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Transcript of Ch 09 Show
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Copyright 2002 Harcourt, Inc. All rights reserved.
CHAPTER 9Bonds and Their Valuation
Key features of bonds
Bond valuation
Measuring yield
Assessing risk
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Copyright 2002 Harcourt, Inc. All rights reserved.
Key Features of a Bond
1. Par value: Face amount; paid
at maturity. Assume $1,000.
2. Coupon interest rate: Statedinterest rate. Multiply by parvalue to get dollars of interest.Generally fixed.
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3. Maturity: Years until bondmust be repaid. Declines.
4. Issue date: Date when bondwas issued.
5. Default risk: Risk that issuer
will not make interest orprincipal payments.
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Copyright 2002 Harcourt, Inc. All rights reserved.
How does adding a call provision
affect a bond?
Issuer can refund if rates decline.
That helps the issuer but hurts theinvestor.
Therefore, borrowers are willing topay more, and lenders require more,on callable bonds.
Most bonds have a deferred call anda declining call premium.
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Copyright 2002 Harcourt, Inc. All rights reserved.
Whats a sinking fund?
Provision to pay off a loan over itslife rather than all at maturity.
Similar to amortization on a termloan.
Reduces risk to investor, shortens
average maturity.But not good for investors if rates
decline after issuance.
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Copyright 2002 Harcourt, Inc. All rights reserved.
1. Call x% at par per year for sinking
fund purposes.2. Buy bonds on open market.
Company would call if kd is below the
coupon rate and bond sells at apremium. Use open market purchaseif kd is above coupon rate and bondsells at a discount.
Sinking funds are generally handled
in 2 ways
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Copyright 2002 Harcourt, Inc. All rights reserved.
Financial Asset Valuation
PV =
CF
1 + k . . . +
CF
1 + k
1 n
1
2
21
CF
k n .
0 1 2 nk
CF1 CFnCF2Value
...
+ ++
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Copyright 2002 Harcourt, Inc. All rights reserved.
The discount rate (ki) is theopportunity cost of capital, i.e.,the rate that could be earned on
alternative investments of equalrisk.
ki = k* + IP + LP + MRP + DRP
for debt securities.
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Copyright 2002 Harcourt, Inc. All rights reserved.
Whats the value of a 10-year, 10%
coupon bond if kd = 10%?
V
k k
B
d d
$100 $1,1
000
1
1 10 10. . . +$100
1+ kd
100 100
0 1 2 10
10%
100 + 1,000V = ?
...
= $90.91 + . . . + $38.55 + $385.54= $1,000.
++
++
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Copyright 2002 Harcourt, Inc. All rights reserved.
10 10 100 1000N I/YR PV PMT FV
-1,000
The bond consists of a 10-year, 10%
annuity of $100/year plus a $1,000 lumpsum at t = 10:
$ 614.46
385.54$1,000.00
PV annuity
PV maturity valueValue of bond
=
==
INPUTS
OUTPUT
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Copyright 2002 Harcourt, Inc. All rights reserved.
10 13 100 1000N I/YR PV PMT FV-837.21
When kd rises, above the coupon rate,the bonds value falls below par, so itsells at a discount.
What would happen if expected
inflation rose by 3%, causing k =13%?
INPUTS
OUTPUT
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Copyright 2002 Harcourt, Inc. All rights reserved.
What would happen if inflation fell, and
kd declined to 7%?
10 7 100 1000N I/YR PV PMT FV
-1,210.71
If coupon rate > kd, price rises abovepar, and bond sells at a premium.
INPUTS
OUTPUT
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Copyright 2002 Harcourt, Inc. All rights reserved.
Suppose the bond was issued 20years ago and now has 10 years tomaturity. What would happen to itsvalue over time if the required rate
of return remained at 10%, or at13%, or at 7%?
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Copyright 2002 Harcourt, Inc. All rights reserved.
M
Bond Value ($)
Years remaining to Maturity
1,372
1,211
1,000
837
775
30 25 20 15 10 5 0
kd
= 7%.
kd = 13%.
kd = 10%.
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Copyright 2002 Harcourt, Inc. All rights reserved.
At maturity, the value of any bondmust equal its par value.
The value of a premium bond woulddecrease to $1,000.
The value of a discount bond wouldincrease to $1,000.
A par bond stays at $1,000 if kdremains constant.
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Copyright 2002 Harcourt, Inc. All rights reserved.
Whats yield to maturity?
YTM is the rate of return earned on
a bond held to maturity. Alsocalled promised yield.
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Copyright 2002 Harcourt, Inc. All rights reserved.
Whats the YTM on a 10-year, 9%
annual coupon, $1,000 par value bondthat sells for $887?
90 9090
0 1 9 10kd=?
1,000PV1...
PV10PVM887 Find kdthat works!
...
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Copyright 2002 Harcourt, Inc. All rights reserved.
10 -887 90 1000N I/YR PV PMT FV
10.91
VINT
k
M
kB
d
N
d
N1 1
1... +
INT
1+ k d
887 901 1 00011 10 10k kd d+ 901 + kd ,
Find kd
++++
++++
INPUTS
OUTPUT
...
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Copyright 2002 Harcourt, Inc. All rights reserved.
If coupon rate < kd, bond sells at adiscount.
If coupon rate = kd, bond sells at
its par value.
If coupon rate > kd, bond sells at apremium.
If kd rises, price falls.
Price = par at maturity.
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Copyright 2002 Harcourt, Inc. All rights reserved.
Find YTM if price were $1,134.20.
10 -1134.2 90 1000
N I/YR PV PMT FV7.08
Sells at a premium. Becausecoupon = 9% > kd = 7.08%,bonds value > par.
INPUTS
OUTPUT
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Copyright 2002 Harcourt, Inc. All rights reserved.
Definitions
Current yield =
Capital gains yield =
= YTM = +
Annual coupon pmtCurrent price
Change in priceBeginning price
Exp totalreturn
ExpCurr yld
Exp capgains yld
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Copyright 2002 Harcourt, Inc. All rights reserved.
Find current yield and capital gains
yield for a 9%, 10-year bond when thebond sells for $887 and YTM = 10.91%.
Current yield =
= 0.1015 = 10.15%.
$90$887
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Copyright 2002 Harcourt, Inc. All rights reserved.
YTM = Current yield + Capital gains yield.
Cap gains yield = YTM - Current yield
= 10.91% - 10.15%= 0.76%.
Could also find values in Years 1 and 2,get difference, and divide by value in
Year 1. Same answer.
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Copyright 2002 Harcourt, Inc. All rights reserved.
Whats interest rate (or price) risk?
Does a 1-year or 10-year 10% bondhave more risk?
kd 1-year Change 10-year Change
5% $1,048 $1,38610% 1,000 4.8% 1,000 38.6%
15% 956 4.4% 749 25.1%
Interest rate risk: Rising kd causesbonds price to fall.
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Copyright 2002 Harcourt, Inc. All rights reserved.
0
500
1,000
1,500
0% 5% 10% 15%
1-year
10-year
kd
Value
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Copyright 2002 Harcourt, Inc. All rights reserved.
What is reinvestment rate risk?
The risk that CFs will have to bereinvested in the future at lower rates,
reducing income.
Illustration: Suppose you just won$500,000 playing the lottery. Youll
invest the money and live off theinterest. You buy a 1-year bond with a
YTM of 10%.
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Copyright 2002 Harcourt, Inc. All rights reserved.
Year 1 income = $50,000. At year-end get back $500,000 to reinvest.
If rates fall to 3%, income will dropfrom $50,000 to $15,000. Had youbought 30-year bonds, income
would have remained constant.
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Copyright 2002 Harcourt, Inc. All rights reserved.
Long-term bonds: High interest raterisk, low reinvestment rate risk.
Short-term bonds: Low interest rate
risk, high reinvestment rate risk.Nothing is riskless!
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Copyright 2002 Harcourt, Inc. All rights reserved.
True orFalse: All 10-year bondshave the same price andreinvestment rate risk.
False! Low coupon bonds have lessreinvestment rate risk but moreprice risk than high coupon bonds.
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Copyright 2002 Harcourt, Inc. All rights reserved.
Semiannual Bonds
1. Multiply years by 2 to get periods = 2n.
2. Divide nominal rate by 2 to get periodicrate = kd/2.
3. Divide annual INT by 2 to get PMT =INT/2.
2n kd/2 OK INT/2 OKN I/YR PV PMT FV
INPUTS
OUTPUT
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Copyright 2002 Harcourt, Inc. All rights reserved.
2(10) 13/2 100/220 6.5 50 1000N I/YR PV PMT FV
-834.72
Find the value of 10-year, 10% coupon,
semiannual bond if kd = 13%.
INPUTS
OUTPUT
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Copyright 2002 Harcourt, Inc. All rights reserved.
You could buy, for $1,000, either a 10%,
10-year, annual payment bond or anequally risky 10%, 10-year semiannualbond. Which would you prefer?
The semiannual bonds EFF% is:
10.25% > 10% EFF% on annual bond, so buysemiannual bond.
EFFi
m
Nom
m
%.
. 1 1 10 10
21 10 25%
2
.
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If $1,000 is the proper price for the
semiannual bond, what is the properprice for the annual payment bond?
Semiannual bond has kNom
= 10%, withEFF% = 10.25%. Should earn sameEFF% on annual payment bond, so:
INPUTS
OUTPUT
10 10.25 100 1000N I/YR PV PMT FV
-984.80
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Copyright 2002 Harcourt, Inc. All rights reserved.
At a price of $984.80, the annualand semiannual bonds would bein equilibrium, because investors
would earn EFF% = 10.25% oneither bond.
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Copyright 2002 Harcourt, Inc. All rights reserved.
kNom = 7.53% is the rate brokerswould quote. Could also calculateEFF% to call:
EFF% = (1.03765)2 - 1 = 7.672%.
This rate could be compared tomonthly mortgages, and so on.
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Copyright 2002 Harcourt, Inc. All rights reserved.
If you bought bonds, would you be
more likely to earn YTM or YTC?
Coupon rate = 10% vs. YTC = kd =
7.53%. Could raise money by sellingnew bonds which pay 7.53%.
Could thus replace bonds which pay$100/year with bonds that pay only$75.30/year.
Investors should expect a call, henceYTC = 7.5%, not YTM = 8%.
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Copyright 2002 Harcourt, Inc. All rights reserved.
In general, if a bond sells at apremium, then (1) coupon > kd, so(2) a call is likely.
So, expect to earn:
YTC on premium bonds.
YTM on par & discount bonds.
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Copyright 2002 Harcourt, Inc. All rights reserved.
Disney recently issued 100-yearbonds with a YTM of 7.5%--thisrepresents the promised return. Theexpected return was less than 7.5%
when the bonds were issued. If issuer defaults, investors receive
less than the promised return.
Therefore, the expected return oncorporate and municipal bonds isless than the promised return.
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Copyright 2002 Harcourt, Inc. All rights reserved.
Bond Ratings Provide One Measure
of Default Risk
Investment Grade Junk Bonds
Moodys Aaa Aa A Baa Ba B Caa C
S&P AAA AA A BBB BB B CCC D
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Copyright 2002 Harcourt, Inc. All rights reserved.
What factors affect default risk and
bond ratings?
Financial performance
Debt ratio
TIE, FCC ratios
Current ratios
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Copyright 2002 Harcourt, Inc. All rights reserved.
Provisions in the bond contractSecured versus unsecured debt
Senior versus subordinated debt
Guarantee provisions
Sinking fund provisions
Debt maturity
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Other factorsEarnings stability
Regulatory environment
Potential product liability
Accounting policies
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Top Ten Largest U.S. Corporate
Bond Financings, as of July 1999
Issuer
Ford Motor Co.AT&T
RJR Holdings
WorldComSprint
Date
July 1999Mar 1999
May 1989
Aug 1998Nov 1998
Amount
$8.6 billion$8.0 billion
$6.1 billion
$6.1 billion$5.0 billion
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Bankruptcy
Two main chapters of Federal
Bankruptcy Act:Chapter 11, Reorganization
Chapter 7, Liquidation
Typically, company wants Chapter 11,creditors may prefer Chapter 7.
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If company cant meet its obligations, itfiles under Chapter 11. That stopscreditors from foreclosing, takingassets, and shutting down the
business.Company has 120 days to file a
reorganization plan.Court appoints a trustee to
supervise reorganization.Management usually stays in control.
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Company must demonstrate in itsreorganization plan that it isworth more alive than dead.
Otherwise, judge will orderliquidation under Chapter 7.
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If the company is liquidated, heresthe payment priority:
1. Secured creditors from sales ofsecured assets.
2. Trustees costs
3. Wages, subject to limits4. Taxes
5. Unfunded pension liabilities
6. Unsecured creditors7. Preferred stock
8. Common stock
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In a liquidation, unsecured creditors
generally get zero. This makes themmore willing to participate inreorganization even though their claims
are greatly scaled back.Various groups of creditors vote on the
reorganization plan. If both the majorityof the creditors and the judge approve,company emerges from bankruptcywith lower debts, reduced interestcharges, and a chance for success.