46

How is the firm value affected by a marginal increase in the face value of debt for

debt levels below and in excess of this critical value?

Draw a diagram depicting the firm value over the face value of debt issued!

What is the optimal face value of debt for this firm?

Discussion:

• Tax loss carry forward

• Other uses of tax shields

47

12.4 Summary

Draw a diagram depicting the firm value over the face value of debt issued for each

of the following cases:

1. MM-Irrelevance of the Capital Structure

2. A nonzero corporate tax rate, zero income tax rate, zero taxation of capital gains

3. A nonzero corporate tax rate and a nonzero income tax rate which, for some

investors, is larger than the corporate tax rate, zero taxation of capital gains

4. The Austrian situation

5. When tax-shields are uncertain

48

13 Signaling and Capital Structure

13.1 Capital structure as a credible signal: Ross 1977

Suppose that the manager has superior information about the future value of the

corporation. How could the manager “signal” this information? Idea: The capital

structure can be used as a credible signal!

Ross, “The Determination of Financial Structure: The Incentive Signaling

Approach”, Bell Journal, 1977.

Assumptions:

• The manager knows the true value of the corporation.

• The interest rate is zero. All parties are risk neutral.

• There are two types of corporations, A and B. Corporations of type A yield a

cash flow of a and corporations of type B yield a cash flow of b.

• Half of the corporations in the economy are of type A, the rest is of type B.

Let D denote the debt level and V0, V1 denote the firm values at time 0 and 1

respectively. Let M denote the wage earned by the manager. Bankruptcy is

personally costly for the manager. In case of default, the manager incurs a cost of γL

( 0, 10 >γγ ).

M If V1 ≥ D 1100 VV γγ + If V1 <D )( 1100 LVV −+ γγ

49

Example: Suppose that a = 150 and b = 100. Let 0γ = 1γ = 0.1 and L = 70. Assume

that the market believes a firm with D> 100 to be of

type A and a firm with D ≤ 100 to be of type B. Are these expectations met?

Consider a firm of type A. What debt level will the manager of such a firm choose?

Now consider a firm of type B. What debt level will the manager of such a firm

choose?

Conclusion:

Discussion:

• Note that the signal is not costly in the world of certainty. However, when the

firms’ cash flows are uncertain, then this signaling via the capital structure

would be costly!

• This model suggests that higher leverage is a good signal. More profitable

corporations are higher levered. Is this confirmed by the empirical evidence?

50

13.2 Signalling and pecking order theory of capital structure

- Myers, S., “ The capital structure puzzle”, Journal of Finance, 1984

- Myers, S. and N. Majluf , “Corporate financing and investment decisions when

firms have information investors do not have,” JFE, 1984

Donaldson (1961) observed that management of large corporations strongly

favoured internal generation as a source of new funds, and were extremely

reluctant to get external finance by issuing stocks.

Brealey and Myers (2000, Principles of corporate finance, 6th edition) show that

in the period 1988-1997, internally generated cash finances 89% of the

investment of the non-financial US firms; Net stock issues are –9,2% of the total

investment (due to large amount of share repurchases); Net increase in debt

amounts to 21,1% percent of the total investment.

On average, stock price falls when firms announce a stock issue, while it rises

when a stock repurchase is announced (See the studies cited by Myers 1984 for

evidence).

Myers and Majluf (1984) and Myers (1984) advance the pecking order theory of

capital structure to explain these stylised facts about corporate financing.

Their theory is based on the asymmetric information between the manager and

the outside investors.

The Myers and Majluf (1984) model of corporate financing

- A firm has one existing asset with value A~ , and one investment

opportunity with NPV B~ , which requires investment I. Both

A~ and B~ are non-negative.

- At date –1, the market has the same information as the manager, they

both know the distributions of A~ and B~ .

- At date 0, the manager knows the realizations of A~ and B~ , which are

a and b respectively, while the investors can only know these

realizations at date 1.

51

- The manager acts in the interest of the ‘old’ shareholders, those

owning shares at the start of t=0. The old shareholders are passive in

the sense that they will neither buy the new stocks nor sell their old

stocks.

- So the manager decides whether to issue-and-invest or to pass up the

investment opportunity at date 0 according to the following rule:

Issue-and-invest if and only if:

)('

' baIIP

Pa +++

≤ (1)

where 'P is the market value of old shareholders’ shares conditioning

on the issue-and-invest decision, I is the value of the new stocks

issued to finance the investment, IP

P+''

is the proportion of the firm

owned by the old shareholders.

- The decision rule of the manager can be rewritten as follows:

Issue-and-invest if and only if:

)( Nbaa ∆−+≤ (1’)

where IIP

IIbaN −+

++=∆'

)( denotes the capital gain or loss

on the newly issued stocks when the truth comes out at t=1,

conditioning on the firm’s issue of shares at t=0.

- This means that the new stocks will only be issued when the

investment’s NPV equals or exceeds the capital gain on the newly

issued shares.

- Given the strategy played by the manager, the equilibrium valuation

of the old shares is:

)~|~( NBAEP ∆<= when no new stock is issued, (2a)

)~|~~(' NBBAEP ∆≥+= when new stocks are issued.(2b)

52

A numerical example.

State 1

(prob=50%)

State 2

(prob=50%)

Asset-in-place a=150 a=50

Investment opportunity

(NPV, with I=100)

b=20 b=10

- The first-best result is that the firm issues and invests in both states, but can

this happen in equilibrium?

- Suppose that the manager chooses to issue-and-invest in both states, then

the investors learn nothing about a and b by observing issuance. So

115)1050(21)20150(

21' =+++=P .

In state 1:

.42.144270215115)(

''

=⋅=+++

= baIIP

PV old

58.125270215100)(

'=⋅=++⋅

+= baI

IPIV new

Similarly, in state 2:

58.85=oldV

42.74=newV

- However, if the manager chooses to pass up the investment opportunity in state

1, Vold would be 150, so the manager would better do nothing.

- Therefore the manager will only issue new stocks in state 2. Consequently, the

equilibrium value of the old stocks is

P =150, 'P =60.

- The average pay-off to the old investors is 105 instead of 115. This is because

the valuable investment opportunity is passed up in state 1: under-investment

due to information problem.

53

The value of financial slack

- Financial slack is defined as the sum of cash, marketable security held by the

firm, plus the amount of risk-free debt that the firm can issue.

- When the financial slack is bigger than the investment required, no positive-

NPV investment opportunity will be passed up.

Can the under-investment problem be alleviated by risky debt?

- With risky debt D=I, the issuance condition (1’) is replaced by:

)( Dbaa ∆−+≤ (1’’)

Where DDD −=∆ 1 is the capital gain or loss to the debt holders.

- Option pricing theory implies that D∆ will have the same sign as N∆ , but

that its absolute value will always be less. (Because risky debt can be thought

of as a stock plus a short call on the assets of an unlevered firm, so it is less

sensitive than the stock to the change of the underlying asset value.)

- So whenever Nb ∆> , we must have Db ∆> . (note that 0≥b ). This means

that whenever the manager is willing to issue stock, he will also be willing to

issue debt. However, the reverse is not true.

- Therefore the under-investment problem can be alleviated if risky debt can be

issued.

- More interestingly, it can be shown that stock will never be issued if the firm

has the capacity to issue debt. Why? The manager will prefer to issue stock

instead of debt if and only if DN ∆<∆ . Since these two items have the same

sign and the latter has smaller absolute value, this can be the case only if

0<∆N , which implies that the investors in the new stocks are sure to lose.

- The above reasoning leads to the pecking order theory of capital structure.

54

The pecking order theory1

- Firms prefer internal finance.

- They adapt their target dividend payout ratios to their investment opportunities.

However, dividends are very sticky. So the internally-generated cash flow may

be more or less than the investment outlays.

- If it is less, firms first draw down its cash balance or marketable securities

portfolio.

- If external finance is required, firms issue the safest security first. That is. They

start with debt, then possibly hybrid securities such as convertible bonds, then

perhaps equity as a last resort.

- There is no well-defined target debt-equity mix, because internal equity sits at

the top of the pecking order while external equity sitting at the bottom.

1 A recent paper by Fama and French - “Financing decisions: Who Issues Stock ? ” JFE, 2005, 549-

582, provides some evidence against this theory:

First, firms frequently issue stocks, in particular 86 % of firms in their sample issued equity between

1993-2003 period. Second, equity is typically not issued under distress, nor are repurchases limited

to firms with low demand for outside equity.

55

14 Capital Structure and Investment Incentives

There are two different conflicts of interest, which may affect the investment policy

of a firm in dependence of its financial structure:

• Conflicts of interest between equity-holders and creditors.

• Conflicts of interest between managers and the corporation.

14.1 Conflicts of Interest between Equity-holders and

Creditors

The argument by Modigliani and Miller is based on the assumption that the capital

budgeting policy is chosen to maximize the firm value independent of the financial

structure. However, the managers who actually decide over the investment policy of

the firm are hired by the equityholders. Hence, it may be more reasonable to assume

that managers maximize the equity value instead of the firm value.

14.1.1 The Asset Substitution Problem

Example: Assume that the manager has to decide which of the following

investment projects to undertake:

inv. project required inv. payoff, state 1 payoff, state 2

I 80 60 150

II 80 110 110

Assume that the two states are equally likely. The discount rate is 0.08 per annum.

Which project should the manager choose when the firm is all-equity financed?

56

Which project should the manager choose when the firm is partially debt-financed?

Suppose that the firm has a debt level of D = 75 with Dk = 0.08.

Hence, the manager has an incentive to choose the project with a lower net present

value. Find the critical debt level such that the manager has an incentive to invest

inefficiently for all debt levels in excess of this critical value.

Assume that the debtholders anticipate the incentive of the manager to invest

inefficiently in order to increase the riskiness of the firm. What would be a “fair”

interest rate?

57

Compute the equity value when the debtholders get a fair rate of return!

Discussion:

• Savings-and Loan Crisis

14.1.2 The Debt Overhang Problem

Suppose that a corporation produces the following cash flows when no additional

investment is undertaken:

payoff, state 1 payoff, state 2

100 200

The corporation has the opportunity to undertake the following investment project:

req. investmt. payoff, state 1 payoff, state 2

100 60 150

Compute the equity value of an all-equity financed corporation if both states are

equally probable! (Assume that the discount rate is zero!)

Suppose that the firm has obligations of D = 120. What is the optimal investment

policy from the equityholders’ perspective?

58

14.1.3 Simple Examples of the Incentive Effects of Leverage

Imagine that there are two different firms facing the same decision alternatives at 0T . At T0, the unlevered firm (firm U) is all equity while the levered firm (firm L)

has debt with a promised payment of $30, due at T1. The debt was sold in a prior period to investors who anticipated the future decisions the firm would face and the future incentives of the stockholders. For each case below consider these three questions:

1. At T0, which decision maximizes the value of the firm? 2. At T0, what will the stockholders decide in firm U and in firm L? 3. How and when is the cost W of leverage borne by the stockholders of the

levered firm? What is the amount of this cost? For simplicity, ignore discounting and risk aversion. Assume that random outcomes have equal probability.

Case One: Risk shifting At T0, the firm can choose between two projects. Project A will pay either $20 or $40 at T1. Project B will pay $32 with certainty at T1.

Case Two: Underinvestment At T0, the firm has $10 in cash on hand and a project in place that will pay $25 at T1. The firm can either (A) pay the cash as a current dividend or, (B) invest the $10 in a new project that will pay $12 at T1.

Case Three: Playing for Time At T0, the firm can be liquidated for $25. If the firm does not liquidate and the economy turns around, the firm will be worth $35 at T1. If the economy is slow to recover, the firm will only be worth $10 at T1. Hint:

To answer question 3 in each case, draw a time line of events that includes the original sale of the debt.

59

Time –2 Time -1 Time 0 Time 1.

D=0 E=V=

D= E= --------- V=

D= E= --------------- V=

D= E= --------- V=

Before Debt Debt Sold

Decision is made

Outcome of investment

14.1.4 Convertible Bonds as a Solution to the Asset Substitution Problem

Example: Consider a levered corporation with a face value of debt of 2.000.000 at

15% p.a.. Suppose this corporation has two alternative investment opportunities,

which are characterized, by the following payoff matrix:

payoff, state 1 payoff, state 2 payoff, state 3

Project 1 2.500.000 2.750.000 3.000.000

Project 2 2.200.000 2.750.000 3.300.000

Suppose that the states are equally likely. Which project will be realized when the

management acts in the equityholders’ interest?

60

Now assume that the company issued convertible bonds instead of straight debt.

Suppose the creditors can demand conversion at time 1 in which case they receive

75% of the firm’s stock outstanding. Analyze the optimal conversion policy of the

creditors!

Which investment project is optimal from the (old) equityholders’ perspective?

The intuitive explanation is that a convertible bond is a bond with an embedded call

option on the firm’s stock. Draw the payoff profile of convertible debt in

dependence of the firm’s cash flow! How is the value of a call option affected by an

increase in the riskiness of the underlying asset?

61

14.1.5 Protective Covenants as a Solution to the Asset Substitution

Problem

• Collateral: rights of segregation in case of default

• Equity ratios

• Pay-out restrictions

• Restrictive covenants concerning the investment policy of the firm

• Call-provisions

14.2 Conflicts of Interest between the Management and the

Corporation

First, we have to discuss what is special about the corporation as a form of

organization, especially when compared to the market. In particular, why do

corporations exist? Couldn’t all the suppliers of productive factors enter into

contracts with each other in order to organize the production process?2

• When there is some central party in this nexus of contracts, then the

contractual complexity can be reduced substantially!

• Alchian, Demsetz, “Production, Information Costs and Economic

Organization”, AER 72, 777-795.

o Basic Question in Team Production: Accounting for the supply of

2 Pioneering article, which addresses this question is by Coase “The Nature of the Firm”, Economica,

1937. Coase attributes creation of centralized structure, such as firm, to reduction in cost of

organizing production compared to market.

62

individual effort!

o A manager is required in order to “match” the productive inputs

with the compensation received! This manager specializes in

monitoring the supply of productive inputs by the other parties.

o Who monitors the manager? Idea: the manager is the residual

claimant!

• The organization of the production process within a corporation and under

the oversight of a central manager-owner is more efficient than the

organization of the production by means of contracts allocated via the

market. The 6 characteristic features of a corporation are:

1 a number of different productive factors

2 a number of different owners of these productive factors

3 one central party to all contractual relations

4 this party has the right to negotiate all contracts with suppliers of

productive factors without any other existing contract being affected

5 this party is the residual claimant

6 this party has the right to sell its central position and residual

claimancy

• Problem: In this theory there is no distinction between the owner and the

manager; the “central party” is both! What happens when the manager of a

company with whom the control rights reside is distinct from the owner of

the residual claims?

• Jensen and Meckling, “Theory of the Firm, Managerial Behavior, Agency

Costs and Ownership Structure”, JFE, 1976, 305-360.

63

Consider an owner-manager who chooses how much to invest in “non-pecuniary”

benefits of hers. Such benefits (a large company car, a kindergarten for her small

child…) do add to the company’s profit. Still, excessive spending on such “fringe

benefits” will be very costly from the owner’s perspective! Suppose the owner-

manager sells a share α of her equity capital.

• Analyze the optimal consumption of fringe benefits before and after the sale

and consider the implications for the firm value!

14.3 Conflicts of Interest and the Capital Structure

The corporation is financed via three basic sources of capital:

• Inside Equity Capital

• Outside Equity Capital

• Debt

In the last subsections, we have seen how the conflicts of interest between the

managers, the equityholders and the creditors bias the firm’s investment policy. We

have also seen more-or-less costly “solutions”. Generally, the conflicts of interest

discussed above will decrease the firm value in dependence of the capital structure

of the corporation. This decrease in the firm value is referred to as the “agency

cost”. The figure below derives the optimal capital structure from an agency

perspective.

Given the agency cost of outside equity and debt, why do firms issue such

securities? Why are not all firms financed by an owner-manager? Portfolio theory

offers an explanation..

64

65

66

15 Free Cash Flow and Capital Structure

• Jensen, “The Agency Costs of Free Cash Flow”, AER 76, 323-329.

• Jensen, “The Eclipse of the Public Corporation”, HBR 89, 61-74.

• Jensen, “The Modern Industrial Revolution, Exit, and the Failure of the Internal

Control System”, JF 93, 83 1-880.

• Lehn and Poulsen, “Free Cash Flow and Stockholder Gains in Going Private

Transactions”, JF 89, 771-787.

Problem: Managers seem to prefer retaining corporate earnings even when there are

no profitable investment opportunities available. Michael Jensen argues that this

problem is decisive in the face of the “Modern Industrial Revolution” we are going

through at the moment.

• Technological advances imply decreasing production costs and excess capacities.

• Ideally, this should trigger firms’ exit.

• There are several reasons why the “exit-process” is inefficient:

o Typical statement of a CEO: This business is going through some

rough times. We have to make major investments so that we will

have a chair when the music stops.

o Asymmetries of information

o Contractual incompleteness

• Control Mechanisms:

o capital markets: takeovers (e.g. oil industry), since the end of the

80ies, the takeover market is subject to regulatory restrictions.

o product markets: these are very “slow” and, hence, cost inefficient

control mechanisms

o internal control systems:

board of directors

shareholder activism

Michael Jensen claims that these internal control systems “failed” in

triggering efficient exit!

67

Empirical Evidence

Michael Jensen constructs two measures for the productivity of investments in R&D

and other real investment opportunities.

• Measure I: Instead of the net real investment, the corporations could have

invested the same amount in securities of equal riskiness. The hypothetical

firm value of a corporation at the end of the period is assumed to be equal to

the initial equity value plus the value of the debt issued by the firm plus any

revenue from its investment in securities.

• Measure II: Now suppose that the firm invests its entire amount spent on

R&D and “real” investment in securities. Hence, the financial investment

now also comprises what was spent on “depreciation” under measure I. As a

consequence, the firm’s real assets are assumed to become worthless, nS = 0.

The hypothetical end-of-period value now only consists of the value of the

debt issued plus the return from investment in these securities of equal

riskiness as the firm’s real investment.

Formally: Let.

tR Investment in R&D

tK other investments

td dividends and share repurchases

tb payments to the debtholders

nVV ,0 value of the corporation at time 0t and tn, resp.

0S , nS , 0B , nB value of the equity and the debt issued by the corporation at

time t0 and nt resp.

r, ρ risk free rate and cost of equity capital resp.

i rate of return on a portfolio of the same riskiness as R&D and other (real)

investments.

VT- total value, created by the firm’s investment, R&D, payout policy at time

tn

68

Suppose the firm invests in R&D and its other real investment opportunities. Then

the total firm value at the end of the period is given by:

[ ]∑ −− ++++= tnt

tntnT rbdVV )1()1( ρ

Now suppose the firm invests the amount spent on R&D and other real investments

in securities with return i. Then, the firm value is given by:

[ ]∑ ∑ −−− ++++++++= tnt

tnt

tnttnT rbdiRKBSV )1()1()1)((0

' ρ

By comparing these two alternative firm values, we get Jensen’s Measure I:

∑ −++−−=− tnttnTT iRKSSVV )1)((' 0

Under measure II, we have nS = 0. Hence, measure II is given by:

∑ −++−−=− tnttnnTT iRKBVVV )1)(('

Michael Jensen constructs these measures using empirical data of 432 US

corporations over the period 1980-1990. The following, tables contain his findings:

69

The Modern Industrial Revolution, Exit and Control Systems

Table II

Total R&D and Capital Expenditures for Selected Companies

and the Venture Capital Industry, 1980—1990 ($ Billions)

Year GM IBM Xerox Kodak Intel GE Venture Capital

Industry Merck AT&T

Total R&D Expenditures 1980 2.2 1.5 0.4 0.5 0.1 0.8 0.6 0.2 0.4 1981 2.2 1.6 0.5 0.6 0.1 0.8 1.2 0.3 0.5 1982 22 21 0.6 0.7 0.1 0.8 1.5 0.3 0.6 1983 2.6 2.5 0.6 0.7 0.1 0.9 2.6 0.4 0.9 1984 3.1 3.1 0.6 0.8 0.2 1.0 2.8 0.4 2.4 1985 4.0 3.5 0.6 1.0 0.2 1.1 2.7 0.4 2.2 1986 4.6 4.0 0.7 1.1 0.2 1.3 3.2 0.5 2.3 1987 4.8 4.0 0.7 1.0 0.3 1.2 4.0 0.6 2.5 1988 53 4.4 0.8 1.1 0.3 1.2 3.9 0.7 2.6 1989 5.8 5.2 0.8 1.3 0.4 1.3 3.4 0.8 2.7 1990 5.9 4.9 0.9 1.3 0.5 1.5 1.9 0.9 2.4 Total 42.7 36.8 7.1 10.1 2.5 11.9 27.8 5.4 19.3

Total Capital Expenditures 1980 7.8 6.6 1.3 0.9 0.2 2.0 NA 0.3 17.0 1981 97 63 1.4 1.2 0.2 2.0 NA 0.3 17.8 1982 6.2 6.7 1.2 1.5 0.1 1.6 NA 0.3 16.5 1983 4.0 4.9 1.1 0.9 0.1 1.7 NA 0.3 13.8 1984 6.0 5.5 1.3 1.0 0.4 2.5 NA 0.3 3.5 1985 9.2 6.4 1.0 1.5 0.2 2.0 NA 0.2 4.2 1986 11.7 4.7 1.0 1.4 0.2 2.0 NA 0.2 3.6 1987 7.1 4.3 0.3 1.7 0.3 1.8 NA 0.3 37 1988 6.6 5.4 0.5 1.9 0.5 3.7 NA 0.4 4.0 1989 9.1 6.4 0.4 2.1 0.4 5.5 NA 0.4 3.5 1990 10.1 6.5 0.4 2.0 0.7 2.1 NA 0.1 3.7 Total 87.5 64.2 9.9 16.1 3.3 27.0 NA 3.7 91.2

Net Capital Expenditures (Capital Expenditures less Depreciation) 1980 3.6 3.8 0.5 0.5 0.1 L2 NA 0.2 9.9 1981 5.3 3.5 0.6 0.7 0.1 1.1 NA 0.2 9.9 1982 1.7 3.1 0.4 0.9 0.1 0.6 NA 02 7.7 1983 -1.1 1.3 0.3 0.2 0.1 0.6 NA 0.1 3.9 1984 1.1 2.3 0.5 0.2 0.3 1.3 NA 0.1 0.7

1985 3.5 3.4 1.2 0.6 0.1 0.8 NA 0.07 0.9 1986 5.6 1.3 0.2 0.5 0.0 0.6 NA 0.04 -3.2 1987 0.8 0.7 -0.3 0.6 0.1 02 NA 0.07 -0.6 1988 -0.7 1.5 -0.2 0.7 0.3 0.3 NA 0.2 -5.9 1989 2.0 2.2 -0.2 0.8 0.2 0.7 NA 0.2 1.1 1990 2.7 2.3 -0.3 0.7 0.4 0.6 NA 0.4 0.3 Total 24.5 25.4 2.7 6.4 1.8 8.0 NA 1.8 24.7

Total Value of R&D plus Net Capital Expenditures 67.2 62.2 9.8 16.7 4.3 19.9 27.8 7.2 44.0

Ending Equity Value of the Company. 12/90 26.2 64.6 3.2 13.5 13.5 50.0 > 60 34.8 32.9

NA = Not available. Source: Annual reports, COMPUSTAT, Business Week R&D Scoreboard, William Shaman. Venture Economics for total disbursements by industry. Capital expenditures for the venture capital industry are included in the R & D expenditures, which are the total actual disbursements by the industry.

70

71

The Journal of Finance

Table IV Difference between Value of Benchmark Strategy for

Investing R & D and Net Capital Expenditure and Actual Strategy under Three Assumptions

regarding Ending Value of Equity and Intermediate Cash Flows for Benchmark

Strategy (Performance Measures 1-3)

Panel A: Performance measures for the 35 companies at the bottom of the ranked list of 432companies in the period 1980-1990 on performance measure 2. r = 10 percent Performance Measure (Millions) Rank Company 1 2 3 432 General Motors Corp. (115,188) (100,720) (90,024) 431 Ford Motor Co. (29,304) (25,447) (20,392) 430 British Petroleum P.L.C. (ADR) (35,585) (23,699) (19,958) 429 Chevron Corp. (25,497) (15,859) (10,586) 428 Du Pont (E.l.) de Nemours (21,122) (15,279) (8,535) 427 Intl. Business Machines Corp- (49,395) (11,826) (5,394) 426 Unisys Corp. (14,655) (11,427) (11,899) 425 United Technologies Corp. (10,843) (9,032) (7,048) 424 Xerox Corp. (13,636) (8,409) (7,978) 423 Allied Signal Inc. (8,869) (7,454) (5,002) 422 Hewlett-Packard Co. (9,493) (6,373) (8,605) 421 ITT Corp. (9,099) (6,147) (3,611) 420 Union Carbide Corp. (8,673) (5,893) (3341) 419 Honeywell Inc. (7,212) (5,361) (5,677) 418 Lockheed Corp. (5,744) (5,339) (5,149) 417 Digital Equipment (7,346) (5,082) (7,346) 416 Penn Central Corp. (5,381) (4,846) (4,938) 415 Eastman Kodak Co. (12,397) (4,630) (1,762) 414 Chrysler Corp. (5,054) (4,604) (3,041) 413 Atlantic Richfield Co. (13,239) (3,977) (1,321) 412 Northrop Corp. (4,489) (3,904) (3,743) 411 Goodyear Tire & Rubber Co. (4,728) (3,805) (2,532) 410 Phillips Petroleum Co. (11,027) (3,614) (5,427) 409 Honda Motor Ltd. (Amer. shares) (4,880) (3,435) (3,898) 408 Texaco Inc. (11,192) (3,354) 3,830 407 Texas Instruments Inc. (5,359) (3,350) (4,276) 406 NEC Corp. (ADR) (4,803) (3,326) (3,736) 405 National Semiconductor Corp. (3,705) (3,246) (3,632) 404 General Dynamics Corp. (4,576) (2,966) (3,783) 403 Grace (W.R.) & Co. (4,599) (2,776) (2,314) 402 Imperial Chem. Inds. P.L.C. (ADR) (7,223) (2,575) (1,287) 401 Tektronix Inc. (3,414) (2,500) (3,070) 400 Advanced Micro Devices (2,647) (2,419) (2,603) 399 Wang Laboratories (CLB) (2,815) (2,368) (2,564)

398 Motorola Inc. (3,863) (2,270) (2,588)

72

The Journal of Finance Table V

Ordinary Least Squares Estimates of

Premiums for Full Sample and Subsamples of 1980—1983, 1984—1987, Low Management Holdings, and High Management Holdings

Full Sample 1980- 1983

1984- 1987

Low Mgmt.Holdings

High Mgmt. Holdings

Intercept

CFEQ

TAXEQ

SALESGR5

0333 (14.8)***

0.177 (1.79)* 0.044 (0.24) 0.008 (0.13)

0.397(11.9)*** 0.119

(0.91) -0.235 (-0.98)0.002 (0.03)

0.268 (794)***

0.299 (2.01)**

0.111 (1.59) 0.111 (0.69)

0.250 (7.21)***

0.350 (2.69)***

0.222 (0.82) 0.495 (2.88)

0.350 (10.3)***

0.056 (036) -0.015 (-0.06) -0.034 (-0.49)

N R-Squared

236 0.017

91 0.015

145 0.052

119 0.119

107 0.004

* Statistically significant at 10% confidence level. ** Statistically significant at 5% confidence level ***Statistically significant at 1% confidence level

the entire sample.3 This average is 6.44% for firms below the median, and 41.0% for firms above the median. Table V reports the results from ordinary least squares regressions of premiums on the three independent variables. The results generally are consistent with the free cash flow hypothesis. When estimated over the entire sample, the coefficient on CF/EQ is positive and significant at the 90% level. When the sample is decomposed into two periods, we find that the significant relation between CF/EQ and premiums holds only during the latter period. Similarly, decomposing the sample into firms with low and high equity holdings by managers reveals that the significant relation between CF/EQ and premiums holds only for the sample of firms in which managers owned relatively little equity prior to the going private transaction. The R-squared corresponding to the estimate over the sample consisting of firms with relatively low managerial equity holdings is notably higher (11.9%) than the corresponding R-squared for the entire sample (1.7%). The only equation in which SALESGR5 enters with a significant estimated coefficient is the one estimated over the sample consisting of low managerial equity holdings. This coefficient enters with a positive coefficient, which seemingly is inconsistent with the free cash flow hypothesis. As we mentioned above, however, it is possible that, for some firms, SALESGR5 may actually proxy for the tendency of managers to expend free cash flow on value-reducing projects that expand the size of their firms. If so, one might interpret the positive coefficient on SALESGR5 as consistent with the free cash flow hypothesis. However, recall that the sales growth variables generally entered the logit.

3 These data were obtained from the most recent proxy statement preceding the going private transaction and

were available for 253 firms in the sample.

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Conclusion: A large number of corporations have invested in projects with a

negative NPV. Hence, it seems that the investments of corporations in industries

with a small growth potential in the long run are frequently inefficient. How can the

managers of these corporations be forced to pay out their “free cash flow” instead of

investing it inefficiently? A possible solution: leverage!

Equity is soft, debt hard. Equity is forgiving, debt insistent.

Equity is a pillow, debt a sword.4

15.1 Leveraged Buy Outs

One possibility to increase the leverage of a corporation is a leveraged buy out

(LBO).

• A LBO is a going-private transaction.

• Frequently, the management stays with the corporation.

• The leverage increases from 18% to 90% on average.

• The original equityholders earn high premia (on average 40%-50% of the pre-

buy-out equity value).

• Empirical investigations show that the increases in the share price in the

course of leveraged buyouts are positively correlated with the amount of free

cash flow of a corporation.

• The equity of the corporation remains with the management (approximately

20%) and the board of directors (approximately 60%).

• The size of the board of directors decreases.

• The compensation of the management is more related to corporate

performance after a LBO than before.

• The cash flows earned by a corporation 3 years after a LBO are on average

96% higher than in the year before the LBO.

4 Bennet and Glassman, JACF, 1988.

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LBO association5:

• LBO partnership

• Company management

• Institutional investors

• Diversification is possible since LBO partnerships fund a number of LBOs.

Voluntary exchange offers (equity is exchanged against bonds without an LBO)

have similar effects.

15.2 Free Cash Flow, Empire Building and Capital Structure

In the last subsection, we argued that leverage may reduce the management’s

opportunities to invest inefficiently. Given that capital structure decisions are made

by the management, can we ever expect the management to restrict its inefficient

investment voluntarily? Or does the management face other threats inducing it to

commit not to invest inefficiently by choosing a high enough debt level? One such

threat may be the possibility of a takeover. Jeff Zwiebel developed a formal model:

• Managers enjoy empire building.

5 In monitoring bought-out companies, KKR and other LBO firms developed a distinctively new form of business organisation, which in the jargon of institutional economics is called the LBO association. Although it looks a bit like a conglomerate in that it is diversified and acquisitive, the LBO association is not a corporation and does not function like a holding company; it is a set of limited partnerships organised as discrete equity funds the LBO association allows its constituent companies to float on their own bottoms. There is no consolidation of accounts, inter company transfers of cash, or cross-subsidisation. There are no forced inter firm sales, commonly imposed information systems, or any other attempts to achieve either uniformity in practice or operating, financial and technical synergies.

There is no ‘black book', KKR's Henry Kravis explained. ‘We try to work with whatever structures and systems a company has used historically and go from there.' Nor is the LBO association a mere portfolio of investments, since each company is actively overseen and influenced by the general equity partners. As it evolved, the LBO association became a means for imposing a common oversight regime through a commonly experienced group of LBO-seasoned hoard directors. Through its long-standing relationship with law firms, accountants and consultants, KKR could bring legal, financial and management expertise to meet specific organisational needs and could apply its experience in high-level financings, including public offerings and balance sheet restructurings. Most of all, KKR, whose professionals dominated each constituent company's board, could watch its investments closely and knowledgeably to a degree uncommon in the world of corporate governance.

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• Managers can only be fired in the course of a takeover or in bankruptcy.

• What is the role of the capital structure in such a context?

Time Line: There are two periods, both of which are structured as follows:

Notation:

• There are two types of managers, type G (good) and type B (bad).

o A G-type has an investment opportunity with a NPV of 10 with

probability 0.8 and an investment opportunity with a NPV of -10

with probability 0.2.

o A B-type has an investment opportunity with a NPV of 10 with

probability 0.45 and an investment opportunity with a NPV of -10

with probability 0.55.

• The manager derives utility A from being head of a company for one period.

Undertaking an investment project gives the manager an additional utility of B

(empire building).

• Managers can only be fired in case of a takeover or in case of bankruptcy.

• Whenever a manager is fired, the new management invests in a project with

zero NPV.

• The costs of a takeover are 1.5.

• Let L0 and L1 denote the liquid assets of the firm at the beginning of the first-

and second period respectively.

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The second period:

• The management will always invest independent of the firm’s capital

structure (in particular: the manager will also undertake investments with a

negative NPV!).

• Is there a takeover at the beginning of the period?

o Firm value without a takeover when the manager is of type B:

L1 + 10(0.45 – 0.55) = L1 -1.

o Firm value with takeover: L1 – 1.5

o Hence, there is no takeover when the manager is of type B! In case

the manager is of type G, then a takeover would be even less

profitable!

Summary: In the second-and-last period the managers invest independent of

the capital structure and independent of their type both in positive and

negative NPV projects. There is never a takeover.

The first period:

(a) The Firing Decision at the End of the First Period

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• First, consider the decision whether or not to fire the manager at the end

of the first period whenever the firm defaults on its obligations.

o When the corporation defaults on its obligations at the end of the

first period, then the manager is fired when she is of type B:

Firm value without firing the manager:

L1 + 10(0.45 - 0.55) = L1 -1.

Firm value when the manager is fired: L1

o By contrast, the manager is not fired when she is of type G:

Not firing the manager yields a firm value of

L1 + 10(0.8-0.2) = L1 + 6.

Firing the manager yields a firm value L1.

(b) The Takeover Decision at the Beginning of the First Period

(ba). The case of an all-equity financed firm:

Suppose the manager is of type B. Then the value of the corporation

without a takeover is

L0 + 2(10)(0.45 - 0.55) = L0 - 2.

By contrast, if there is a takeover and the manager is fired, then the

firm value is L0 -1.5. As a consequence, a takeover will take place!

Now consider the case when the manager is of type G: Then the

value of the corporation without a takeover is given by

L0 + 2(10)(0.8 - 0.2) = L0 + 12.

By contrast, the value of the corporation with a takeover is L0 -1.5.

As a consequence, there won’t be a takeover!

(bb) The case of a levered firm:

Consider a company with a debt level of L0 - 10 < D* <L0 + 10.

When the manager is of type B, then the manager would be fired

whenever the company is bankrupt. Hence, for the stipulated debt-

level, the manager will be fired whenever she undertakes a project

with negative NPV and the firm subsequently defaults.

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Consider the utility of a manager who can only invest in a negative-

NPV-project. If the manager actually invests in this project, then

she will be fired at the end of the first period since the firm will be

unable to meet its obligations. Hence, the manager’s utility is A + B

+ 0 when she undertakes a negative-NPV-project. By contrast,

when she does not invest, then there will be no bankruptcy at the

end of the first period and her utility is A + A + B. As a result, the

manager will never invest in a negative NPV-project when the debt

level is L0-10<D*<L0.

Now consider the takeover decision. Without a takeover, the firm

value is given by

L0 + 0.45(10) + 10(0.45 – 0.55) = L0 + 3.5,

since the manager will only invest in positive NPV projects in the

first period. By contrast, upon a takeover, the firm value is given by

L0 – 1.5. As a conclusion, there will be no takeover at the beginning

of the first period when the debt level satisfies L0 – 10 < D* <L0.

When the manager is of type G, then the manager would not be

fired in the case of default. Hence, such a manager would always

invest even when only negative-NPV-projects are available.

Without a takeover, the firm value is given by

L0 + 10(0.8 – 0.2)2 = L0 + 12.

Without a takeover, the firm value is L0 – 1.5. As a result, no

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takeover will take place!

• Now consider the manager’s capital structure choice at the beginning of the first

period.

o When the manager is of type G, then she is indifferent between

alternative debt levels. There will never be a takeover in equilibrium

and the manager will always invest independent of whether the NPV

of the project is positive or negative. Moreover, the manager won’t

be fired in the case of default

o When the manager is of type B:

Suppose the firm is all-equity financed. Then, a takeover will

immediately take place and, hence, the utility of the manager is

zero.

Now suppose the firm issues a debt level D*. Then, there won’t

be a takeover and the manager gets a utility of A+0.45B+A+B.

As a result, the manager will choose to issue debt level D*.

Summary: The model shows that managers will voluntarily choose a high enough

debt level to commit not to undertake “empire-building-investments”. By doing so,

these managers are able to avoid being taken over!

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16 Liquidation, Reorganization and the Capital

Structure

16.1 The Austrian Bankruptcy Code

Reorganization (Ausgleich)

• Reorganization is a formal legal procedure in the course of which the creditors

grant (i) partial debt forgiveness or (ii) a deferral of repayment.

• Codified in the Ausgleichsordnung

• The set of facts triggering reorganization:

o insolvency

o debt overload

• The borrower has to file for reorganization (Ausgleichsantrag) within 60 days

after the occurrence of either the insolvency or the debt overload.

• The application for reorganization must be accompanied by (i) a

reorganization plan (Ausgleichsvorschlag) and (ii) by all necessary infor-

mation about the company and the way the company plans to raise the

required funds under the reorganization plan.

• The reorganization court secures the property of the company and arranges

for the going-concern of the company during the reorganization procedure.

• The reorganization court can rule out particular transactions made by the

borrower.

• After the reorganization application, there cannot be a liquidation until after

the decision by the court to open the liquidation procedure

(Konkurseroeffnung).

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• After the reorganization procedure has been opened, the borrower may not

o sell real estate properties (Liegenschaften)

o accept guarantees (Buergschaften eingehen)

• Ausgleichstagsatzung:

o the voting creditors (stimmberechtigte Glaeubiger) vote whether or

not to accept the reorganization proposal

o creditors with senior claims have to be repaid in full

o creditors with ordinary claims have to receive a fixed quota of at

least 40% payable within 2 years a fixed quota of at least 50%

payable within 18 months

o acceptance of the reorganization proposal requires

a simple majority of votes

creditors representing at least 75% of the total obligations of

the company must accept the reorganization proposal

• Liquidation

o has to be filed for by the borrower within 60 days after the occur-

rence of (i) insolvency or (ii) debt overload.

o can be triggered by a creditor who can prove that there are creditors

with due claims and that the company is unable to meet these

obligations.

o After the formal opening of the liquidation procedure (Konkur-

seroeffnung) the borrower looses the right of free disposition (Recht

der freien Verfuegung) over the estate in bankruptcy (Konkurs-

masse).

o The items belonging to the estate in bankruptcy are to be sold by the

court and the proceeds are paid out to the creditors. Another

possibility is to exploit the estate in bankruptcy out of court

(außergerichtliche Verwertung).

o Forced Reorganization:

The borrower can apply for forced reorganization. Forced

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reorganization requires (i) the approval of the court and (ii) a

majority vote in the Zwangsausgleichstagsatzung.

The creditors must receive a quota of at least 20%.

16.2 The US Bankruptcy Code

o Bankruptcy is triggered by the inability of the borrower to meet due

obligations.

o In practice, it is almost always the management, which files for

bankruptcy.

o The management can decide whether it files for bankruptcy under

Chapter 7 (liquidation) or Chapter 11 (reorganization).

Chapter 7-liquidation: Carried through by the receiver

(Masseverwalter). The proceeds from the liquidation are

distributed according to the Absolute Priority Rule: senior (prior)

claims have to be repaid before junior claims!

Chapter 11 - reorganization:

o Chapter 11-reorganization is much more complex. Important features

are:

Automatic Stay: Imposes a stay on all claims under which the

company cannot be forced to make a payment to any creditor.

Debtor in Possession: Under Chapter 11, it is possible to raise

additional junior debt capital.

The management must propose a reorganization plan within 120

days.

16.3 Bankruptcy and Capital Structure Up to now, we have considered the tradeoffs due to (i) the tax-advantages of

leverage and (ii) agency costs. A different frequently heard argument is that a

corporation trades tax-advantages of leverage against possible bankruptcy costs

when setting its capital structure. Two important questions arise:

o What are bankruptcy costs?

o Are bankruptcy costs of relevant magnitude?

83

Bankruptcy costs:

o direct bankruptcy costs: e.g. lawyers’ expenses, costs of the formal legal

procedures,

o indirect bankruptcy costs: e.g. disturbance of the relationship of the

corporation to its customers and suppliers, loss of key personal, fire sales

of assets , delayed liquidation, costs incurred by creditors

Haugen and Senbet, “The Insignificance of Bankruptcy Costs to the Theory of the

Optimal Capital Structure”, JF 1978, 383-392.

Argument 1: Formal Bankruptcy and the Liquidation Decision are unrelated!

Let

LV liquidation value of the company

MV going-concern value of the company

o Assume that the equity-holders and the debt-holders have the same

expectations concerning the firm value, then liquidation occurs only if

LV > MV .

o Now assume that the equity-holders have distinct expectations. Let LDV and

LSV denote the expected firm value of the debt-holders and the stockholders

respectively.

In case of: MLD VV > and MLS VV < MLS VV > and MLD VV <

bankruptcy

no bankruptcy

Conclusion: Whether or not there is formal bankruptcy, the outcome will be

the same!

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Argument 2: Formal bankruptcy will only take place when the direct and indirect

bankruptcy costs are smaller than the cost of avoidance of bankruptcy.

Why? By an arbitrage argument! Can you think of one?

As a conclusion, bankruptcy cost cannot be significant and relevant for the capital

structure policy.

Counterargument: The “privatization” of the bankruptcy procedure -as proposed by

Haugen and Senbet - is not always successful!

In this case, when securities are fairly priced, the original shareholders (and not

creditors) of a firm pay the present value of the costs associated with bankruptcy

and financial distress.

16.4 A Theory of Workouts6 and the Effects of Re-

organization

Gertner and Scharfstein, “A Theory of Workouts and the Effects of

Reorganization”, JF 1989, 747-769.

6 When a financially distressed firm is successful at reorganizing outside the bankruptcy , it is called

a workout

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16.4.1 A Free-Rider Problem

Example:

• A corporation is in financial distress and the investors expect a formal

bankruptcy procedure.

MV = 105m ignoring bankruptcy costs

A formal bankruptcy procedure would imply bankruptcy costs of

25m.

There are 1m bonds outstanding with a market value of 75 each.

There are 1000 bondholders holding 1000 bonds each.

The total value of the equity capital is 5m

• An arbitrageur has bought up the entire equity and wants to buy back 50% of the

bonds in order to avoid a formal bankruptcy procedure.

• In her tender offer, the arbitrageur offers 80 per bond for 500.000 bonds.

o What is the value of the bonds when the tender offer is not

successful?

o What is the value of the bonds when the formal bankruptcy can be

avoided?

• When every bondholder thinks that the success of the tender offer is not affected

by her decision whether or not to tender, then the tender offer is not successful.

tender successful tender not successful

Tender

don’t tender

o Conclusion: There is a free-rider problem.

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16.4.2 A Solution to the Free-Rider Problem

• Assume the arbitrageur files for reorganization and proposes the following

reorganization plan: Every bondholder receives a payment of 80 per bond in

exchange for 500 bonds. How will the bondholders vote?

reorganization successful reorg. not successful

Yes

No .

• Conclusion:

Intuitive Explanation:

o Under an informal reorganization, the creditors are treated differently in

dependence of whether they tender or don’t tender. Since the creditors

view themselves to be non-pivotal, they have an incentive to reject the

tender offer.

o Under a formal reorganization, the creditors receive the same amount of

money independent of their vote. The creditors are now pivotal and,

hence, they will accept the reorganization.

16.4.3 Other Arguments for Formal Reorganization Procedures Given the direct cost of formal bankruptcy procedures, why aren’t there only

informal reorganizations?

o Free Rider Problem (discussed above)

o Asymmetric Information between the management and the equi-

tyholders and also between the equityholders and the debtholders:

the management has more information about the firm value of a

corporation than the creditors have

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the management can offer the creditors new claims in exchange

for their existing securities; but what is the value of these claims?

Maybe it is better to let a court decide how the firm’s cash-flow

is to be shared among the creditors.

16.4.4 A New Approach to Corporate Reorganizations

Bebchuk, “A New Approach to Corporate Reorganizations”, Harvard Law Review,

1992, 775-804.

• A reorganization is essentially a sale of the corporation to the existing

claimholders.

• A fundamental problem in any reorganization is the uncertainty about the

value of the corporation.

• Existing bankruptcy procedures can be compared to a “bargaining” between

all claimholders. However, the formal bargaining in court is very costly.

• In any reorganization, there are legal provisions regulating the types of

majority (e.g. simple majority) that are to be achieved for a reorganization to

be successful.

• Lucian Arye Bebchuk proposes a mechanism by which the “bargaining

process” can be made less time-consuming and more cost-effective.

Example: A corporation has the following capital structure:

• 100 stockholders with one stock each

• 100 bondholders with a senior claim of USD 1 each

• 100 bondholders with a junior claim of USD 1 each

This corporation is insolvent and shall be reorganized. Bebchuk proposes the

following procedure:

88

• The securities to be issued by the corporation in the course of the

reorganization are to be grouped into 100 similar portfolios referred

to as “units”.

This may involve splitting some of these securities: For example,

consider a corporation which has to issue 100 shares of common

stock and 50 shares of preferred stock in the course of the reorga-

nization. This would imply that there are 100 units consisting of 1

common stock and 0.5 preferred stocks each.

• Let V denote the per-unit-value of the reorganized corporation.

Suppose that the reorganization takes place on January 1st.

If V were observable, then the various groups of investors should

optimally receive:

value of V group of investors distribution of units

V ≤ 1 senior creditors

junior creditors

equityholders

1 <V ≤ 2 senior creditors

junior creditors

equityholders

2 < V senior creditors

junior creditors

equityholders

If V is not observable then Bebchuck proposes the following “Dis-

tribution of Rights”:

Senior Creditors Each senior creditor receives one type-A right. A type-A right

may be redeemed by the company on January 5 for USD 1. If the

right is not redeemed, on January 5 its holder will be entitled to

receive one unit of the reorganized corporation.

89

Junior Creditors Each junior creditor receives one type-B right. A type-B right

may be redeemed by the company on January 5 for USD

1. If the right is not redeemed, on January 5 its holder will

receive the option to purchaser one unit of the reorganized

corporation for USD 1.

Equityholders Each equityholders receives one type-C right. A type-C right

may not be redeemed by the company. The holder of such a

right on January 5 will have the option to purchase one unit

of the reorganized corporation for USD 2.

How are these rights “executed”?

o If the equityholders think that V > 2, then they will execute their

type-C rights. They pay USD 200 (in total) and receive the

reorganized corporation. The corporation distributes the paid-in

amount of USD 200 to the holders of type-A and type-B rights.

o If the investors think that 1≤ V <2, then type-C rights will not be

executed but the holders of type-B rights will execute their

options. They pay USD 100 (in total) and receive the corporation.

The corporation distributes the paid-in amount of USD 100 to the

holders of type-A rights.

o If the investors think that V ≤ 1, then neither the holders of type-B

or type-C rights will execute their options. Holders of type-A

rights receive one unit of the reorganized corporation each.

What is the advantage of this method?

o Even when the value of each of these rights is uncertain, no party

ever receives less than it is entitled to. No party is treated unfairly!

o There is no lengthy and costly bargaining necessary!

90

17 Capital Structure: The Big Picture

Basic Result: The firm value is equal to

(i) the value of the all-equity financed firm +

(ii) the net present value of the tax-savings due to tax-shields generated by

leverage -

(iii) present value of agency costs of debt +

(iv) present value of agency benefits of debt-

(iv) bankruptcy costs.

The tax-advantage of debt:

• What tax-advantages of leverage exist under the tax-regime?

• Is the corporation paying taxes right now?

• Will the corporation pay taxes in the future?

Agency Costs: Equityholders vs. Debtholders: Underinvestment and Risk-Shifting.

• What is the effect of future growth potentials and investment

opportunities on the firm value? If there is a strong effect, then the

agency costs of risk-shifting and underinvestment could be significant.

This would imply a low leverage.

• By contrast, in case of a mature corporation, there are not as many vital

future investment projects to be undertaken. Hence, the agency costs of

risk-shifting and underinvestment are smaller. This implies a higher debt

level.

Agency Costs: Manager vs. Investors: Empire-Building, Shirking

• Are there profitable investment projects and profitable opportunities to

enter into new markets? In case there aren’t, a higher debt level can help

to reduce the free cash-flow, which would otherwise be used up by the

management’s empire building.

Expected Reorganization and Bankruptcy Costs:

• increase in the riskiness of the cash-flow

• increase in the riskiness of the corporation’s assets

91

Corporate Risk Management

92

1. Risk Management and Corporate Strategy

Def: Risk management is the assessment and management of the corporation’s exposure to various sources of risk.

Many large corporations now have entire departments devoted to hedging and risk

management.

1.1. Hedging in frictionless “Modigliani-Miller” markets:

In the absence of taxes and transactions costs, hedging decisions do not affect the

value of the firm.

93

1.2. Motives for hedging in markets with frictions

1.2.1. Hedging and expected tax payments

Example:

1.2.2. Hedging and the cost of financial distress

Costs of financial distress include: costs due to conflicts of interest between debt

holders and equity holders; due to the reluctance of important stakeholders to do

business with a firm having financial difficulties.

1.2.3. Hedging and the ability to plan future capital needs

94

1.2.4. Hedging and management compensation

1.2.5. Hedging and decision quality

1.3. Some empirical evidence on hedging

- Larger firms are more likely to hedge than smaller firms

- Firms with more growth opportunities are more likely to use derivatives

- Highly levered firms are more likely to use derivatives

- Risk management practices in the gold mining industry.

95

2. The Practice of Hedging

Firms’ future cash flows may be exposed to a number of risk factors: interest rate

changes, fx-rate changes, commodity price changes etc.

This can be represented in the following way:

∑ ++=i

ii FbaC ε~~

where

C~ = cash flow in million

iF = risk factors

ε~ =noise term

ib =exposure with respect to risk factor i.

Objective of hedging: acquire financial instruments to minimize the risk exposure or

to achieve target betas.

Financial instruments used frequently: forwards, futures, options, swaps etc.

Hedge ratio: size of the hedge position per unit of the underlying asset.

96

2.1. How to estimate risk exposures?

1) Backward looking: Regression analysis

Hereby one would regress historical cash flows on historical realizations of risk

factors. This can also be done for first differences, i.e. regressing changes in cash

flows on changes in cash risk factor realizations.

Example:

2) Forward looking: Simulation (=scenario analysis)

Hereby one specifies a number of possible future scenarios. A scenario is defined by

a cash flow and the relevant risk factor realizations.

Example:

97

2.2. Risk measures

Frequently, management wishes to summarize the risk structure of a firm in a single number:

- Variance of cash flows

- Standard deviation of cash flows

- Value at Risk or Cash Flow at Risk (CaR)

The variance of cash flows due to the risk factors considered is given by

),cov(11

2nm

K

nnm

K

mFF∑∑

==

= ββσ

Example

98

2.3. Using forwards to hedge

Example: Metallgesellschaft: had locked in the selling price at which its customers

could purchase heating oil. Let us consider the commitment for the 10th year. The

unhedged cash flow is given by:

Amount*)~(~101010 SPC −=

Where

C10 = cash flow in 10 years

P10 = committed price for heating oil in 10 years

S10 = spot price for crude oil in 10 years.

(This ignores the costs of refining crude oil into heating oil)

In the previous notation, the relevant risk factor is the spot price of crude oil in 10

years, and the Beta factor would be equal to minus the amount of heating oil

committed to Metallgesellschaft’s customers. Thus, if the “amount” were 1 million

barrels, then Beta would be minus one million.

This could be hedged, using a forward contract. To eliminate the exposure, one

would need to buy forward one million barrels of crude oil (assuming that one can

produce 1 million barrels of heating oil using 1 million barrels of crude oil).

The cash flow of the hedged asset is then given by:

Amount*))~()~((~10,10101010 +−+−= tt

hedged FSSPC

Where Ft,t+10 is the 10-year forward price for crude oil.

99

Ft,t+10 As can be seen, the beta with respect to the risk factor “spot rate for crude oil

in 10 years” is now zero.

2.4. Hedging short-term commitments with maturity matched futures

contracts

Note that there is a no-arbitrage relationship:

T

ftTtt rSF )1(, +=+

Where

Ft,t+T, and St are the forward price and the spot price of an asset respectively.

As an example, if the spot price of one ounce of gold is $400 and the risk free rate is

10%, then the one year forward price is $440.

Example for a futures hedge: Suppose we own one ounce of gold to be sold in one

year. Then, selling a one-year futures contract would be overhedging. This is so

since the gain or loss in a futures position due to a change in the spot price is given

by

Tf

t

Ttt rS

F)1(, +=

∂

∂ +

100

whereas the gain or loss in the underlying spot position is only +/-1. Thus, the hedge

ratio should be set to (1+rf)-T.

Example:

2.5. Hedging long-dated commitments with short-maturing futures or

forwards when there is a convenience yield

We first note that the no-arbitrage relationship between the spot and the forward (futures) price of an asset changes if the asset pays a dividend at a rate d. In this case the relationship becomes

T

Tft

Ttt drS

F)1(

)1(, +

+=+ .

Many commodities are like dividend paying assets because there is a benefit from

owning them aside from their potential for price appreciation. This benefit is

referred to as convenience yield.

101

Now consider hedging a long-term commitment. The problem in this context is that

many financial instruments such as futures have short maturities, whereas corporate

exposures are frequently long-term.

Example: Assume that oil has a convenience yield of 2% p.a. Therefore the forward

commitment to buy one barrel of oil in 10 years is equivalent to a spot position of

(1/(1,02)10). Alternatively, to buy oil forward in 1 year is equivalent to (1/(1,02)).

Thus, to hedge a 10-year commitment with 1-year forwards requires a hedge ratio of

837,0

02,11

02,11

10

= .

This position must be “rolled over” at maturity. Note that there is no need to adjust

the hedge before the roll-over date. To see this, recall that, for example, after 6

months the hedge ratio is still given by

837,0)

02,11(

02,11

5,0

5,9

= .

After one year the new hedge ratio becomes

853,0

02,1102,11

9

= .

102

As discussed above, futures positions must be tailed since, ceteris paribus, they are

more risky than the equivalent forward positions, due to marking to market.

Continuing the above example, the futures position required in the first year would

be

761,01,102,11

02,11

10

=⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

.

This would need to be adjusted during the year. E.g. after 6 months the hedge ratio

should be

798,01,102,11

02,11

5,0

5,0

5,9

=⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

.

Case Study (ctd): Deutsche Metallgesellschaft

In simplified terms, the position of Deutsche Metallgesellschaft in the early 90s can

be described as follows. They had an obligation to sell 1,25 million barrels of oil per

month at a fixed price for a period of 10 years. This amounts to a delivery

obligation of 150 million barrels of oil. Metallgesellschaft used short term oil

futures contracts to hedge this exposure. But rather than buying futures for 150

million barrels, how much should they have bought?

103

If the convenience yield and the risk free rate of interest per month are assumed to

be 0,565 percent each, and one-month futures contracts are used, then the futures

position to hedge month t’s exposure is

00565,100565,125,1

1−t .

This implies a total amount of

12021 00565,125,1...

00565,125,1

00565,125,17,108 millionmillionmillionmillion +++= .

This differs significantly from the 150 million barrels, which amounts to the total

obligation.