Bond Value Prob

Principles
of
Corporate
Finance
Ninth Edition
Chapter 24
Credit Risk and
the Value of
Corporate Debt
Slides by
Matthew Will
McGraw Hill/Irwin
Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved
24- 2
Topics Covered
Yields on Corporate Debt
The Option To Default
Bond Ratings and the Probability of Default
Predicting the Probability of Default
Value at Risk
24- 3
Defaulting Debt Levels
Face value of defaulting debt
100,000
90,000
70,000
60,000
50,000
40,000
30,000
20,000
10,000
0
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
$ Millions
80,000
24- 4
Valuing Risky Bonds
The risk of default changes the price of a bond and the
YTM.
Example
We have a 5% 1 year bond. The bond is priced at par of
$1000. But, there is a 20% chance the company will go into
bankruptcy and only pay $500. What is the bond’s value?
A:
24- 5
Valuing Risky Bonds
Example
We have a 5% 1 year bond. The bond is priced at par of $1000. But,
there is a 20% chance the company will go into bankruptcy and only pay
$500. What is the bond’s value?
A: Bond Value
Prob
1,050
.80
=
840.00
500
.20
=
100.00
940
Value 
 $895
1.05
1050
YTM 
 1  17.3%
895
.
940.00 = expected CF
24- 6
Valuing Risky Bonds
Example – Continued
Conversely - If on top of default risk, investors require an
additional 3 percent market risk premium, the price and YTM
is as follows:
940
Value 
 $870.00
1.08
1050
YTM 
 1  20.7%
870.00
10
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
Yield Spread, %
24- 7
Yield Spreads
12
Aaa
Baa
8
High yield
6
4
2
0
2005-04-13
2005-04-29
2005-05-17
2005-06-03
2005-06-21
2005-07-08
2005-07-26
2005-08-11
2005-08-29
2005-09-15
2005-10-03
2005-10-20
2005-11-07
2005-11-25
2005-12-13
2005-12-30
2006-01-19
2006-02-06
2006-02-23
2006-03-13
2006-03-29
2006-04-17
2006-05-03
2006-05-19
2006-06-07
2006-06-23
2006-07-12
2006-07-28
2006-08-15
2006-08-31
2006-09-19
Spread, %
24- 8
Credit Default Swap Data
Credit default swaps insure holders of corporate bonds against default. Dow
Jones indexes of spreads on default swaps measure the annual insurance
premium.
6
5
4
3
High grade
2
BB Bonds
High yield
1
0
24- 9
The Default Option
Example - Circular File borrowed $50 per share, but then the firm fell
on hard times and the market value of its assets fell to $30. Circular’s
bond and stock prices fell to $25 and $5, respectively. Thus Circular’s
market-value balance sheet is:
Circular File Company (market values)
Asset value
$30
$25
$ 5
$30
$30
Bonds
Stock
Firm value
Circular File Company (market values)
Asset value
$30
$30
$25
$ 5
$30
Bonds=Asset value – call value
Stock=value of a call
Firm value=Asset value
24- 10
The Default Option
Example (continued) - The value of Circular’s common stock is the
value of a call option on the firm’s assets with an exercise price of $50.
24- 11
Interest Rates, Risk, and Maturity
5
Leverage = 100%
Leverage = 60%
Leverage = 40%
Leverage = 20%
4
3
2
1
Maturity, years
25
23
21
19
17
15
13
11
9
7
5
3
0
1
Difference
between
promised yield
on bond and
risk-free rate,
percent
24- 12
Key to Bond Ratings
Moody's
Investment Grade
Aaa
Aa
A
Baa
Junk Bonds
Ba
B
Caa
Ca
C
S&P's & Fitch
AAA
AA
A
BBB
BB
B
CCC
CC
C
The highest quality bonds
are rated triple-A.
Investment grade bonds
have to be equivalent of
Baa or higher. Bonds that
don’t make this cut are
called “high-yield” or
“junk” bonds.
24- 13
Bond Ratings and Financial Ratios
Three years of median ratio data by bond rating
(2002– 2004).
Ratio
EBIT interest cover *
return on capital %
Total debt/capital %
AAA
23.8
27.6
22.9
AA
19.5
27
28.3
* Earnings before interst and tax divided by interest
A
8
17.5
37.5
BBB
4.7
13.4
42.5
BB
2.5
11.3
53.7
B
1.2
8.7
75.9
CCC
0.4
3.2
113.5
24- 14
Bond Ratings and Default
Default rates of corporate bonds 1981-2005 by
S&P’s rating at time of issue
Rating at Time
of Issue
AAA
AA
A
BBB
BB
B
CCC
Percentage Defaulting Within
1 Year after
5 Years after 10 Years after
issue
Issue
Issue
0
0
0
0.3
1.2
5.9
30.4
0.1
0.3
0.6
3.1
12.7
30.5
56
0.6
0.9
1.9
6.6
24
44.8
67.7
24- 15
Predicting Default
A comparison of financial
statements from firms that have
gone bankrupt with those firms
that have not gone bankrupt
reveals information valuable to
the lending decision.
Financial ratios of 544 failing
and non-failing firms.
24- 16
Credit Analysis
Predicting Default - William Beaver, Maureen McNichols, and Jung-Wu
Rhie, studied defaulting and non-defaulting firms and concluded the
chance of failing during the next year relative to the chance of not
failing was best estimated by the following equation:
Log (relative chance of failure)
 6.445  1.192 ROA  2.307liabilitie s / assets  .346 EBITDA / liabilitie s
Relative chacne of failure  e L
24- 17
Credit Analysis
Credit analysis is only worth while if the
expected savings exceed the cost.
– Don’t undertake a full credit analysis unless the
order is big enough to justify it.
– Undertake a full credit analysis for the doubtful
orders only.
24- 18
Asset Value and Default
The market value of WorldCom assets, as default approached
90,000
80,000
70,000
Market value of assets
50,000
40,000
30,000
20,000
Default date
Default points
10,000
02
7/
20
02
19
/0
/2
0
/6
10
3/
5/
20
02
02
28
/0
3/
20
02
/0
21
/0
2/
20
02
1/
20
01
15
7/
12
/2
0
01
/2
0
11
1/
/0
9/
20
01
0
27
Value, $ millions
60,000
19
02
02
7/
20
/0
/2
0
/6
10
02
02
5/
20
3/
20
/0
02
02
01
2/
20
/0
01
01
1/
20
/0
/2
0
12
3/
28
21
15
7/
/2
0
11
9/
20
/0
1/
27
Probability of default
over next year
24- 19
Default Probability
Moody’s estimate of WorldCom’s probability of default
25
20
15
10
5
0
Default date
24- 20
Value at Risk (VaR)
Value at Risk = VaR
 Newer term
 Attempts to measure risk
 Risk defined as potential loss
 Limited use to risk managers
Factors
 Asset value
 Daily Volatility
 Days
 Confidence interval
24- 21
Value at Risk (VaR)
Standard Measurements
 10 days
 10   day  10
 99% confidence interval
99%    2.33
 VaR
VaR  ( 10  2.33)  asset valu e 
24- 22
Value at Risk (VaR)
Example
You own a $10 mil portfolio of IBM bonds. IBM has a
daily volatility of 2%. Calculate the VaR over a 10 day
time period at a 99% confidence level.
 10  .02  10
 6.32%
99%( )  .0632  2.33
 14.74%
VaR  .1473 10,000,000
 $1,473,621
24- 23
Value at Risk (VaR)
Example
 You also own $5 mil of AT&T, with a daily volatility of
1%. AT&T and IBM have a .7 correlation coefficient.
 What is the VaR of AT&T and the combined portfolio?
VaRIBM  $1,473,621
VaRAT &T  $368,405
VaRAT &T  IBM  $1,842,026
VaR Portfolio  $1,751,379
DiversificationBenefit
 $90,647
24- 24
Ratings Changes
Rating at end of year
Start of
year, %
AAA
AA
A
BBB
BB
B
CCC
AAA
92.08
0.62
0.05
0.03
0.03
0
0.1
AA
7.09
90.83
2.09
0.21
0.08
0.08
0
A
0.63
7.76
91.37
4.1
0.4
0.27
0.29
BBB
0.15
0.59
5.79
89.38
5.53
0.34
0.58
BB
0.06
0.06
0.44
4.82
83.25
5.39
1.55
B
0
0.1
0.16
0.86
8.15
82.41
10.54
CCC
0
0.02
0.04
0.24
1.11
4.92
52.8
Default
0
0.01
0.05
0.37
1.45
6.59
34.14
24- 25
Yields and Ratings
Alcan bond price changes, relative to changes in
the bond rating
Rating after 1-year
AAA
AA
A
BBB
BB
B
CCC
Default
Percent yield
for given
rating
4.43
4.56
4.8
5.4
9.45
11.7
15.15
-
Implied percentage
change in price for
Alcan bonds
2.9
1.9
0.2
-4
-27.5
-37.3
-49.4
-52.9
average yields for rated bonds October 2003
average recovery rate for unsecured bonds 1988-2002
24- 26
Web Resources
Click to access web sites
Internet connection required
www.mooodys.com
www.standardandpoors.com
www.chinca.org/
www.bondsonline.com
www.moodyskmv.com/
www.riskmetrics.com