CHAPTER 7 Bonds and Their Valuation

1
CHAPTER 7Bonds and Their Valuation

• Key features of bonds
• Bond valuation
• Measuring yield
• Assessing risk
• Suggested problems on pages 224-226
• 7-1 through 7-10 (all 10 problems)

2
What is a bond?

• A debt security that will last at least one year
  from when it is issued
• Examples Treasury bonds, Treasury notes,
  corporate bonds, municipal bonds (Orange County
  muni bonds)
• The issuer issues the bonds to borrow
• The issuer agrees to make payments of principal
  and interest, on specific dates, to the holders
  (i.e., investors) of the bond.
• Examples The U.S. Treasury is the issuer of
  T-bonds.
• Once issued by the borrower, most bonds are
  invested in, owned, and traded among large
  financial institutions.
• Exceptions The U.S. Treasury makes it easy for
  us to invest in T-notes and T-bonds at
  www.TreasuryDirect.gov

3
Key Features of a Bond

• Par value (Principal) is the amount borrowed by
  the issuer and is paid back at maturity.
  Sometimes people call this the face value.
• Coupon interest rate is stated interest rate paid
  by the issuer. Multiply by par value to get
  dollar payment of interest. Usually this is a
  fixed rate that doesnt change. Exception
  Treasury Inflation-Protected bonds.
• Issue date is the date when the bond was issued.
• Maturity date is the date when the par value
  (Principal) of the bond must be repaid.
• Maturity is a term sometimes used to describe
  the amount of time between now and the maturity
  date
• Yield to maturity - rate of return earned on a
  bond held until maturity (also called the
  promised yield, opportunity cost and
  discount rate)

4
Key Features of a Bond

• Par value (Principal) is the amount borrowed by
  the issuer and is paid back at maturity.
  Sometimes people call this the face value.
• Example 1,000
• Coupon interest rate is stated interest rate paid
  by the issuer. Multiply by par value to get
  dollar payment of interest. Usually this is a
  fixed rate that doesnt change. Exception
  Treasury Inflation-Protected bonds.
• Example 10. Dollar payment 10 x 1,000
  100.
• Issue date is the date when the bond was issued.
• Example Oct 23, 2008
• Maturity date is the date when the par value
  (Principal) of the bond must be repaid.
• Example Oct 23, 2011
• Maturity is a term sometimes used to describe
  the amount of time between now and the maturity
  date
• Example 3 years
• Yield to maturity - rate of return earned on a
  bond held until maturity (also called the
  promised yield, opportunity cost and
  discount rate)

5
This is REALLY IMPORTANTHow do we calc. the
value of financial assets?
How much is this thing worth???? How much should
we pay? It should be worth the PV of its cash
flows!
6
Also REALLY IMPORTANT for bonds, r in
denominator is not the coupon rate.
Use the coupon rate to calculate the annual
cash flows. These are in the numerator. What is
r in the denominator????
7
The r in the denominator goes by many names
yield, opportunity cost, discount rate

• The r in the denominator equals the rate that
  could be earned on alternative investments of
  equal risk.
• This is return people expect to earn if they lend
  money that has the same risk that the bond has.
• This return has to compensate the investor for
  the risk-free rate, inflation, maturity risk,
  default risk, and the liquidity premium
• r r IP MRP DRP LP
• The r in the denominator is also called the
  yield to maturity or sometimes we just say
  yield.

8
What is the value of a 3-year, 10 annual coupon
bond, if rd 10? Assume a par value (face)
1,000.
Annual payment 100 10 annual coupon
1,000 face value. Note 100 is in the
numerator rd 10 is in the denominator.
9
What is the value of a 10-year, 10 annual coupon
bond, if rd 10? Assume a par value (face)
1,000.
Annual payment 100 10 annual coupon
1,000 face value. Note 100 is in the
numerator rd 10 is in the denominator.
10
Now use the financial calculator What is the
value of a 10-year, 10 annual coupon bond, if rd
10? Assume a par value (face) 1,000.

• 1) A bond is just an annuity (pmt coupon in )
  PLUS lump sum at time n.
• 2) Hint lump sum principal is also called face
  value -- initials FV!! For FV, enter the
  principal only. (Do not add the last payment to
  it. The annuity accounts for all of the coupon
  payments.)
• 3) Use end mode because 1st payment at end of 1st
  period.
• 4) Use P/yr 1. Enter n 10, FV 1000, I/yr
  10, PMT 100.
• 5) Note the 10 entered in I/yr is the 10
  discount rate, not the coupon rate.
• 5) Solve for PV. Thats what the bond is worth
  today to buy or sell.
• 6) If coupon rate discount rate, PV FV! And
  we say bond is trading at par. Although the
  coupon rate discount rate in this example, this
  will not always be the case.

10
10
100
1000
INPUTS
N
I/YR
PMT
PV
FV
OUTPUT
-1000
11
What if the same company whose bonds we just
looked at issues 10-year bonds with the same risk
but a 13 annual coupon rate? Again assume a par
value of 1,000.

• Because the bonds have the same risk, investors
  will expect the same return.
• In other words, the discount rate (i.e., yield,
  opportunity cost) will have to be the same as on
  the last problem (10).
• This bond has an annual coupon payment of 130 (
  13 x par value).
• This bond sells for 1,184, which is more than
  its par value of 1,000. We say that it
  therefore sell at a premium (to par). It is
  worth more than par because the coupon rate
  exceeds the yield to maturity.

10
10
130
1000
INPUTS
N
I/YR
PMT
PV
FV
OUTPUT
-1184.34
12
What if the same company whose bonds we just
looked at issues 10-year bonds with the same risk
but a 7 annual coupon rate? Again assume a par
value of 1,000.

• This bond has an annual coupon payment of 70.
  Since the risk is the same the bond has the same
  yield to maturity as the previous bonds (10).
  This bond sells at a discount (815.66 lt 1,000).
  It sells for below par because the coupon rate
  is less than the yield to maturity.

10
10
70
1000
INPUTS
N
I/YR
PMT
PV
FV
OUTPUT
-815.66
13
Changes in Bond Value over Time

• What would happen to the value of each of these
  three bonds as time passes if required rate of
  return remains at 10?
• As time passes, n gets smaller. Graph shows
  how PV changes.
• Check for yourself calculate each of our 3 bonds
  when maturity 5.

VB
1,184 1,000 816
13 coupon rate
10 coupon rate.
7 coupon rate
Years to Maturity
10 5 0
14
Bond values over time

• At maturity, the value of any bond must equal its
  par value.
• If rd remains constant
• The value of a premium bond would decrease over
  time, until it reached 1,000.
• The value of a discount bond would increase over
  time, until it reached 1,000.
• A value of a par bond stays at 1,000.

15
What is the yield to maturity (or YTM or
yield on a 10-year, 9 annual coupon, 1,000
par value bond, selling for 887?

• Must find the rd that solves this equation.
• INT stands for the coupon payment (in ). M
  is the par value.
• This is the same equation as on slide 7-5, just
  using different notation.
• Hint Use your financial calculator.

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Find YTM for a bond price that is trading at a
price of 887. Par 1,000. N 10. Coupon
rate 9.

• Solving for I/YR, the YTM of this bond is 10.91.
  
• We say that this bond sells at a discount (to
  par). It does so because YTM gt coupon rate.
• Hint Enter PV as negative, PMT and FV positive.

10
90
1000
- 887
INPUTS
N
I/YR
PMT
PV
FV
OUTPUT
10.91
17
Another example Find YTM for the same bond as
the last example if the bond price is 1,134.20.
Par 1,000. N 10. Coupon rate 9.

• Solving for I/YR, the YTM of this bond is 7.08.
  
• We say this bond sells at a premium (to par).
  This is because YTM lt coupon rate.
• Hint Enter PV as negative, PMT and FV positive.

10
90
1000
-1134.2
INPUTS
N
I/YR
PMT
PV
FV
OUTPUT
7.08
18
What is interest rate (or price) risk? Does a
1-year or 10-year bond have more interest rate
risk?

• Interest rate risk is the concern that rising rd
  will cause the value of a bond to fall.
• rd 1-year Change 10-year Change
• 5 1,048 1,386
• 10 1,000 1,000
• 15 956 749

• The 10-year bond is more sensitive to interest
  rate changes, and hence has more interest rate
  risk.

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Illustrating Interest Rate Risk
10-Year Bond
1-Year Bond
20
What is reinvestment rate risk?

• Reinvestment rate risk is the concern that rd
  will fall, and future CFs will have to be
  reinvested at lower rates, hence reducing income.
• EXAMPLE Suppose you just won
• 500,000 playing the lottery. You
• intend to invest the money and
• live off the interest.

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Reinvestment rate risk example

• You may invest in either a 10-year bond or a
  series of ten 1-year bonds. Both 10-year and
  1-year bonds currently yield 10.
• If you choose the 1-year bond strategy
• After Year 1, you receive 50,000 in income and
  have 500,000 to reinvest. But, if 1-year rates
  fall to 3, your annual income would fall to
  15,000.
• If you choose the 10-year bond strategy
• You can lock in a 10 interest rate, and 50,000
  annual income.

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Conclusions about interest rate and reinvestment
rate risk
Short-term AND/OR High coupon bonds Long-term AND/OR Low coupon bonds
Interest rate risk Low High
Reinvestment rate risk High Low

• CONCLUSION Nothing is riskless!

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YTM can be broken down into 2 components
current yield and capital gains yield
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An example Current and capital gains yield

• Find the current yield and the capital gains
  yield for a 10-year, 9 annual coupon bond that
  sells for 887, and has a face value of 1,000.
• Current yield 90 / 887
• 0.1015 10.15

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Calculating capital gains yield

• YTM Current yield Capital gains yield
• CGY YTM CY
• 10.91 - 10.15
• 0.76
• How did we get the YTM of 10.91?
• Solve for I/yr
• N 10, PV -887, pmt 90, FV 1,000.

26
Alternative method forCalculating capital gains
yield

• Could also find the expected price one year from
  now and divide the change in price by the
  beginning price, which gives the same answer.
• One year from now N 9. Calculate PV for N 9.
  
• PV 893.78
• CGY (893.78 - 887)/887 0.76

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Semiannual bonds

1. Multiply years by 2 number of periods 2N.
2. Divide nominal rate by 2 periodic rate (I/YR)
   rd / 2.
3. Divide annual coupon by 2 PMT ann cpn / 2.

2N
rd / 2
cpn / 2
OK
OK
INPUTS
N
I/YR
PMT
PV
FV
OUTPUT
28
What is the value of a 10-year, 10 semiannual
coupon bond, if rd 13?

1. Multiply years by 2 N 2 10 20.
2. Divide nominal rate by 2 I/YR 13 / 2 6.5.
3. Divide annual coupon by 2 PMT 100 / 2 50.

20
6.5
50
1000
INPUTS
N
I/YR
PMT
PV
FV
OUTPUT
- 834.72
29
Some bonds are issued with a call provision

• Allows issuer to refund the bond issue. The
  issuer wants to do this if interest rates in the
  economy decline (helps the issuer, but hurts the
  investor).
• Borrowers are willing to pay a higher yield, and
  lenders require a higher yield, for callable
  bonds.
• Treasury bonds do not have call provisions.
• Used by some corporations. Most common use is by
  corporations with poorer credit ratings (higher
  default risk).
• Bottom line all else equal, if bond has call
  provision, PV is lower and YTM is higher. And we
  need to calculate the Yield to Call (YTC).

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What is the yield to call (or YTC) on a
10-year bond with a 14 annual coupon, 1,000 par
value bond, that can be called in 5 years for a
9 call premium? Assume today the bonds sell for
1,000.

• INT stands for the coupon payment (in ).
• N number of years to the date when the issuer
  can call the bond.
• Call price par value 9 of call premium
  1.091,000 1090.
• Hint Use your financial calculator.
• N 5, PV -1,000, PMT 14 of 1,000 140, FV
  1090.
• Solve for Yield to Call I/yr 15.03.

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When is a call more likely to occur?

• In general, if a bond sells at a premium, then
  (1) coupon gt rd, so (2) a call is more likely.
• So, expect to earn
• YTC on premium bonds.
• YTM on par discount bonds.

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Other types (features) of bonds

• Convertible bond may be exchanged for common
  stock of the firm, at the holders option.
• Warrant long-term option to buy a stated number
  of shares of common stock at a specified price.
• Putable bond allows holder to sell the bond
  back to the company prior to maturity.
• Income bond pays interest only when interest is
  earned by the firm.
• Indexed bond interest rate paid is based upon
  the rate of inflation.

33
What is a sinking fund?

• Provision to pay off a loan over its life rather
  than all at maturity.
• Similar to amortization on a term loan.
• Reduces risk to investor, shortens average
  maturity.
• But not good for investors if rates decline after
  issuance.

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Default risk

• If an issuer defaults, investors receive less
  than the promised return. Therefore, the
  expected return on corporate and municipal bonds
  is less than the promised return.
• Influenced by the issuers financial strength and
  the terms of the bond contract.

35
Evaluating default riskBond ratings
Investment Grade Junk Bonds
Moodys Aaa Aa A Baa Ba B Caa C
S P AAA AA A BBB BB B CCC C

• Bond ratings are designed to reflect the
  probability of a bond issue going into default.

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Factors affecting default risk and bond ratings

• Financial performance
• Debt ratio
• TIE ratio
• Current ratio
• Bond contract provisions
• Secured vs. Unsecured debt
• Senior vs. subordinated debt
• Guarantee and sinking fund provisions
• Debt maturity

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Other factors affecting default risk

• Earnings stability
• Regulatory environment
• Potential antitrust or product liabilities
• Pension liabilities
• Potential labor problems
• Accounting policies
• THE ECONOMY

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And speaking of default risk Whats
Bankruptcy?

• Two main chapters of the Federal Bankruptcy Act
• Chapter 11, Reorganization
• Chapter 7, Liquidation
• Typically, a companys management wants Chapter
  11, while creditors may prefer Chapter 7.

39
Chapter 11 Bankruptcy (aka Reorganization)

• If company cant meet its obligations
• It files under Chapter 11 to stop creditors from
  foreclosing, taking assets, and closing the
  business and it has 120 days to file a
  reorganization plan.
• Court appoints a trustee to supervise
  reorganization.
• Management usually stays in control.
• Company must demonstrate in its reorganization
  plan that it is worth more alive than dead.
• If not, judge will order liquidation under
  Chapter 7.

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Chapter 11 Bankruptcy (aka Reorganization) --
continued

• In a liquidation, unsecured creditors generally
  get zero. This makes them more willing to
  participate in reorganization even though their
  claims are greatly scaled back.
• Various groups of creditors vote on the
  reorganization plan. If both the majority of the
  creditors and the judge approve, company
  emerges from bankruptcy with lower debts,
  reduced interest charges, and a chance for
  success.

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Chapter 7 Bankruptcy (aka Liquidation)

• In a liquidation, the company is deemed to be
  worth more dead than alive.
• If bankruptcy court orders liquidation
• Assets are auctioned off
• Cash is then distributed in pecking order of
  priority of claims as specified in the Chapter 7
  Bankruptcy code
• People who hold the common stock usually get
  nothing because the cash usually isnt enough to
  cover the debts.

42
You may be surprised to learn

• Many companies go bankrupt
• Many of them emerge from bankruptcy
  reorganizations and thrive
• Examples United Airlines, GM?
• If you have bonds in the company that goes
  bankrupt, how much you recover will depend on the
  terms of your type of bond and also how much of a
  haircut was negotiated.
• Common shareholders, unlike bondholders, usually
  get nothing! That stock youre considering that
  looks like a good gamble at 1/share may go to 0!