auto company default & investment thesis

University of Notre DameMathematical Methods in Financial Economics

The paper is an analysis of three car companies – one healthy, one middling, and one on the verge of bankruptcy – in terms of past performance measures using theoretical principles. A major difference between the theoretical findings and actuality was determined and will be addressed. Ultimately, car buying decisions may be a consumer choice, but automobile company stock & bond investment decisions are more complex; this paper explains various rationales.

Investing in Auto Companies

INTRODUCTIONIn September and October 2008, the financial press seemingly had a surprise or crisis every day. While stock prices fell for all the companies, American Big 3 Auto companies1 took a huge hit.2 Moreover, with gas prices over $3.50 per gallon through most of 2007,3 people began to reconsider their gas-guzzling SUVs, for years the darlings of the American automobile manufacturing industry. Even now, General Motors, Ford and Chrysler sell significant amounts light and heavy trucks (relative to other sales). So, gas price increases, consumer behavioral shifts, and the ongoing recession have all conspired to send stock prices downward, decreasing the equity cushion upon which firm assets are financed and throwing the companies at the mercy of creditors and the Obama administration.

Asset pricing theories tell us that, under normal (i.e. not bailout selective) circumstances, some industry firms should now belong to bondholders.4 In this paper we have analyzed three car companies: one (GM) who is struggling to stay solvent and reliant upon government largesse; another, Ford, which seems to have “survived” and will not require back-up funding facilities from the government; and the last (Volkswagen) which has been, by most fundamental and performance measures, a top-notch investment over the past three years.5 We have calculated and analyzed the theoretical representation of each company’s financial well-being, and then compared those results with actuality to try to describe anomalous behavior.

This paper will have three sections. Section 1 shall provide the background of the industry and explain the consumer behavior in buying new cars. In section 2, we delve into principles of financial accounting to show that “good companies” have more equity and less debt. Section 3 brings stock price and firm assets volatility into consideration to calculate the so-called “Distance-to-Default” (DTD) of these companies. In section 4, we present our findings and try to explain the anomalies between the theoretical and actual results, and try to explain them.

1 “Big 3”: Ford (F.N), GM(GM.N), and Chrysler (privately held)

2Chrysler is privately held; however, due to the company’s recent bankruptcy, one may safely assume that Chrysler, along with Ford and GM,

suffered similarly.3

See Exhibit A for 2006-present U.S. gasoline prices 4

Except, apparently, Chrysler, whose capital was inexplicably reorganized as equity and distributed to the UAW pension plan and Fiat, leaving bondholders with enormous losses, on April 30, 2009 5

See Exhibit B for automobile manufacturing company relative performance since April 2006

Page 1


SECTION ONE

The industry overviewThe auto industry comprises of three main sectors – parts suppliers to the manufacturers (also known as OEMs, or original equipment manufacturers), the manufacturers themselves, and the dealers, retailers and distributors. There is a good symbiosis and a “many- to-many relationship” in the supply chain. For example, an OEM may supply to three auto companies and one auto company will have multiple, if not thousands of suppliers who supply directly to them. By the same token there, is a chain of second- and third-tier suppliers. The following are some examples of the network:

Parts Suppliers (OEMs)

o Delphi, Tenneco, Lear, SPX

Automobile Manufacturers

o Ford, GM, Toyota, VW, Nissan, Honda

Retailers, Outlets, & Services

o Firestone, Penske, AutoNation, O’Reilly, Gurley Leap Automotive Group

Market ShareThere is a competitive oligopoly among the manufacturers. While GM has lost market share in recent years, primarily to Toyota, in 2008 it still had the biggest market share. The following chart shows the market share of the companies.6

GM 18.7%

Ford 15.5%

Chrysler 12.8%

Toyota 17.3%

Honda 10.0%

Other 25.7%

Share (2008)

The consumer6

Source: “Car & Automobile Manufacturing in the US.” IbisWORLD, 31 December 2008.

Page 2


Manufacturers sell cars to dealers, which in turn sell directly to the consumer. The automotive industry is entirely consumer driven. It is consumer’s perception that determines how good a car is. While consumers penalize improperly manufactured cars, they often forget to reward the improvements in the companies that they have already penalized. For instance, consumers penalize GM for not having fuel efficient cars, but they fail to realize how the company has progressed in terms of producing fuel efficient cars, managing their dealers and suppliers. Advances in technology and competition have brought the car prices down making consumers to bid the prices down. The consumer price index for new cars has come down drastically since 2000 which makes these big companies like GM sell cars for less than what it takes to produce. Because of their size and UAW legacy costs, they have had extreme difficulties steering their costs lower; therein lies the crux of the industry’s recent suffering.

This chart outlines how consumer automobile prices have decreased in the United States, indexed to 2001. The new car portion of the consumer price index is the only major sector of U.S. CPI to have decreased over the time period, a function of both sales declines and household capital investment decisions.7

10/1/00 6/1/02 2/1/04 10/1/05 6/1/07 2/1/09$0.88

$0.90

$0.92

$0.94

$0.96

$0.98

$1.00

$1.02

CPI Transportation, new cars

SECTION TWO

Assets=Debt+ EquityA company’s assets are financed primarily through two channels: common equity, or ownership rights, and debt, or borrowed money. From these two sources, the owners’ agents – management – invest in capital assets: building a factory, buying inventory, and so on. The greater a company’s debt burden, the less equity holders will receive in the event of a company sale or liquidation. Although highly leveraged financings are an interesting and vital area of finance, most publicly traded companies seek to maximize shareholder returns by minimizing the equity-to-capital ratio.

7 Sources: U.S. Bureau of Labor Statistics, Moody’s DismalScientist.com

Page 3


In case of default, the debt is paid off first; equity shareholders receive anything left over. As a result of this risk, they require a higher rate of return on their investments compared to the debt holders, whose rate is generally fixed. The following diagram shows the different layers of debt:

Assets Funding

Assets

Senior Debt

Subordinated Debt

Preferred Equity

Common Equity

DT

D

Capital structuresThe capital structures for GM, Ford and VW are as follows:

VW Ford GM

Assets Funding

Assets

Senior Debt

Common Equity

Assets Funding

Assets

Senior Debt

Subordinated Debt

Common Equity

Assets Funding

AssetsSenior Debt

Common Equity

From the above figure we can see that, compared with firm assets, GM had the highest level of debt and VW has the lowest, making obvious our assumption that the market rewards companies with less debt. From the point-of-view of a default event, it is intuitive that GM should default easily and VW will not.

Page 4


SECTION THREE

Distance to DefaultIn case of a default, the value of the assets goes down to levels where it becomes insufficient to cover the debt of the firm. But it does not always happen linearly. The value of the assets fluctuates in Brownian motion (like the value of equity) and market events may cause the implied asset values to go below the debt level. Distance-to-default (DTD) is the number of standard deviations that the value of a company’s assets must decline in order for its assets to be worth less than the value of its liabilities. In theory DTD is the indicator of the default of a company

There are several parameters needed to calculate DTD:

Equity market prices Equity shares outstanding (together, with equity market prices, determines firm equity value,

or market capital) Equity option implied volatilities Balance sheet leverage8

Equity implied volatilityThe contingent claims model is based on the Black-Scholes-Merton (BSM) option-pricing model; however, instead of pricing financial options on equity shares, we replace the theoretical value of a European call option (Ce) with the value of equity (VE). As with a “typical” option, the VE is the greater

of zero or firm assets (VA) less firm debt (D) in the form of V E=[V A−D ]+¿ ¿.9

This form of option pricing is more commonly seen in binomial models, yet the same principle – that option values are nonnegative – holds in the BSM model. In fact, some of the key parts of financial option pricing and contingent claims modeling are identical. In fact, contingent claims uses implied equity volatilities as a function of the BSM inputs and market-given price Ce, such that (Cσ e,S0,K,rf, ,T), σdetermined by iteration, is identical to the volatility used in options pricing.

Contingent Claims ModelAs outlined in Exhibit C, the value of equity VE is greater than zero only when the value of firm assets VA

is greater than the firm’s debt D. In reality, one might merely compare the balance sheet value of assets to debt, yet this oversimplifies the matter greatly. In fact, it entirely discounts the fact that firms service their debt between quarterly financial reporting. Moreover, the balance sheet value of assets is generally based on historical cost less write-downs. In the event of default, the assets will be sold at current prices, so this, too, hampers a simple analysis.

8 In a most robust DTD analysis, this would separate the different levels of debt subordination. The auto makers have relatively simple capital

structures, with little subordinate or bank funding. We assumed that all debt, then, is senior level. 9

See Exhibit C for sample representations of equity, debt, and implied assets paths

Page 5


The solution, then, is to determine how the market measures firm assets levels and volatility. In our analysis, we relied upon Matlab to iterate these data, which are essential to final analysis. After all, should the firm’s assets be highly volatile and dip below aggregate debt levels when a debt payment comes due – and, assuming that VA is normally distributed – then the firm risks actual default (versus legal default, which may require that the firm sort out its debts in court).

We now may compare the inputs of BSM option-pricing and BSM contingent claims models:

BSM Option-Pricing BSM Contingent Claims

Option Value C e=S0N (d1)−K e−rc τ N (d2) V E=V AN (d1 )−De−rc τ N (d2)

whered1=

1σ √ τ [ ln( S0

K )+(rc+ 12σ2)τ ] d1=

1σ A √ τ [ ln(V A

D )+(r+12σ A

2 )τ ]d2=d1−σ √ τ d2=d1−σ A √ τ

NB: Given values are denoted by blue font.

Ce, VE Market-given option price Market capitalization

S0, VA Market-given stock price Value of firm assets

K, D Option strike price Value of firm debt

, σ σA Implied equity volatility Implied asset volatility

rc, rContinuously compounded risk-free interest rate

Risk-free interest rate10

τ Options term-to-maturity; yearsDebt term-to-maturity; issue-weighted; years

Put most succinctly, contingent claims analysis supposes that the firm equity is an option on the firm assets, where debt is the strike price. The underlying, S0 and VA, is dependent on the normal distribution of returns on it, such that

10 Our analysis used annualized 10-year U.S. Treasury yields.

Page 6

Investing in Auto Companies Figure 2 Volatile Assets Relative to Debt Distress Barrier and “Minimum Capital Barrier”

Assets Value

Expected asset Distribution of Asset value at T value path

Default Barrier

V 0

T Time

Probability of Default

Probability of Declining below Minimum Capital but not below Default Barrier

In Michael Gapen’s model,11 the minimum capital barrier and the default barrier are not one in the same due to differences between banking and other industries, yet the concept holds. Instead, we may assume, just as in Exhibit C, that as long as the value of assets VA exceeds the level of debt D, then the option VE is nonnegative.

The value of firm assets VA(VE,D,r, )τ , implied and calculated by Matlab, are given to the normal

distribution overlaid on the Gapen chart. They are distributed normally by 1

σ A√τ just as stock prices

are in regular option-pricing. Further, in typical option-pricing, the N(d1) term is also the option delta

such that N (d1)=δC eδS

, and is also known as the hedge ratio; in contingent claims analysis, we find the

equivalent, N (d1)=δ V E

δ V A. This helps investors seeking capital structure arbitrage opportunities to

determine how much stock to hold relative to the asset value (which they cannot hold directly). It also

takes us a step closer to arriving at VA and σA, since V E=σ Aσ EV A. Replacing the unknowns in BSM

V E=V AN (d1 )−De−rc τ N (d2),

we may now solve for VA and σA.

Remember that DTD is related to but distinct from probability of default. Distance-to-default is d1; probability of default is N(d2), or

P {V A<D }=N (d2 ) (V A¿ , σ A

¿ , τ )= 1σ A √τ [ ln

V A¿

D+(r−1

2σ A

2 )τ ].Distance to default of our companies

11 Gapen, Michael. “Estimating the Market Value of the Implicit Guarantee to Fannie Mae and Freddie Mac Using Contingent Claims,” Board of Governors of the Federal Reserve System.

Page 7

∂D


One conclusion very evident by our analysis is that firm DTD is highly volatile. One reason, we concluded, is that equity markets, and therefore VE, σE, and, therefore, their distillates are generally uneven. Take, for instance, Volkswagen. Interestingly, VW temporarily became the world’s largest firm by market capital on October 27, 2008 because a) Porsche announced plans to raise its stake in VW to 75%, an event that usually causes stocks to rise, and b) it had, at that time, the highest short interest among German companies (12.5% of shares outstanding), which caused shares to skyrocket 82% in U.S. Dollar terms to over €1000. From April 22 to October 27, 2008, equity volatility σ2 averaged 48.4% daily – high, yes, but not relative to other automobile manufacturers.

Thereafter, through April 22, 2009, volatility averaged 110.6%, a 129% increase. The distribution of returns is given by

-45.3% -32.6% -19.9% -7.2% 5.5% 18.2% 30.9% 43.6% 56.3% 69.0% More0

20

40

60

80

100

120

1 0 2 5

104

70 0 0 0 1

Daily Returns

Daily Return ± X%

Frequ

ency

Note other data categories over the two periods:

Volkswagen 4/22/2008 to 10/27/2008 10/28/2008 to 4/22/2009

Debt D $36.63B $38.02B

Equity VE $61.50B $82.25B

Equity vol σE2 48.4% 110.6%

Assets VA $98.47B $87.26B

Asset vol σA2 2.0% 4.7%

Page 8


Risk-free rate rf 3.89% 2.86%

Probability of default d2 39.6% 84.9%

DTD N(d2) 0.003σ -2.012σ

Market events over the past year, during which VW, Ford, and GM returned 27%, (41%), and (91%), respectively, contributed such a significant amount to volatility and thereby DTD and probability of default that the data need to be put into context. Take GM, for example. On exactly zero days over the year did its value of assets VA exceed debt.12 Therefore, the theoretical value of GM’s equity, VE, as an option on assets is $0.00. This makes sense given this 1st quarter 2009: “We cannot cut costs fast enough to offset that ($6 billion) revenue loss.” While cutting costs $3 billion during the three months ending March 31, 2009, GM still burned through $10.2 billion in cash, which includes numerous government backstops.13 Deutsche Bank values the share price at $0.00.

Our analyses, however, indicate an improving situation at GM, particularly relative to the much stronger VW. Why? The reasoning is twofold: On the one hand, debt interest payments are assumed by the market to be backed by the U.S. government, propping the stock price between $1-2 per share; the second is that the market price of assets may be significantly out-of-line with reality. That is, it really is too big to fail. If GM were to have to sell plants, technologies, designs, and so on at fire sale prices, would there not be some significant premium attached to those assets? Moreover, the situation may be improving because it just cannot get worse. VW, on the other hand, has been in such good position fundamentally that their relative fundamentals would likely take a different path back to historical means.14

The overall situation is, of course, muddled by the deep and global recession. Consumers are beginning to spend again, but not necessarily on large durables, and particularly not on cars, when the probability that a company will not exist to cover warranties and service. The current (April 22) outlook is as follows:

Category leaders denoted in bold VW Ford GM

Debt D €38.08B $29.82B $24.45B

Equity VE €69.77B $10.32B $1.03B

Equity vol σE2 81.6% 91.2% 279.5%

Assets VA €70.03B $34.37B $12.07B

Asset vol σA2 5.3% 0.1% 0.7%

12 Our data do not even include off-balance sheet liabilities such as pension and healthcare costs. These surely should push the weak even closer to

default, as they indeed have, in Chrysler’s case.13

Source: “GM’s Cash Drain Continues.” www.seekingalpha.com, 7 May 2009.14

See Exhibit C for selected graphical evidence of default for Volkswagen, Ford, and General Motors

Page 9

http://www.seekingalpha.com/


Risk-free rate rf 2.98% 2.98% 2.98%

Probability of default d2 99.4% 24.6% 90.8%

DTD N(d2) -2.532σ 0.686σ -1.331σ

Given Ford’s lack of reliance on government funding, it does make sense that they would be farther from default and less likely than their Big 3 counterpart to actually miss debt payment(s). But, as explained above, Volkswagen, despite its far greater relative equity cushion, is made to suffer in the DTD analysis because its stock price behaved rather inconsistently over the year. As with betaβ t+1

i ,

which may assign a too-high cost of equity rt+1i to a firm whose results are outsized, past performance is

not always the best indicator of future results. The other side of the argument is that VW may perhaps be due to fall only because it had performed so well; that is, it may be a victim of its own success.15

SECTION FOUR

Why they are still out thereAs mention in Section 3, a number of factors are driving (no pun intended) auto manufacturers’

continued existence, the largest likely being the explicit government support for an industry-wide restructuring. If we had extended the analysis to include OEMs, retailers, and after-market service suppliers we feel the data may suggest widespread defaults and bankruptcies.

Another element of uncertainty surrounds exactly how the U.S. Treasury and Obama administration value the different claims on the firms. In the case of Chrysler which, unfortunately, was not able to be analyzed due to lack of public equity data, UAW and Fiat were given preferential claims over bondholders. As a result, any default analysis is moot. That is not to say that an investor should not take the temperature of the political climate at all; however, those functions are mathematically impossible to capture in a standard analysis.

A number of hedge funds specializing in distressed debt had invested in Chrysler (and likely

GM and Ford) bonds. What may be interesting, as well, would be to plot P (where P=q [ (1+r )−d ]p [u−(1+r ) ] )

against the stock priced of the auto manufacturers, to determine the point at which E (rB )>E(rS). At current bond levels, which are below the average recovery rates of defaulted bonds,16 investors should be tempted to dive into these “cheap” bonds.17 Two problems with this reasoning persist, however.

15 See Exhibit D for selected graphical evidence for default

16 Recovery rate is the approximate price of the bond about 1-week after default announcement.

17 See Exhibit E for historical default-recovery rates

Page 10


The first is whether these prices sufficiently capture firm distress; perhaps they are due to fall further, as evidenced by the Obama administration punishing Chrysler bondholders by forcing them to accept approximately 20% of par for their investments. The other problem is the E(rS) term, which may also signal high rates of return given the relative cheapness of the equity securities. Perhaps the best notion, then, is to stay away altogether!

100% in distressAccording to Bank of America-Merrill Lynch research, 100% of automobile industry bonds

denominated in U.S. Dollars are in distress, or carry spreads over comparable U.S. Treasuries greater than 1000 bps.18 Distress is not uncommon in the industry, particularly during a recession. As previously mentioned, cash-strapped consumers likely put off expensive purchases until the economy as a whole recovers. In the meantime, auto makers and associated firms sink into high yield debt territory, augmented by extremely low risk-free rates.

The question, then, is who is really in distress and who is forced to operate at higher capital costs due to contagion. From our analyses, we can safely say that Ford is one such firm.

Questioning Assumption of fixed sigmaIn general, the BSM model holds volatility σ2 constant at either a historical rate or the market

implied rate given by stock option prices. We chose to use the market implied rate because of the current importance of taking a purview of the market-assigned risk implied in prices. Not to say that the market has more information than we do; contrarily, uncertainty should drive up required rates of return on both stocks and bonds. This scenario is hellish for hedge funds seeking to remain above their high-water marks, but not necessarily painful for long-term investors who can afford to assign lower risk measures to firms they expect to continue to operate in perpetuity. Volatility, then, can be taken with a grain of salt depending on one’s particular holding period and fundamental opinion.

Questioning assumption of fixed rRegarding the changes in distress over time, we did not, in fact, hold the risk-free rate rf

constant. Why not? For one, data is easily obtained from the Federal Reserve website. More importantly, however, is to consider what the risk-free level means for a firm. Under normal operating conditions, a lower rf is an indicator of cheaper financing and ability to expand capacity. This year has been different, to be sure, but the measure is no less important in a credit-driven recession. Programs such as TALF, which allowed Ford to issue nearly $3 billion of asset-backed securities in March, will undoubtedly lower firm financing costs. As a result, we believe that it is very important to look at DTD and probability of default through the lens of prevailing credit conditions.

Conclusion

18 See Exhibit F for historical automobile industry distress levels as a percentage of outstanding U.S. Dollar debt

Page 11


Fair or not, Ford seems to be the best bet amongst the three rivals. GM is just too much of a question mark, despite the government’s insistence and willingness to prop it up in the face of gale-force headwinds. Volkswagen, for all of its fundamental strength, may currently be too volatile to give a proper indication of operating efficacy. Moreover, in light of other macroeconomic indicators such as $/€ exchange, VW may actually be due for a steep decline relative to its weaker peers.

In light of the initial thesis – that value would be available in pockets and that DTD analyses should allow investors to see past damning fundamental and market data – we agree that Distance-to-Default is a nice tool for investors to understand structural market shifts as well as the microeconomic back stories belying otherwise unfriendly appearing investments. This goes for both stock and bond investments, though, at this point, it is unduly difficult to differentiate between the two in terms of risk-adjusted return comparisons. However, for investors with a long-term outlook seeking value at the bottom of this particular market, we believe it may be offered in Ford’s capital structure but not necessarily in its competitors’. This is particularly true given the current political environment, which while having shown a willingness to save beleaguered auto makers, may somewhat arbitrarily usurp value for the benefit of certain investor groups.

Page 12


EXHIBIT A

U.S. Gasoline (Mid-Grade) Average Prices: 12/31/2006-5/7/2009

Source: Bloomberg

Page 13

$3.50

$3.00

$2.50

$2.00

$1.50

$1.00


EXHIBIT B

Automobile Manufacturing Firm Relative Stock Performance, April 2006-2008

4/24/20066/3/2006

7/13/2006

8/22/2006

10/1/2006

11/10/2006

12/20/20061/29/2007

3/10/2007

4/19/2007

5/29/20077/8/2007

8/17/2007

9/26/2007

11/5/2007

12/15/20071/24/2008

3/4/2008

4/13/2008

5/23/20087/2/2008

8/11/2008

9/20/2008

10/30/200812/9/2008

1/18/2009

2/27/20094/8/2009

$0.00

$0.50

$1.00

$1.50

$2.00

$2.50

$3.00

$3.50

$4.00

3-yr Stock Return

GM F

TM NSANY

HMC VOW

TTM

Page 14


EXHIBIT C

Selected Default Risk Evidence: Volkswagen, Ford, & General Motors

Volkswagen (A3/A-/BBB+)

1/12/0

9

1/16/0

9

1/20/0

9

1/24/0

9

1/28/0

9

2/1/0

9

2/5/0

9

2/9/0

9

2/13/0

9

2/17/0

9

2/21/0

9

2/25/0

9

3/1/0

9

3/5/0

9

3/9/0

9

3/13/0

9

3/17/0

9

3/21/0

9

3/25/0

9

3/29/0

9

4/2/0

9

4/6/0

9

4/10/0

9

4/14/0

9

4/18/0

9

4/22/0

9

0

50

100

150

200

250

300

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Spread

DTD

DTD

Spre

ad to

DBR

10-

yr (b

ps)

Correl: (0.25)

Page 15

4/22/08

8/22/08

12/22/08

4/22/09

€0

€50

€100

€150

€200

€250

€300

Capital Structure

VE D

VA

€billi

ons

4/22/08

8/22/08

12/22/08

4/22/09

0

50

100

150

200

250

300

350

400

0

1

2

3

4

5

6

7

8

Volatility

σE σA

σE σA

4/22/08

8/22/08

12/22/08

4/22/09

0%

20%

40%

60%

80%

100%

120%

-4

-3

-2

-1

0

1

2

Distress Signals

P{De

fault}

Distance to Distress (d2)

P{D}

DTD

Correl: (1.00)


EXHIBIT C (cont’d)

Ford (Ca/CCC+/CC)

3/10/09 4/10/090

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

-0.5

0.0

0.5

1.0

1.5

2.0Spread

DTD

P{D}

Spre

ad to

UST

10-

yr (b

ps)

DTD

, P{D

efau

lt}

Correl (Spread, DTD): (0.73)Correl (Spread, P{D}): 0.75

Page 16

4/22/08

8/22/08

12/22/08

4/22/09

$0

$5

$10

$15

$20

$25

$30

$35

$40

Capital Structure

VE D

VA

$billi

ons

Is VA < D?

4/22/08

8/22/08

12/22/08

4/22/09

0

50

100

150

200

250

300

350

-0.5

0.0

0.5

1.0

1.5

2.0

Volatility

σE σA

σE σA

4/22/08

8/22/08

12/22/08

4/22/09

0%

20%

40%

60%

80%

100%

120%

-5

-4

-3

-2

-1

0

1

2

Distress Signals

P{De

fault}

DTD (d2)

Correl: (0.93)

DTD

P{D}


EXHIBIT C (cont’d)

General Motors (C/CC/C)

3/11/0

9

3/13/0

9

3/15/0

9

3/17/0

9

3/19/0

9

3/21/0

9

3/23/0

9

3/25/0

9

3/27/0

9

3/29/0

9

3/31/0

9

4/2/0

9

4/4/0

9

4/6/0

9

4/8/0

9

4/10/0

9

4/12/0

9

4/14/0

9

4/16/0

9

4/18/0

9

4/20/0

9

4/22/0

9

0

2,000

4,000

6,000

8,000

10,000

12,000

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

Spread

DTD

P{D}

Spre

ad to

UST

20-

yr (b

ps)

DTD

, P{D

}

Correl (Spread, DTD): 0.77Correl (Spread, P{D}): (0.79)

EXHIBIT D

Page 17

4/22/08

8/22/08

12/22/08

4/22/09

$0

$5

$10

$15

$20

$25

$30

$35

$40

$45

$50

Capital Structure

VE D

VA

$bill

ions

VE=[VE -D]+

=0

4/22/08

8/22/08

12/22/08

4/22/09

0

50

100

150

200

250

300

350

400

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

Volatility

σE σA

σE σA

4/22/08

8/22/08

12/22/08

4/22/09

84%

86%

88%

90%

92%

94%

96%

98%

100%

102%

-3

-2

-1

0

Distress Signals

P{De

fault}

DTD (d2)

Correl: (0.95)

DTD

P{D}

Dashed red line indicates

date of CEO Waggoner resignation


Theoretical & Sample Financing Paths; Equity as an Option of Firm Assets

Page 18

0 25 50 75 100 125 150 175 200 225 2500

5

10

15

Theoretical Basis

Equity Debt Assets

Asset Value

Secu

rity

Valu

e

0 25 50 75 100 125 150 175 200 225 25005

101520

Reality

Equity (MV) Debt (BV)Assets (MV)

Asset Value

Secu

rity

Valu

e

VE=[VA-D]+


EXHIBIT E

Historical Default and Recovery Rates

1/1/781/1/83

1/1/881/1/93

1/1/981/1/03

1/1/08

$0

$10

$20

$30

$40

$50

$60

$70

$80

0%

2%

4%

6%

8%

10%

12%

14%

Trailing 12-Mo Wtd Avg Recovery Rate vs Trailing 12-Mo High Yield Default Rate

Recovery Rate

Default Rate

Recove

ry Rat

e

Defau

lt Rate

Source: Moody’s

1978-2008 average recovery rate 45.38% of parCurrent levels of marketable bonds:

Ford 47.15%General Motors 15.08%

Page 19


EXHIBIT F

Historical Automobile Industry Distress Levels as a Percentage of U.S. Dollar Bonds Outstanding

12/1/966/1/97

12/1/976/1/98

12/1/986/1/99

12/1/996/1/00

12/1/006/1/01

12/1/016/1/02

12/1/026/1/03

12/1/036/1/04

12/1/046/1/05

12/1/056/1/06

12/1/066/1/07

12/1/076/1/08

12/1/08

0

10

20

30

40

50

60

70

80

90

100

Recession

%

Source: Merrill Lynch

Pct of distressed USD bonds (YTM > 1000 bps)1

1Automotives only

Page 20

auto company default & investment thesis

Economy & Finance