Bonds

1

• Bonds
• Definition
• A bond is a type of annuity
• A bond is a long or short term debt instrument (a
  loan) issued by corporations and municipal, state
  and federal agencies.
• A bond is a contract its an IOU
• When a corporation or government agency issues
  bonds (request a loan, borrows money), it is said
  to be issuing debt
• When you buy a bond, you become a creditor to the
  issuing agency which, in turn, becomes a debtor
  to you
• Bonds are issued in uniform denominations (i.e.
  1,000, 10,000, etc.) most corporate and govt
  bonds are 1,000
• Bonds are traded (bought and sold) mostly OTC
• Bonds are the most predominate method for
  financing business and government projects
• Bonds are a fundamental investment class
• Some Terms
• Principal, Face Value, Maturity Value, and Par
  Value The amount of money the firm borrows and
  promises to repay at some future date, usually at
  the maturity date
• Coupon Interest Rate rcpn , the stated annual
  rate of interest paid on a bond.
• Coupon Payment
• The specified number of dollars of interest paid
  each period. Bonds most commonly pay semiannual
  interest.
• Its called a coupon because..
• Original Maturity The number of years (or
  months) to maturity at the time the bond is
  issued. Also referred to as the term. Some
  bonds have been issued with 100 year original
  maturity

2

• More Terms
• Maturity Date A specified date on which the par
  value of a bond must be repaid.
• Maturity The time left until a bond matures.
• What do you call a 10-year original maturity bond
  that was issued 8 years ago and thus has only 2
  years left to maturity? Answer a 2-year bond
• Main Types of Bonds (By Issuers)
• Treasury Bonds issued by the U.S. Government
  also known as treasuries or government bonds
  three types (by maturity)
• T-bills maturity of 1 year or less
• Treasury Notes maturity 2 maturity
• Treasury Bonds 10 maturity the maximum
  maturity currently available for new bonds is 30
  years
• Corporate Bonds issued by private firms
• Municipal Bonds
• issued by state and local govts called munis
  
• interest earned on most munis is tax deductible
• Foreign Bonds
• Subject to all risk/reward characteristics of
  domestic bonds
• Additional risk due to currency exchange rate
  fluctuation

3

• Bond Ratings
• Bonds from companies with similar risk
  characteristics are grouped together into
  categories as shown below

Risk (kd)
Higher
Lower

• Each of the rating categories above will have a
  different term structure of interest rates (see
  next slide)
• Each rating category is also referred to as a
  bond market (i.e. all AAA bonds are traded in
  the AAA bond market)
• Standard Poors and Moodys are two firms that
  provide these bond ratings
• A firms bond rating can change over time
• Bond Rating Factors Influenced by
• Financial health/strength of the issuing company
• Mortgage (collateral) provisions
• Seniority of the debt
• Restrictive covenants
• Sinking fund or deferred call
• Litigation possibilities
• Regulation effects on issuer
• Bond Issue(s) or Series
• Companies dont issue one bond at a time
• They issue several million worth at a time with
  each bond usually having a 1,000 Face/Maturity
  Value
• Example Intel issues 50m worth of bonds on 1
  Sep 2004, each bond has a Maturity Value of
  1,000 that equates to 50,000 bonds
• This single grouping of bonds is called a bond
  issue or series
• All bonds in a series have the same bond rating
  and YTM (more on YTM later)

4
Example Interest Rate Term Structure for
Different Bond Ratings
Bonds in different rating category but with the
same maturity will have a different rd.
Why? Answer
WSJ Bond Yields (as of 27 Feb 2009)
5

• Coupon Interest Rate
• This is the cost of debt to the issuer (borrower)
  
• A coupon bond pays periodic interest
• A zero-coupon bond pays interest only once
  (simple interest) (more on this later) applies
  mainly to short-term bonds
• For both types of bonds, the principle is repaid
  at maturity
• Coupon Payment
• Example a 10k face value bond has a coupon rate
  of 5.0000 per annum, paid annually. How much is
  the coupon payment?
• CPN(Cpn) Face Value(rcoupon/m) 10k(0.05/1)
  500
• Example a 10k face value bond has a coupon rate
  of 5 per annum, paid semiannually. How much is
  the coupon payment?
• CPN(Cpn) Face Value(rcoupon/m) 10k(0.05/2)
  250

6

• Bond Valuation
• Bonds are valuated using the TVM principles and
  techniques we learned in Ch 4
• Bonds can be modeled as simple present value
  problems
• Example Consider a 1,000 face value bond that
  pays annual interest and has a maturity of 5
  years. Draw the Cash Flow diagram.
• The Ch 4 version cash flow diagram for a bond
  looks like this

M Face Value 1,000 FV
0
1
2
3
4
5
Note In Ch 4, the interest payments were implied
PV ?
In this chapter, the bond cash flow diagram looks
like this
Bond Buyers (Holder, Lender) Perspective
Face Value (M) ? FV
Coupon (Interest) Payments (CPN or INT)
0
1
2
3
4
5
Fair Market Value or VB or Vd PV

• The interest payments are implied, but we will
  treat them as if they were specified thus the
  bond looks an annuity (in arrears)
• We will treat and analyze bonds as though they
  are annuities but they really arent (theres
  only 1 payment each period, not 2 as is the case
  for an annuity as described in Ch 4)

Bond Sellers (Issuer, Borrower) Perspective
Fair Market Value or VB or Vd PV
1
0
2
3
4
5
Face Value (M) ? Future Value
Coupon (Interest) Payments (CPN or INT)
7
Bond Valuation (continued)

• m the number of compounding periods/payments per
  year
• T the number of years left until maturity
• n the number of years or months or days, etc.
  (number of compounding periods/payments) until
  the bond matures n m x T
• M Face Value the principle the Par Value
• Coupon Rate(rcoupon) This is the interest the
  borrower promises to pay the lender. It is an
  APR.
• Coupon Payment (CPN) This is the interest
  payment (periodic or simple) CPN Face
  Value(rCPN/m)
• rd The current market interest rate for borrowed
  money.
• it is the current cost of money for all bonds of
  the same maturity and risk category (bond rating)
• it is the current ROR for bonds thus it is an
  opportunity cost/best investment opportunity wrt
  risk
• since our investment will grow at this rate we
  must also use it as the discount rate to compute
  PV
• Fair Market Value (VB or Vd)
• This is the theoretical value of a bond it is
  the PV of the bonds future cash flows Why?
• Answer The value of any financial asset is
  determined by discounting all future cash flows
  to the present (i.e. find the PV _at_ t 0) and
  adding them up
• rd changes all the time due to factors weve
  preciously discussed
• Since rd changes all the time, a bonds Fair
  Market Value changes all the time
• Answer rd is the rate at which we will discount
  all future cash flows to find PV. If the
  discount rate changes, PV must change.

8

• Bond Valuation (continued)
• Things that will not change during the life of a
  bond
• M (the face value)
• the Coupon Rate (promised interest rate)
• the Coupon Payment (promised interest payment)
• Pricing a bond (Finding VB or Vd)
• We want to know how to determine the appropriate
  current market value/theoretical value of bonds
  so we know how much to pay for or charge for that
  bond
• Basic Approach Find Present Value of an Annuity
• bonds are not really annuities
• bonds are really simple cash flow problems
• as discussed in Ch 4, annuities have two
  payments
• the implied payments (the interest earned on
  previous periods balance)
• the specified payments
• bonds have only one periodic payment (the
  interest earned on previous periods balance)
• however, we will treat the bonds interest
  payments as specified payments and thus treat
  them like annuities
• it is necessary to do this in order to do more
  complicated analysis on bonds that is beyond the
  scope of this course

9

• Bond Valuation (continued)
• When the bond is issued, the Cpn Rate is
  generally to the rd at that time in order to
  sell the bond at par value
• Example 1 Two years ago Jamaica Jims Cruise
  Lines (BB bond rating) issued 100m worth of
  1,000 bonds with an original maturity of 4 years
  and annual coupon payments. The bonds have a CPN
  Rate of 6.0000 since that was the cost of debt
  (rd) for a 4-year loan for all BB rated firms at
  the time. The current market interest rate (rd)
  for BB bonds with 2 year maturity is 5.0000.
  (i.e. the current cost of a 2-year loan for all
  BB rated firms is 5.0000). What is the current
  fair market value (VB) of these bonds?

M 1000
CPN
Cpn Rate rcpn 6 Current Mkt Interest Rate
rd 5
0
2
1
PV VB ?
Heres an explanation of what happens at each
time period
0
1
2
i 6
60 60 x 0.06
Beginning Balance 0.00 0.00
60.00 Interest Earned
0.00 60.00 63.60
Repay Principle 1,000.00
Ending Balance 0.00 60.00
1,123.60
M Face Value
Future Value
Each specified payment is the interest on the
principle in this case Face Value(rcpn/m)
1,000(0.06/1) 60.00
10
Bond Valuation (continued) Example 1 (continued)
Numerical Solution 1) Find CPN CPN Face
Value(rcpn/m) 1k(0.06/1) 60 2) Find VB VB
CPN/(1 rd /m)1 CPN/(1 rd /m)2 CPN/(1
rd /m)n M(1 rd /m)n 60/(1
0.05)1 60/(1 0.05)2 1000/(1 0.05)2
60/(1.05) 1060/(1.05)2 60/1.05
1060/1.1025 57.1429 961.4512
1,018.59 Why do we discount the cash flows
using rd? Why is the current fair market value
greater than the face value?

• Financial Function Solution
• 1) Find CPN CPN Face Value(rcpn/m)
  1k(0.06/1) 60
• 2) Clear your calculator 2nd, CLR TVM
• 3) Set/ensure 1 payment per year 2nd, P/Y, 1,
  ENTER
• 4) Set payment timing to end of year 2nd, BGN,
  2nd, SET (Note the BGN should NOT appear in
  the display)
• 5) Enter parameters
• Enter N 2, N
• Enter discount rate (rd) 5, I/Y
• Enter CPN payment 60, PMT
• Enter Face Value 1000, FV Note the FV(Future
  Value) of two payments of 60 over two years is
  not 1,000! When working with bonds, the FV key
  on the TI BA II PLUS can be interpreted as
  meaning Face Value
• Find VB CPT,PV and voila! PV(VB)
  1.018.59

11
Bond Valuation (continued) Example 2 (other
than 1 compounding period per year) What is the
current fair market value (VB) of a 3-year,
10,000 Face Value bond that has a coupon rate of
6.0000 p.a. and has semiannual coupon payments?
The current market interest rate (rd) for this
bond is 7.0000.
12

• Bond Valuation (continued)
• What Happens When rd Cpn Rate?
• When the market interest rate (rd) equals the
  coupon interest rate (rcpn) the market value of a
  bond equals its face value (VB M)
• Example What is the current fair market value
  (VB) of a 2-year, 1,000 Face Value bond that has
  a coupon rate of 6 APR and has annual coupon
  payments? The current market interest rate (rd)
  for this bond is 6. (rcpn rd). Answer 1,000
• VB CPN/(1 rd)1 CPN/(1 rd)2 CPN/(1
  rd)n M/(1 rd)n
• VB 1,000(0.06)/(1 0.06)1 1,000(0.06)/(1
  0.06)2 1,000/(1 0.06)2
• 60/1.06 60/1.1236 1,000/1.1236
• 56.6038 53.3998 899.9964
• 1,000
• When the fair market value of a bond equals its
  face value, the bond is said to be trading at
  par (recall face value par value)
• When the bond is first issued, the Cpn Rate is
  generally to rd in order to sell the bond at or
  very close to par value

13

• Relationship Between rd and VB
• When rd goes down (over time), VB goes up rd?,
  VB?
• When rd goes up (over time), VB goes down rd?,
  VB?
• Example A 1,000 bond issued by Home Depot
  paying a semi-annual coupon rate of 6.2500 APR
  with 2 years left to maturity has a current rd of
  7.7200.
• a) What is the VB of this bond? Answer 973.23
• b) What is the VB of this bond if rd fell to
  4.5000?
• Answer 1,033.12
• c) What is the VB of this bond if rd rose to
  8.5000?
• Answer 959.40

Cpn Rate 6.25
_at_ rd 6.25, this bond trades at par (VB
1,000)
Value
_at_ rd 6.25, VB
_at_ rd 1,000
rd (YTM)
14

• More Bond Terms Concepts
• Premium Bond a bond whose current market value
  is greater than its par value (rd
• Discount Bond a bond whose current market value
  is less than its par value (rd Cpn Rate)
• When a bond is first issued it is referred to as
  a new issue
• Once a bond has been on the market a while, its
  referred to as a seasoned issue or an outstanding
  bond
• Bond Mkt Price vs. Fair Mkt Value/Theoretical
  Value
• A bonds theoretical value is almost always equal
  to or very close to its bond market price (the
  price paid by bond traders)
• This is because there is very little uncertainty
  about bond valuation parameters
• the amount of each future cash flow is known (the
  coupon rate never changes)
• the cash flow termination date is known (we know
  exactly how many payments will be received)
• all of the above are contractually guaranteed
• everyone in the bond market knows how to
  determine fair market/theoretical value of a bond
  
• Since bond traders know how to determine bond
  FMVs, they wont pay more or sell for less than
  FMV (not including transaction costs)
• Market forces (supply demand) will sometimes
  cause minor discrepancies between Market Price
  and Fair market Value
• You I will have to pay a fee to buy bonds from
  bond brokers for us price ? fair market value

15
Yield to Maturity (YTM) Definition The average
rate of return earned on a particular bond issue
if it is held to maturity. This is the bond
traders rate of return and it is what is
reported on CNBC and in the WSJ Approach Given
all the normal bond parameters (i.e. face value,
coupon rate and maturity) and the current price
of the bond, find YTM (this is like solving for
an annuity interest rate) Example (finding
YTM) The current price of a 4-year, 10,000 AA
bond issued by GM paying an annual coupon rate of
5.0000 p.a. is 9,913.89. What is the yield to
maturity (YTM) of this bond?
CPN
M 10,000
rcpn 5
rd YTM ?
Price 9,913.89

• Calculator Solution
• 1) Find CPN CPN Face Value(rcpn/m)
  10k(0.05/1) 500
• 2) Enter parameters
• Enter number of periods 4, N
• Enter Price -9913.89, PV
• Enter CPN payment 500, PMT
• Enter Face Value 10000, FV
• Find YTM CPT,I/Y and voila! YTM (rd)
  5.2442 This is how a bonds value is reported
  (WSJ, CNBC, etc.)
• Is this a premium or discount bond?
• Interpretation
• If you buy this bond today and dont sell it then
  this bond will earn 5.24 until it matures.
• The price is based on what the market currently
  demands. Since its price is less than par, the
  current bond investing opportunity must be more
  than this bonds coupon (5.2442 vs. 5.0000)

16
Example (finding YTM w/ other-than-annual cpn
payments) The current FMV of a 1,000 BB bond
issued by Home Depot paying a semi-annual coupon
rate of 6.2500 APR with 2 years left to maturity
is 973.23. What is the yield to maturity of this
bond?
17

• Why would we want to know YTM?
• Answer to determine if the bonds (or series of
  bonds) current yield (YTM) is in line with its
  rating
• The value of particular firms bonds is a result
  of market perception of that firms financial
  health
• Each bond issue/series from a particular firm has
  a particular YTM
• YTM usually equals rd (i.e. all BB bonds will
  have the same rd and price is very close or equal
  to FMV)
• If theres a mismatch between the YTM for a
  particular firms bonds and the rd for all other
  bonds of similar rating (Moodys or SP), the
  market sees something either very good or very
  bad about that firm and the bonds price wont
  equal FMV
• Another Way of Reporting Bond Prices
• Bond values are also reported as a percent of par
  value
• Example 1,000 face value 5 year BB bonds are
  currently selling for 1,025.15. Their price is
  reported as 102.515

18
What happens to the Price (Value) of a bond over
time? Example A 1,000 face value bond with an
annual coupon rate of 5.0000 p.a., paying annual
coupon payments and a maturity of 5 years is
issued at t 0. What is its value at t 1 if
its trading at par?
CPN
M 1,000
Cpn Rate 5 rd 5
0
1
2
5
3
4
VB1 ?

• VB1 1,000 (rd Cpn Rate, its trading at par)
• What is the bonds value at t 1 if market
  interest rates have dropped to 2.8000?
  Answer VB1 1,082.17
• What is the value of the bond with only 3 years
  remaining until maturity (t2) if the market rate
  is 2.8000? Answer VB2 1,062.47
• What is the value of the bond with only 1 year
  remaining until maturity (t4) if the market rate
  is 2.8000 ? Answer VB4 1,021.40
• As a bond approaches maturity, value fluctuation
  due to changes in rd decreases
• the value of a premium bond would decrease
  towards 1,000.
• the value of a discount bond would increase
  towards 1,000.
• At maturity, the value of any bond must equal its
  par value (after the last coupon payment is paid)

19
What happens to the Value of a bond over time?
(continued)
Value Fluctuation Due to Changes in kd
rd Value
M
rd Coupon Rate
Years to Maturity

• Point As time goes on, the fair market value of
  a bond approaches (converges) to its par value.
• Point Regardless of how long ago a bond was
  issued, its current market value is based on
  time remaining until its maturity
• all previous coupon payments are irrelevant
• all that matters is the remaining expected future
  cash flows

20

• Bond Sensitivity to a Change in rd
• The prices of bonds with longer remaining
  maturity are much more influenced by a change in
  rd than the price of bonds with shorter remaining
  maturity
• Price volatility of long maturity bonds is
  greater than that of short maturity bonds
• Long maturity bonds are riskier than shorter
  maturity bonds this is reflected by the higher
  rd

FV 1,000 rcoupon 7.50 Annual Coupon
20-yr Bond
rd rcoupon VB FV
1-yr Bond
21

• Implications of Bond Sensitivity to a change in
  rd
• When market interest rates are falling, its good
  to have an inventory of long-term bonds to sell
• when rd decreases, bond values rise
• since long-term bond prices are more sensitive
  (react more) to changes in rd, the profits from
  selling them will be greater than for short term
  bonds
• When market interest rates bottom out and start
  to rise, its better to deal in (buy, hold, sell)
  short-term bonds
• when rd increases, bond prices fall
• shorter-term bonds are less sensitive to changes
  in rd and will have lower int. rate (price) and
  reinvestment risk
• Can we foresee what interest rates might be?
• Why are Bonds Traded?
• Answer
• 1) Speculation on value change due to interest
  rate change
• 2) Desire to invest in a mode that is less risky
  than stocks

22

• Other Risks Associated With Bonds
• Interest Rate Risk (Bond Price Risk) This is the
  uncertainty concerning the future value of a bond
  due to changes in rd
• Reinvestment Risk
• The risk that income from a bond portfolio will
  vary because cash flows have to be reinvested at
  current market rates
• When a bond matures, the owner may not be able to
  reinvest the face value of that bond at a rate at
  least a favorable as the one currently paid by
  that bond.
• These two types of risk are what is really being
  compensated by the Maturity Risk Premium (MRP)
• Point Shorter term bonds have less exposure to
  these types of risk than longer term bonds.
• Thats why MRP is smaller for short-term bonds
  than for long-term bonds
• A possible decision criteria for selecting bond
  maturities

23

• Capital Gains Yield
• This is how much you earn if/when you sell a bond
• It is capital gain(loss) due to changes in rd
• Its a percentage
• Its like computing Rate of Return (ROR)
• Example At the beginning of the year, a 1,000
  bond paying 8.25 APR semiannually bought for
  1,048 (FMV). At the end of the year, this bond
  was sold for 1,059 (FMV). What is the capital
  gains yield on this bond?
• Capital Gains Yield (End Value - Begin. Value)/
  Begin. Value
• (1,059 - 1,048)/1,048
• 0.010496 1.0496
• Total Yield
• This is the total return from interest and
  capital gains
• Usually computed over a 1 Year period
• Total Return EAR of Cpn Rate Cap. Gains Yield
• (Important Assumption interest payments are
  reinvested at the coupon rate. This is not
  always the case but its easier to learn total
  return if we make this assumption.)

24

• Types of Bond
• Mortgage Bonds A bond with some fixed asset
  presented as collateral
• higher claim priority than unsecured bonds
• usually have lower interest rates
• Debentures A long-term bond that is not secured
  by a mortgage on a specific property
• higher interest rates than secured bonds Why?
• Subordinated Debentures A bond that is
  specifically designated to be of lower claim
  priority than other bonds
• Bonds with Provisions (Indentures, Restrictions)
• Convertible bonds A bond that can be converted
  to a fixed number of stock shares specified at
  time of issue (its like a stock option)
• have a lower coupon rate than non-convertible
  bonds Why?
• offers the holder a chance at capital gains
  through stock
• Warrants
• Similar to a convertible bond but the price of
  the stock is specified at time of issue, not the
  number of shares
• offer a chance at capital gains if stock price at
  time of conversion is higher than the specified
  stock price
• Income Bond pays interest only if the issuing
  firm has sufficient income to pay the interest
• A real safe deal from the issuers stand point
  this type of bond cant bankrupt a firm

25

• Putable Bonds a bond that can be redeemed for
  cash at the bond holders option
• pay lower interest rates Why?
• when would it be a good idea to redeem this bond?
• Callable Bond a bond that has a call provision
  which allows the issuer to redeem the bond for
  cash at the issuers option prior to the stated
  maturity date
• pay higher interest rates. Why?
• when would it be a good idea to redeem this bond?
• Call premium Compensation paid to the holder by
  the issuer if/when the bond is called

26

• Pricing a Zero-Coupon Bond
• Recall that a zero-coupon bond pays interest only
  at maturity (simple interest), it does not pay
  periodic interest
• this is is true for some types of zero-coupon
  bonds
• In reality most zero-coupon bonds pay no interest
• they are, instead, sold at a discount they are
  issued as Original Issue Discount (OID) bonds
• the cost of borrowing money using a zero-coupon
  bond is reflected by the issue price, which is
  significantly lower than par value
• At issue, the coupon rate is usually equal to rd
  
• Example 1 A firm with a BB bond rating wants to
  issue a 1-year 1,000 zero-coupon bond. What is
  the price of the bond at issue if rd for 1-year
  BB bonds is 3.0000?

FV 1000
i 3
0
1
VB ?
N1, I/YR3, FV1000 PV (VB) 970.87