Principles of
Corporate Finance
Chapter 24
Eighth Edition
Credit Risk
Slides by
Matthew Will
McGraw-Hill/Irwin
Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved
24- 2
Topics Covered
The Value of Corporate Debt
Bond Ratings and the Probability of Default
Predicting the Probability of Default
Value at Risk
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Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved
24- 3
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:
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Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved
24- 4
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
McGraw-Hill/Irwin
.
940.00 = expected CF
Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved
24- 5
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
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24- 6
Interest Rates, Risk, and Maturity
5
Leverage = 100%
Leverage = 60%
Leverage = 40%
Leverage = 20%
4
Difference
between
promised yield
(YTM) on
bond and riskfree rate,
percent
3
2
1
25
23
21
19
17
15
13
11
9
7
5
3
1
0
Maturity, years
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24- 7
Key to Bond Ratings
Moody's
Investment Grade
Aaa
Aa
A
Baa
Junk Bonds
Ba
B
Caa
Ca
C
McGraw-Hill/Irwin
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.
Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved
24- 8
Bond Ratings and Financial Ratios
Three years of median ratio data by bond rating
(1998 – 2000).
Ratio
EBIT interest cover *
return on capital %
Gross profit margin %
Total debt/capital %
AAA
21.4
34.9
27
22.9
AA
10.1
21.7
22.1
37.7
A
6.1
19.4
18.6
42.5
BBB
3.7
13.6
15.4
48.2
BB
2.1
11.6
15.9
62.6
B
0.8
6.6
11.9
74.8
CCC
0.1
1
11.9
87.7
* Earnings before interst and tax divided by interest
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24- 9
Bond Ratings and Default
Default rates of corporate bonds 1981-2003 by
S&P’s rating at time of issue
Rating at Time
of Issue
AAA
AA
A
BBB
BB
B
CCC
McGraw-Hill/Irwin
Percentage Defaulting Within
1 Year after
5 Years after 10 Years after
issue
Issue
Issue
0
0
0.1
0.4
1.4
6.1
30.9
0.1
0.3
0.7
3.4
12.4
26.8
53
0.5
0.9
2
6.9
21
35.4
58.4
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24- 10
Bond Ratings and Yield Spreads
Yield spreads
Note these are promised yields Actual Returns?
12
Yield spread, percent
Moody's Aaa
10
Moody's Baa
High yield - "Junk" bonds
8
6
4
2
McGraw-Hill/Irwin
20
02
20
00
19
98
19
96
19
94
19
92
19
90
19
88
19
86
19
84
19
82
19
80
19
78
0
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24- 11
Credit Analysis
Multiple Discriminant Analysis - A technique used
to develop a measurement of solvency, sometimes
called a Z Score. Edward Altman developed a Z
Score formula that was able to identify bankrupt
firms approximately 95% of the time.
Altman Z Score formula
Z = .72
NWC
retained earnings
EBIT
shareholde r' s equity
sales
 .85
+ 3.1
+ .42
+ 1.0
total assets
total assets
total assets
total liabilitie s
total assets
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24- 12
Market Based Analysis
KMV
The market value of WorldCom assets, as default approached
90,000
Value, $ millions
80,000
70,000
Market value of assets
60,000
50,000
40,000
Default date
30,000
20,000
Default points
10,000
McGraw-Hill/Irwin
7/
20
02
/0
19
/6
/2
00
2
10
02
5/
20
3/
3/
20
02
/0
28
2/
20
02
/0
21
1/
20
02
/0
15
12
/2
00
1
7/
11
/2
00
1
1/
27
/0
9/
20
01
0
Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved
24- 13
Default Probability
Moody’s estimate of WorldCom’s probability of default
Probability of default
over next year
25
20
15
10
Default date
5
McGraw-Hill/Irwin
10
/6
/2
00
2
19
/0
7/
20
02
3/
5/
20
02
02
/0
3/
20
28
02
/0
2/
20
21
02
/0
1/
20
15
12
/2
00
1
7/
11
/2
00
1
1/
27
/0
9/
20
01
0
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24- 14
Value at Risk (VaR)
Value at Risk = VaR
Newer term
Attempts to measure risk
Risk defined as potential loss
Factors
Asset value
Daily Volatility
Days
Confidence interval
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24- 15
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 
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24- 16
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
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24- 17
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
DiversificationBenefit
 $90,647
VaR Portfolio  $1,751,379
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24- 18
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
McGraw-Hill/Irwin
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
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24- 19
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
-
average yields for rated bonds October 2003
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