interest that

is lower than the market rate for similar

securities, investors will demand a discount on

the bond

What Are Similar Securities?

- Similar securities are bonds or other investment

vehicles issue by other corporations (different

than the one being considered) that have similar

business and financial risks - The similarities could be
- Similar credit ratings
- Similar business activities
- Similar capital structure

Bond Prices

YTM gt Coupon Rate

YTM lt Coupon Rate

Definitions

- Premium
- The excess of the price received over the face

value of a bond - YTM lt Coupon Rate
- Bond sold at a premium
- Discount
- The amount by which the issue price is less than

the face value of a bond - YTM gt Coupon Rate
- Bond sold at a discount

The Issuance of Bonds at a Discount Example 2

- On January 1, Muller, Inc., issues 700 6,

20-year bonds with a face value of 1,000, at 96,

with interest to be paid semiannually, on June 30

and December 31

This Bond with its 6 coupon, is priced to yield

6.25 at 960

Bond Price (Valuation) from Cash Flow Perspective

Excel

- Bond Valuation from Bondholders Point of View
- PV(rate,nper,pmt,fv,type)
- PV(YTM/n,nx,PMT,FV,0)
- Bond Valuation from Bond Issuers Point of View
- PV(rate,nper,pmt,fv,type)
- PV(YTM/n,nx,-PMT,-FV,0)
- Finding YTM rate from Bondholders Point of View
- RATE(nper,pmt,pv,fv,type,guess)
- RATE(nx,PMT,-PV,FV,0)

Example 3

Example 3

Example 3

CF Is From Point Of View Of Issuer

Bond Values And Why They Fluctuate

- Bond Valuation
- As time passes, interest rates change in the

market place - As new information about the company, the

industry, the economy comes out, interest rates

change - As time passes the amount of cash paid out to the

bondholder does not change - Because of this the value of the bond will

fluctuate - Rates ?, Bond Value ?
- Rates ?, Bond Value ?

Graphical Relationship Between Price and YTM

Valuing a Discount Bond with Annual Coupons

Payments (Example 4)

- Consider a bond with a coupon rate of 10 and

coupons paid annually. The par value is 1000 and

the bond has 5 years left until maturity. The

yield to maturity is 11. What is the value of

the bond ? What is the price to you, buying in

the secondary market? - Using the formula
- B PV of annuity PV of lump sum
- B 1001 1/(1.11)5 / .11 1000 / (1.11)5
- B 369.59 593.45 963.04
- Answer You would be willing to pay 963.04 cash

out (negative) for the future cash flows. or

said this way The bond with a 10 coupon is

priced to yield 11 at 963.04.

Valuing a Premium Bond with Annual Coupons

Payments (Example 5)

- Suppose you are looking at a bond that has a 10

annual coupon rate and a face value of 1000.

There are 20 years to maturity and the yield to

maturity is 8. What is the value of the bond ?

what is the price to you? - Using the formula
- B PV of annuity PV of lump sum
- B 1001 1/(1.08)20 / .08 1000 / (1.08)20
- B 981.81 214.55 1196.36
- Answer You would be willing to pay 1196.36

cash out (negative) for the future cash flows.

or said this way The bond with a 10 coupon is

priced to yield 8 at 1196.36.

Interest Rate Risk

- The risk that arises for bond owners from

fluctuating interest rates - How much interest rate risk a bond has depends

on - How sensitive its price is to interest rate

change - The sensitivity depends on two things
- All things being equal, the longer the time to

maturity, the greater the interest rate risk - All things being equal, the lower the coupon

rate, the greater the interest rate risk

Interest Rate Risk And Time To Maturity

Interest Rate Risk To Loss Of Principal (current

price)

- Longer time to maturity
- Small changes in market rate have substantial

affect on bond value - Face value is discounted over many periods and

thus compounding magnifies small interest rate

changes - Lower Coupon rate
- Bond with lower coupon rate is proportionally

more dependent on the face value - (Bond with larger coupon rate has a larger cash

flow early in life, so value less sensitive to

discount rate)

Interest Rate Risk Increases At A Decreasing Rate

Computing YTM

- Yield-to-maturity is the rate implied by the

current bond price - Finding the YTM requires trial and error

(iteration) if you do not have a financial

calculator and is similar to the process for

finding i 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)

YTM with Annual Coupons (Example 6)

- 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?

YTM with Semiannual Coupons (Example 7)

- 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?

Use One Bond YTM To Find Price Of Another Bond

Example 8

Below Market rate discount

Above premium

Bonds and Stocks

- Like stock, bonds bring capital (money) into the

corporation so that it can invest in profitable

projects - Bondholders are creditors
- They have a fixed claim to cash flow
- Stockholders are owners
- They have a residual claim to cash flow

Bonds and Stocks

- Debt is not an ownership interest in the firm
- Creditors do not have voting rights
- Interest is tax deductible
- Dividends are not tax deductible
- Unpaid debt is a liability
- Legal claim against assets
- If debt is not paid creditors have the legal

claim to assets before shareholders - One of the costs of issuing debt is the

possibility that you will not be able to make

interest payments ? creditors force firm into

bankruptcy ? firm is terminated - This does not arise when equity is issued
- Corporations try to create hybrid financial

instruments that are Debt/Equity in order to

have - Tax benefits of debt
- Bankruptcy benefits of equity

Differences Between Debt and Equity

- Debt
- Not an ownership interest
- Creditors do not have voting rights
- Interest is considered a cost of doing business

and is tax deductible - Creditors have legal recourse if interest or

principal payments are missed - Excess debt can lead to financial distress and

bankruptcy

- Equity
- Ownership interest
- Common stockholders 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

stockholders have no legal recourse if dividends

are not paid - An all equity firm can not go bankrupt

Bond Terms and Types

- Bonds Long-term debt
- Privately placed
- Directly placed with the lender
- Public-issue bonds
- Offered to the public
- Finance jargon
- Long-term debt funded debt
- Short-term debt unfunded debt
- Example A firm planning to fund its debt

requirements may be replacing short-term debt

with long-tern debt

Bond Terms and Types

- Trustee (Investment Bank, other)
- Appointed by the corporation to represent

bondholders - Must make sure terms are obeyed
- Must manage sinking fund
- Must represent bondholders in default
- Indenture
- The written agreement between the corporation

and the lender detailing the terms of the debt

issue

Bond Types

- Registered Form
- The form of bond issue in which the registrar of

the company records ownership of each bond - Payment is made directly to the owner of the bond
- Bearer Form
- The form of bond issue in which the bond is

issued without record of the owners name - Payment is made to whoever holds the bond
- Uncommon in the USA

Bond Types

- Security
- Generic term that means Stocks or Bonds or other

investment vehicles that are backed by an asset - A document indicating ownership or creditorship

a stock certificate or bond - Dictionary definition of Security
- Something deposited or given as assurance of the

fulfillment of an obligation a pledge collateral

Bond Types

- Debt securities are classified according to the

collateral and mortgages used to protect the

bondholder - Securities Backed By Collateral
- Collateral any asset pledged on the debt (often

means assets such as stocks or bonds financial

assets) - If the borrower does not pay the interest and

principal to the bondholder, the bondholder can

take the collateral - Mortgage Securities
- Debt secured by a mortgage on real assets

(property, but not cash or inventory) of the

borrower - Called
- Mortgage Trust Indenture, or Trust Deed
- Most utility and railroad bonds are secured by a

pledge of assets

Bond Types

- Unsecured Debt
- These creditors have a claim on property not

otherwise pledged - Debenture
- Unsecured debt (maturity gt 10 years)
- Most financial and industrial companies public

bonds are debentures - Note
- Unsecured debt (maturity lt 10 years)
- Subordinate Debt
- Must give preference to superior debt
- Debt is not subordinate to equity

Bond Types

- Sinking Fund
- An account managed by the trustee for the

purposed of repaying the bonds, or early bond

redemption - Bond Issuer must put away some money each period

to save up in order to pay off the bond - Protective Covenant
- A part of the indenture limiting certain actions

that might be taken in order to protect the

lender - Negative (thou shalt not)
- Example Limit the amount of dividends paid
- Positive (thou shalt)
- Example CA/CL must be greater than 1.5

Bond Types

- Call Provision
- An agreement giving the corporation the option to

repurchase the bond at a specific price prior to

maturity - Call Premium (Pay for the Option)
- The amount by which the call price gt par value
- Example Bond face 1,000, Call Price 1,100
- Call Price goes down over time
- Deferred Call Provision
- Can call only after a certain date
- Call Protected Bond
- Cant be redeemed by issuer
- Make-Whole Call
- When bond called, bondholder gets PV of future

cash flows at a reasonable rate - Derivative security jargon
- Call Buy
- Put Sell

Financial Markets

- Primary Markets
- Original sale of equity or debt
- Corporation issues security
- Secondary Markets
- After original sale of equity or debt
- You sell/buy security
- Dealer Markets (Over-the-counter markets (OTC))
- Dealers buy and sell for themselves
- Most debt is sold this way
- Example NASDAQ
- Auction Markets (Exchanges)
- Brokers and agents match buyers and sellers
- Most of the large firms equity is sold this way
- Example NYSE

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

Bond Ratings And What They Mean

- Bond Rating firms
- Moodys
- Standard and Poors (SP)
- They rate
- The likelihood of default
- The probability that creditors are protected
- They ask they question What is the risk

associated with the firm issuing the debt? - They do not rate the probability of bond value

change due to interest rate risk - The Debt Crisis of 2007 shows that Ratings can be

less than accurate - How do they take risky loans and repackage them

to get a AAA Super Senior rating? (Thats what

they did!)

Bond Ratings Investment Quality

- High Grade
- Moodys Aaa and SP AAA capacity to pay is

extremely strong - Moodys Aa and SP AA capacity to pay is very

strong - Medium Grade
- Moodys A and SP A capacity to pay is strong,

but more susceptible to changes in circumstances - Moodys Baa and SP BBB capacity to pay is

adequate, adverse conditions will have more

impact on the firms ability to pay

Bond Ratings - Speculative

- Low Grade
- Moodys Ba, B, Caa and Ca
- SP BB, B, CCC, CC
- Considered speculative with respect to capacity

to pay. The B ratings are the lowest degree of

speculation. - Very Low Grade
- Moodys C and SP C income bonds with no

interest being paid - Moodys D and SP D in default with principal

and interest in arrears

Some Different Types of Bonds

- Government Bonds
- Treasury Bill
- Years lt 1
- Treasury Note
- 1lt years lt 7
- Treasury Bonds
- Other
- No default risk
- Treasury issues are exempt from state income tax

(must pay Fed IT)

- U.S. NATIONAL DEBT CLOCK The Outstanding Public

Debt as of 13 Nov 2007 at 112801 PM GMT

is - The estimated population of the United States is

303,525,093so each citizen's share of this debt

is 30,039.21. The National Debt has continued to

increase an average of1.49 billion per day

since September 29, 2006!

Some Different Types of Bonds

- Municipal Bonds Munis
- State and local government debt
- Example Bond to build Highway
- These do have varying degrees of default risk
- Almost always callable
- Coupons exempt from federal income taxes (must

pay State IT) - Attractive to high-income/high-tax bracket

investors - Because of this the yields are lower
- Which do you (with 25 Fed tax Bracket) prefer

corporate bond that yields 5, or a muni (with

comparable risk and maturity) that yields 3.90? - .039 gt .05(1-.25) .0375

Some Different Types of Bonds

- Zero Coupon Bonds
- A bond that makes no coupon payments, and thus is

initially priced at a deep discount - Issuer must deduct interest every year
- Tax Benefit ? A deductions for taxes (fewer taxes

paid ? like cash coming in) even though no cash

going out (interest expense) - Bondholder must accrue interest revenue every

year - Taxes paid on revenue ? Cash going out (taxes

paid) even though cash is not coming in (interest

revenue) - Regular amortization table is constructed to

track interest accrual

Pure Discount Loans (Zero Coupon)

- Borrow an amount today, then pay back principal

and all interest at the end of the loan period - Example US Government Treasury Bills, or T-bills

(government loans lt 1year)

Example 9Pure Discount Loans (Zero Coupon)

Example 10Interest Only Bond v. Zero Coupon Bond

Interest Only Bond v. Zero Coupon Bond

Interest Only Bond v. Zero Coupon Bond

Interest Only Bond v. Zero Coupon Bond

Floating-Rate Bonds

- Coupon Payments are adjustable
- Rated can be tied to an interest rate index such

as the Treasury bill interest rate or 30-year

Treasury bond rate - Rate and payments are adjusted periodically
- Holder may have the right to redeem the note at

par on the coupon payment date after some

specified amount of time - This is called a Put Provision
- The coupon rate has a floor and ceiling
- Capped or Collared means they have an upper

and lower barrier

Other Bonds

- Income Bonds
- Coupon payments are dependent on the company

income - Convertible Bonds
- Debt that can be converted to a fixed amount of

equity anytime before maturity at the holders

option - Half Debt half equity?
- How do you list it on the Balance Sheet?
- Put Bond
- Allows holder to force the issuer to buy the bond

back at a stated price (reverse of a call) - CoCo and NoNo Bonds
- These have many features that require complex

valuing techniques. Because the features can be

valuable to the bondholder, the YTM could be

negative!

Bond Markets

- Because the bond market is almost entirely OTC,

it has little or no transparency (cant see a

great deal of Buy/Sells to gage market value of

bonds) - US Treasury market is the largest security market

in the world - Terminology
- Bid Price
- The price a dealer is willing to pay for a

security - Ask Price
- The price a dealer is willing to take for a

security - Bid-ask spread
- Bid Ask Dealers Profit

The Impact Of Inflation On Interest Rates

- Inflation
- Increase in price over time
- Example
- Price of milk now 3.39/gal.
- Price of milk in 1 year 3.56/gal.

Inflation and Interest Rates

- Real Rates
- Base interest rate that does not take inflation

into consideration - The percentage change in buying power
- Interest rates or rates of return that have been

adjusted downward from the nominal rate for

inflation - Nominal Rates
- Interest rates or rates of return that have not

been adjusted downward for inflation - change in the number of dollars you have
- The nominal rate of interest includes our desired

real rate of return plus an adjustment for

expected inflation

The Fisher Effect (Irving Fisher)

- The Fisher Effect defines the relationship

between real rates, nominal rates and inflation - R r h rh
- r (R-h)/(1h) (1R)/(1h) - 1
- (1 R) (1 r)(1 h)
- R nominal rate
- r real rate
- h expected inflation rate
- Approximation
- R r h

Example 11

Example 6.6

- 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
- Because the real return and expected inflation

are relatively high, there is significant

difference between the actual Fisher Effect and

the approximation.

The Fisher Effect

- Real rate is hard to observe directly, so we

observe it indirectly - r (R-h)/(1h) (1R)/(1h) - 1
- Real Rate is fairly constant
- Take into consideration taxes
- r (R(1-taxrate)-h)/(1h)

The Term Structure Of Interest Rates And

Determinants Of Bond Yields

- The risks associated with loaning money are added

into a base interest rate known as the real rate

Bond Yields represent 6 effects

- Some Components of Interest Rates
- Real Rate
- Inflation Premium
- Interest Rate Risk Premium
- Default Risk Premium
- Taxability Premium
- Liquidity Premium

Real Rate

- Compensation investors demand for foregoing the

use of their money - Basic component underlying every interest rate
- When real rate high, all rates tend to be high
- Doesnt really determine shape of term structure

(overall effect)

Inflation Premium

- The portion of a nominal interest rate that

represents compensation for expected future

inflation - Very strongly influences the shape of term

structure - Inflation expected increase ? structure upward
- Inflation expected decrease ? structure downward

Interest Rate Risk Premium

- Compensation demanded for bearing interest rate

risk - longer-term bonds have a much greater risk of

loss resulting from changes in interest rate than

so short-term bonds - This premium increases at a decreasing rate

Term Structure Of Interest Rates (Based On Pure

Discount Bonds)

- This shows the relationship between short and

long-term interest rates - Tells us what the nominal interest rates are on

default-free (Treasury), pure discount securities

of all maturities - This shows the relationship between nominal

interest rates on default-free, pure discount

securities and time to maturity - These rates are pure because they involve no

risk of default - The term structure tells us the pure time value

of money for different lengths of time - Upward sloping long-term rates gt short-term

rates - Downward sloping long-term rates lt short-term

rates

Upward-Sloping Yield Curve

Downward-Sloping Yield Curve

Term Structure Of Interest Rates

- Assumes
- Real Rates remain constant
- Inflation linear
- Rates could be Humped
- Rates increase at first, but then decline as we

look at longer-termed notes

Treasury Yield Curve

- A plot of the yields on Treasury Notes and Bonds

relative to Maturity - Treasury Yield Curve and the Term Structure Of

Interest Rates re almost the same thing - The difference is
- Treasury Yield Curve
- Based On Coupon Bond Yields
- Term Structure Of Interest Rates
- Based On Pure Discount Bonds

Treasury Yield Curve (Coupon Bond Yields)

Default Risk Premium

- Bonds other than Treasury Credit risk/default

risk - The portion of a nominal interest rate or bond

yield that represents compensation for the

possibility of default - Lower rated bonds have higher yields

Taxability Premium

- The portion of a nominal interest rate or bond

yield that represents compensation for

unfavorable tax status - Remember municipal versus taxable
- Bonds that are taxed at both the state and

Federal level are less favorable than a bond that

is only taxed at the Fed. level

Liquidity Premium

- The portion of a nominal interest rate or bond

yield that represents compensation for a lack of

liquidity - Liquidity
- How quickly an asset can be converted to cash
- Example
- Maybe the bond is hard to sell quickly and

therefore would require a premium for that lack

of liquidity - Less liquid bonds have higher yields than more

liquid bonds

Three Principles in Bond Finance

- Rates are inversely related to price
- Market rate ?, Bond Price ?
- Par, Discount, Premium
- Market rate Coupon Rate
- Bond sells at Par or Face Value
- Market rate gt Coupon Rate
- Bond sells at a Discount
- Market rate lt Coupon Rate
- Bond sells at a Premium
- The more years there are to maturity, the higher

the interest rate risk becomes - Interest rate risk to loss of principal

Bond Vocabulary

- Current Yield
- Annual Interest Payment/Closing Price
- Not equal to YTM (unless bond sells for par) it

does not include the capital gain from discounted

face value (principal) - Premium Bond
- CY gtYTM
- Discount Bond
- CY ltYTM
- In all cases ?(Current Yield) (Expected

one-period capital gain/loss yield of the bond)

must be equal to the YTM

Securitization

- Securitization The process of Securitization

involves the collection or pooling of loans and

the sale of securities backed by those loans

(Cash flows in loan) - Whereas, Banks once made loans and kept them on

their books, now they can initiate loans and then

sell the loans to someone else. - Securitization packaging a set of cash flows

and then selling claims (bonds or other) against

them - Claims asset backed securities
- This means that the cash is the asset that backs

it