Title: Interest Rates and Bond Valuation
1Interest Rates and Bond Valuation
2Key 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
3Chapter 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
4Issuer (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
5Issuer (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
6Buyer 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
7Bond 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
8Bond 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
9Bonds
- 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)
10Bonds
- 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
11Example 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
12This Bond with its 9 coupon, is priced to yield
8.74 at 1,030
13But If The Loan Has A Face Value Of 750,000, Why
Did The Bondholder Pay 772,500?
14- 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
15What 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
16Bond Prices
YTM gt Coupon Rate
YTM lt Coupon Rate
17Definitions
- 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
18The 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
19This Bond with its 6 coupon, is priced to yield
6.25 at 960
20Bond Price (Valuation) from Cash Flow Perspective
21Excel
- 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)
22Example 3
23Example 3
24Example 3
CF Is From Point Of View Of Issuer
25Bond 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 ?
26Graphical Relationship Between Price and YTM
27Valuing 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.
28Valuing 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.
29Interest 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
30Interest Rate Risk And Time To Maturity
31Interest 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)
32Interest Rate Risk Increases At A Decreasing Rate
33Computing 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)
34YTM 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?
35YTM 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?
36Use One Bond YTM To Find Price Of Another Bond
Example 8
Below Market rate discount
Above premium
37Bonds 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
38Bonds 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
39Differences 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
40Bond 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
41Bond 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
42Bond 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
43Bond 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
44Bond 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
45Bond 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
46Bond 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
47Bond 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
48Financial 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
49Bond 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
50Bond 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!)
51Bond 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
52Bond 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
53Some 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)
54- 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!
55Some 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
56Some 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
57Pure 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)
58Example 9Pure Discount Loans (Zero Coupon)
59Example 10Interest Only Bond v. Zero Coupon Bond
60Interest Only Bond v. Zero Coupon Bond
61Interest Only Bond v. Zero Coupon Bond
62Interest Only Bond v. Zero Coupon Bond
63Floating-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
64Other 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!
65Bond 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
66The 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.
67Inflation 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
68The 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
69Example 11
70Example 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.
71The 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)
72The 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
73Bond Yields represent 6 effects
- Some Components of Interest Rates
- Real Rate
- Inflation Premium
- Interest Rate Risk Premium
- Default Risk Premium
- Taxability Premium
- Liquidity Premium
74Real 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)
75Inflation 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
76Interest 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
77Term 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
78Upward-Sloping Yield Curve
79Downward-Sloping Yield Curve
80Term 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
81Treasury 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
82Treasury Yield Curve (Coupon Bond Yields)
83Default 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
84Taxability 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
85Liquidity 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
86Three 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
87Bond 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
88Securitization
- 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