Chapter 3: Creating value with risk managementChapter objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1Section 3.1. Bankruptcy costs and costs of financial distress. . . . . . . . . . . . . . . . . . . . . . 4

Section 3.1.1. Bankruptcy costs and our present value equation. . . . . . . . . . . . . 6Section 3.1.2. Bankruptcy costs, financial distress costs, and the costs of risk

management programs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Section 3.1.3. Bankruptcy costs and Homestake. . . . . . . . . . . . . . . . . . . . . . . . 10

Section 3.2. Taxes and risk management. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11Section 3.2.1. The tax argument for risk management. . . . . . . . . . . . . . . . . . . 16

1. Carry-backs and carry-forwards . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162. Tax shields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173. Personal taxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

Section 3.2.2. The tax benefits of risk management and Homestake . . . . . . . . . 18Section 3.3. Optimal capital structure, risk management, bankruptcy costs and taxes. . . 19

Section 3.3.1. Does Homestake have too little debt? . . . . . . . . . . . . . . . . . . . . . 26Section 3.4. Poorly diversified stakeholders. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

Section 3.4.1. Risk and the incentives of managers. . . . . . . . . . . . . . . . . . . . . . . 29Section 3.4.2. Managerial incentives and Homestake. . . . . . . . . . . . . . . . . . . . . 33Section 3.4.3. Stakeholders. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33Section 3.4.4. Are stakeholders important for Homestake? . . . . . . . . . . . . . . . . 34

Section 3.5. Risk management, financial distress and investment. . . . . . . . . . . . . . . . . . 35Section 3.5.1. Debt overhang. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36Section 3.5.2. Information asymmetries and agency costs of managerial discretion.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38Section 3.5.3. The cost of external funding and Homestake. . . . . . . . . . . . . . . . 41

Section 3.6. Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42Key concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43Review questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44Literature note . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45BOX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46Figure 3.1. Cash flow to shareholders and operating cash flow. . . . . . . . . . . . . . . . . . . 49Figure 3.2. Creating the unhedged firm out of the hedged firm. . . . . . . . . . . . . . . . . . . 50Figure 3.3. Cash flow to shareholders and bankruptcy costs . . . . . . . . . . . . . . . . . . . . . 51Figure 3.4. Expected bankruptcy cost as a function of volatility . . . . . . . . . . . . . . . . . . 52Figure 3.5. Taxes and cash flow to shareholders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53Figure 3.6. Firm after-tax cash flow and debt issue . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

Chapter 3: Creating value with risk management

December 1, 1999

© René M. Stulz 1997, 1999

Chapter 3, page 1

Chapter objectives

1. To understand when risk management creates value for firms.

2. To show how taxes, financial distress and bankruptcy costs, contracting costs, information

asymmetries, managerial incentives, stakeholder interests, large shareholders are reasons why risk

management creates value.

3. To determine what sorts of risk have to be hedged to create value.

Chapter 3, page 2

Chapter 2 shows that a risk management program cannot increase firm value when the cost

of bearing a risk is the same whether the risk is born within or outside the firm. This result is called

the risk management irrelevance proposition. The irrelevance proposition holds when financial

markets are perfect. If the proposition holds, any risk management program undertaken by the firm

can be implemented with the same outcome by an investor through homemade risk management. The

usefulness of the risk management irrelevance proposition is that it allows us to find out when

homemade risk management is not equivalent to risk management by the firm. This is the case

whenever risk management by the firm affects firm value in a way that cannot be mimicked by

investors on their own. In this chapter, we identify situations where there is a wedge between the cost

of bearing a risk within the firm and the cost of bearing it outside the firm. Such a wedge requires the

existence of financial markets imperfections.

To show why the risk management irrelevance proposition is right, chapter 2 uses the example

of a gold producing firm. We continue using this example in this chapter. The firm is exposed to gold

price risk. The risk can be born within the firm. In this case, the firm has low income if the price of

gold is unexpectedly low and high income if it is unexpectedly high. If the irrelevance proposition

holds, the only ex ante cost of bearing this risk within the firm is that shares are worth less if gold

price risk is systematic risk because shareholders require a risk premium for gold price risk. The only

cost to the firm of having the gold price risk born outside the firm is that the firm has to pay a risk

premium to induce capital markets to take that risk. The risk premium capital markets require is the

same as the one shareholders require. Consequently, it makes no difference for firm value whether

the gold price risk is born by shareholders or by the capital markets.

The risk management irrelevance proposition makes clear that for risk management to

Chapter 3, page 3

increase firm value it has to be more expensive to take a risk within the firm than to pay capital

markets to take it. In terms of our gold producing firm example, risk management creates value if an

unexpectedly low gold price has costs for the firm that it would not have for the capital markets. An

example is a situation where, if the gold price is unexpectedly low, the firm does not have funds to

invest and hence has to give up valuable projects. For this situation to occur, it has to be that the firm

finds it costly to raise funds on capital markets if the gold price is unexpectedly low. In this case, the

unexpected low gold price implies that shareholders lose income now, but in addition they lose future

income because the firm cannot take advantage of investment opportunities. The firm does not incur

this additional cost resulting from a low gold price if the gold price risk is born by the capital markets.

To take the gold price risk, the capital markets require a risk premium. The cost of having the capital

markets take the gold price risk is less than the cost the firm has to pay if it bears the risk within the

firm. If the firm bears the risk within the firm, the cost is the risk premium required by the firm’s

claimholders (the shareholders in an all-equity firm; the shareholders and debtholders otherwise) plus

the loss of profits due to the inability to invest optimally if the gold price is low.

In this chapter, we investigate how risk management can be used to increase firm value. We

discuss the reasons why a firm might find it more expensive to bear a risk within the firm than pay the

capital markets to bear that risk. This chapter will therefore show where the benefits of risk

management come from. More precisely, we show how risk management can decrease the present

value of bankruptcy costs and costs of financial distress, how it can decrease the present value of

taxes paid, how it can enable firms to make it more likely that they can take advantage of the positive

net present value projects available to them, and how it enables firms to provide better incentives for

managers. In the next chapter, we integrate these various sources of gain from risk management into

Chapter 3, page 4

an integrated theory of risk management.

Section 3.1. Bankruptcy costs and costs of financial distress.

In our analysis of when risk management does not create value in chapter 2, we take the

distribution of the firm’s cash flow before hedging, the cash flow from operations, as given. We

assume that the firm sells 100m ounces of gold at the end of the year and then liquidates. The firm

has no debt. The gold price is assumed to be normally distributed with a mean of $350 per ounce.

There are no operating costs for simplicity. All of the cash flow accrues to the firm’s shareholders.

This situation is represented by the straight line in figure 3.1. In that graph, we have cash flow to the

firm on the horizontal axis and cash flow to the holders of financial claims against the firm on the

vertical axis. Here, the only claimholders are the shareholders. In perfect financial markets, all cash

flows to the firm accrue to the firm’s claimholders, so that there is no gain from risk management.

In our analysis of chapter 2, the firm has a cash flow at the end of the year. It distributes the

cash flow to its owners, the shareholders, and liquidates. If the firm hedges, it sells its production at

the forward price so that the firm’s owners get the proceeds from selling the firm’s gold production

at the forward price. If the owners receive the proceeds from the hedged firm, they can recreate the

unhedged gold firm by taking a long forward position in gold on personal account as shown in figure

3.2. Suppose the forward price is $350. If the gold price turns out to be $450, for example, the

unhedged firm receives $350 an ounce by delivering on the forward contract while the unhedged firm

would receive $450 an ounce. An investor who owns the hedged firm and took a long forward

contract on personal account receives $350 per ounce of gold from the hedged firm plus $450 - $350

per ounce from the forward contract for a total payoff of $450 per ounce which is the payoff per

Chapter 3, page 5

ounce of the unhedged firm. Hence, even though the firm is hedged, the investor can create for

himself the payoff of the unhedged firm.

Consider now the case where the firm is a levered firm. We still assume that markets are

perfect and that the distribution of the cash flow from operations is given. With our assumptions,

there are no taxes. At the end of the year, the cash flow to the firm is used to pay off the debtholders

and shareholders receive what is left over. In this case, the firm’s claimholders still receive all of the

firm’s cash flow and the firm’s cash flow is not changed by leverage. However, now the claimholders

are the debtholders and the shareholders. Leverage does not affect firm value because the firm’s cash

flow is unaffected by leverage. Hence, leverage just specifies how the pie - the firm’s operating cash

flow - is divided among claimants - the debtholders and the shareholders. Since the cash flow to

claimholders is the firm’s cash flow, risk management does not affect firm value.

Default on debt forces the firm to file for bankruptcy or to renegotiate its debt. With perfect

financial markets, claims on the firm can be renegotiated at no cost instantaneously. If financial

markets are not perfect, this creates costs for the firm. For instance, the firm might have to hire

lawyers. Costs incurred as a result of a bankruptcy filing are called bankruptcy costs. We now

assume that financial markets are imperfect because of the existence of bankruptcy costs. These costs

arise because the firm has debt that it cannot service, so that it has to file for bankruptcy.

Consequently, the value of the unlevered firm exceeds the value of the levered firm by the present

value of the bankruptcy costs. Later, we will find that there are benefits to leverage, but for the

moment we ignore them. In figure 3.3., these bankruptcy costs create a wedge between cash flow to

the firm and cash flow to the firm’s claimholders. This wedge corresponds to the loss of income for

the owners when the firm is bankrupt.

Chapter 3, page 6

The importance of the bankruptcy costs depends on their level and on the probability that the

firm will have to file for bankruptcy. The probability that the firm will be bankrupt is the probability

that its cash flow will be too small to repay the debt. We know how to compute such a probability

from chapter 2 for a normally distributed cash flow. Figure 3.4 shows how the distribution of cash

flow from operations affects the probability of bankruptcy. If the firm hedges its risk completely, it

reduces its volatility to zero since the claimholders receive the present value of gold sold at the

forward price. Hence, in this case, the probability of bankruptcy is zero and the present value of

bankruptcy costs is zero also. As firm volatility increases, the present value of bankruptcy costs

increases because bankruptcy becomes more likely. This means that the present value of cash flow

to the firm’s claimholders falls as cash flow volatility increases. Therefore, by hedging, the firm

increases firm value because it does not have to pay bankruptcy costs and hence the firm’s

claimholders get all of the firm’s cash flow. In this case, homemade risk management by the firm’s

claimholders is not a substitute for risk management by the firm. If the firm does not reduce its risk,

its value is lower by the present value of bankruptcy costs. Consequently, all homemade risk

management can do is eliminate the risk associated with the firm value that is net of bankruptcy costs.

Section 3.1.1. Bankruptcy costs and our present value equation.

We now use our present value equation to show that risk management increases firm value

when the only financial market imperfection is the existence of bankruptcy costs. Remember that in

the absence of bankruptcy costs, the firm’s claimholders receive the cash flow at the end of the year

and the firm is liquidated. With our new assumptions, the claimholders receive the cash flow if the

firm is not bankrupt. Denote this cash flow by C. If the firm is bankrupt, the claimholders receive C

Chapter 3, page 7

minus the bankruptcy costs. Consequently, the value of the firm is now:

Value of firm = PV(C - Bankruptcy costs)

We know from the previous chapter that the present value of a sum of cash flows is the sum of the

present values of the cash flows. Consequently, the value of the firm is equal to:

Value of firm = PV(C) - PV(Bankruptcy costs)

= Value of firm without bankruptcy costs - Present value of bankruptcy costs

Let’s now consider the impact of risk management on firm value. If the hedge eliminates all risk, then

the firm does not incur the bankruptcy costs. Hence, the cash flow to the firm’s owner is what the

cash flow would be in the absence of bankruptcy costs, which is C. This means that with such a hedge

the claimholders get the present value of C rather than the present value of C minus the present value

of bankruptcy costs. Consequently, the gain from risk management is:

Gain from risk management = Value of firm hedged - Value of firm unhedged

= PV(Bankruptcy costs)

Let’s look at a simple example. We assume that the interest rate is 5% and gold price risk is

unsystematic risk. The forward price is $350. Because gold price risk is unsystematic risk, the

forward price is equal to the expected gold price from our analysis of chapter 2. As before, the firm

Chapter 3, page 8

produces 1m ounces of gold. Consequently, PV(C) is equal to $350M/1.05 or $333.33M. The

present value of the hedged firm is the same (this is because E(C) is equal to 1M times the expected

gold price which is the forward price). The present value of the bankruptcy costs requires us to

specify the debt payment and the distribution of the cash flow. Let’s say that the bankruptcy costs are

$20m, the face value of debt is $250m, and the volatility of the gold price is 20%. The firm is

bankrupt if the gold price falls below $250. The probability that the gold price falls below $250 is

0.077 using the approach developed in chapter 2. Consequently, the expected bankruptcy costs are

0.077*20M, or $1.54M. By the use of risk management, the firm insures that it is never bankrupt and

increases its value by the present value of $1.54M. Since gold price risk is assumed to be

unsystematic risk, we discount at the risk-free rate of 5% to get $1.47M (which is $1.54M/1.05).

In the presence of bankruptcy costs, the risk management irrelevance theorem no longer

holds. Because we assume that gold price risk is diversifiable, the cost of having the capital markets

bear this risk is zero. The risk is diversified in the capital markets and hence there is no risk premium

attached to it. In contrast, the cost of bearing the risk in the firm is $1.47M. The capital markets

therefore have a comparative advantage over the firm in bearing gold price risk. Note that if gold

price risk is systematic risk, then capital markets charge a risk premium for bearing gold price risk.

However, this risk premium is the same as the one shareholders charge in the absence of bankruptcy

costs. Hence, the capital markets still have a comparative advantage for bearing risk measured by the

bankruptcy costs saved by having the capital markets bear the risk. There is nothing that shareholders

can do on their own to avoid the impact of bankruptcy costs on firm value, so that homemade risk

management cannot eliminate these costs.

Chapter 3, page 9

Section 3.1.2. Bankruptcy costs, financial distress costs, and the costs of risk management

programs.

So far, we have described the bankruptcy costs as lawyer costs. There is more to bankruptcy

costs than lawyer costs. There are court costs and other administrative costs. An academic literature

exists that attempts to evaluate the importance of these costs. In a recent study of bankruptcy for 31

firms over the period from 1980 to 1986, Weiss (1990) finds that the average ratio of direct

bankruptcy costs to total assets is 2.8%. In his sample, the highest percentage of direct bankruptcy

costs as a function of total assets is 7%. Other studies find similar estimates of direct bankruptcy

costs. In addition, bankruptcy can have large indirect costs. For instance, management has to spend

a lot of time dealing with the firm’s bankruptcy proceedings instead of managing the firm’s

operations. Also, when the firm is in bankruptcy, management loses control of some decisions. For

instance, it might not be allowed to undertake costly new projects.

Many of the costs we have described often start taking place as soon as the firm’s financial

situation becomes unhealthy. Hence, they can occur even if the firm never files for bankruptcy or

never defaults. If management has to worry about default, it has to spend time dealing with the firm’s

financial situation. Management will have to find ways to conserve cash to pay off debtholders. In

doing so, it may have to cut investment which means the loss of future profits. Potential customers

might become reluctant to deal with the firm, leading to losses in sales. All these costs are often called

costs of financial distress. Specifically, costs of financial distress are all the costs that the firm incurs

because its financial situation has become tenuous. All our analysis of the benefit of risk management

in reducing bankruptcy costs holds for costs of financial distress also. Costs of financial distress

amount to a diversion of cash flow away from the firm’s claimholders and hence reduce firm value.

Chapter 3, page 10

Reducing firm risk to decrease the present value of these costs naturally increases firm value.

Reducing costs of financial distress is the most important benefit of risk management. Consequently,

we study in more detail how risk management can be used to reduce specific costs of financial distress

throughout the remainder of this chapter.

In our example, the gold mining firm eliminates all of the bankruptcy costs through risk

management. If there were costs of financial distress that occur when the firm’s cash flow is low, it

obviously could eliminate them as well through risk management. This is not the case in general

because there may be risks that are too expensive to reduce through risk management. We assumed

that there are no costs to reducing risk with risk management. Without risk management costs,

eliminating all bankruptcy and distress risks is optimal.

Transaction costs of risk management can be incorporated in our analysis in a straightforward

way. Suppose that there are transaction costs of taking positions in forward contracts. As transaction

costs increase, risk management becomes less attractive. If the firm bears a risk internally, it does not

pay these transaction costs. The transaction costs of risk management therefore simply increase the

cost of paying the capital markets to take the risk.

Section 3.1.3. Bankruptcy costs and Homestake.

In the previous chapter, we introduced Homestake as a gold mining firm which had a policy

of not hedging gold price exposure. As we saw, management based their policy on the belief that

Homestake’s shareholders value gold price exposure. We showed that this belief is wrong because

investors can get gold price exposure without Homestake on terms at least as good as those

Homestake offers and most likely on better terms. This raises the question of whether, by not

Chapter 3, page 11

hedging, Homestake’s value was lower than it would have been with hedging. Throughout this

chapter, for each source of value of hedging that we document, we investigate whether this source

of value applies to Homestake.

At the end of the 1990 fiscal year, Homestake had cash balances of more than $300 million.

In contrast, its long-term debt was $72 million and it had unused credit lines amounting to $245

million. Homestake could therefore repay all its long-term debt and still have large cash balances.

Bankruptcy is not remotely likely at that point for Homestake. However, suppose that Homestake

had a lot more long-term debt. Would bankruptcy and financial distress costs have been a serious

issue? Homestake’s assets are its mines and its mining equipment. These assets do not lose value if

Homestake defaults on its debt. If it makes sense to exploit the mines, the mines will be exploited

irrespective of who owns them. It follows from this that neither bankruptcy costs nor financial distress

costs provide an important reason for Homestake to practice risk management. Though the reduction

of financial distress costs is the most important benefit of risk management in general, there are firms

for which this benefit is not important and Homestake is an example of such a firm. In the next

chapter, we will consider a type of firm that is at the opposite end of the spectrum from Homestake,

namely financial institutions. For many financial institutions, even the appearance of a possibility of

financial distress is enough to force the firm to close. For instance, in a bank, such an appearance can

lead to a bank run where depositors remove their money from the bank.

Section 3.2. Taxes and risk management.

Risk management creates value when it is more expensive to take a risk within the firm than

to pay the capital markets to bear that risk. Taxes can increase the cost of taking risks within the firm.

Chapter 3, page 12

The idea that the present value of taxes paid can be affected by moving income into future years is

well-established. If a dollar of taxes has to be paid, paying it later is better. Derivatives are sometimes

used to create strategies that move income to later years and we will see such uses of derivatives in

later chapters. However, in this section, we focus on how managing risk, as opposed to the timing

of income, can reduce the present value of taxes. To understand the argument, it is useful to think

about one important tax planning practice. If an individual knows that in some future year, her tax

rate will be less, that individual should try to recognize income in that year rather than in years with

a higher tax rate. Hence, given the opportunity to defer taxation on current income through a pension

plan, the investor would want to do so if the tax rate when taxes are paid is lower than the tax rate

that would apply now to the income that is deferred. With risk management, rather than altering when

income is recognized to insure that it is recognized when one’s tax rate is low, one alters the risks one

takes to decrease income in a given tax year in states of the world where the tax rate is high and

increase income in the same tax year in states of the world in which the tax rate is low. By doing so,

one reduces the average tax rate one pays and hence reduces the present value of taxes paid.

To understand the role of risk management in reducing the present value of taxes, let’s

consider our gold firm. Generally, firm pay taxes only if their income exceeds some level. To reflect

this, let’s assume that the gold firm pays taxes at the rate of 50% if its cash flow exceeds $300M and

does not pay taxes if its cash flow is below $300M. For simplicity, we assume it is an all-equity firm,

so that there are no bankruptcy costs. Figure 3.5. graphs the after-tax cash flow of the firm as a

function of the pretax cash flow. Note that now there is a difference between the firm’s operating

cash flow and what its shareholders receive which is due to taxes. To simplify further, we assume that

there is a 50% chance the gold price will be $250 per ounce and a 50% chance it will be $450. With

Chapter 3, page 13

this, the expected gold price is $350. Assuming that gold price risk is unsystematic risk, the forward

price for gold is $350. As before, the interest rate is 5%. In the absence of taxes, therefore, the value

of the gold mining firm is the present value of the expected cash flow, $350M discounted at 5%, or

$333.33M. Now, with taxes, the present value of the firm for its shareholders is lower since the firm

pays taxes when the gold price is $450. In this case, the firm pays taxes of 0.5*(450-300)*1M, or

$75M. With taxes, the value of the firm’s equity is:

Value of firm with taxes = PV(Gold sales - Taxes)

= PV(Gold sales) - PV(Taxes)

= PV(Firm without taxes) - PV(Taxes)

= $333.33m - $35.71M

= $297.62M.

Let’s figure out the cost to shareholders of having the firm bear gold price risk. To do that,

we have to compare firm value if the gold price is random with firm value if the gold price has no

volatility and is fixed at its expected value. Remember that the gold price can be either $250 or $450.

If the gold price is $250, the shareholders get $250 per ounce. Alternatively, if the gold price is $450,

they get $375 per ounce ($450 minus taxes at the rate of 50% on $150). The expected cash flow to

the shareholders is therefore 0.5*250 + 0.5*375 or $312.5 per ounce, which is $12.50 less than $325.

In this case, expected taxes are $37.5 per ounce. If the gold price is fixed at its expected value instead

so that cash flow is not volatile, shareholders receive $325 per ounce since they must pay taxes at the

rate of 50% on $50. In this case, expected taxes are $25 per ounce. Taking present values, the equity

Chapter 3, page 14

value is $309.52 per ounce in the absence of cash flow volatility and $297.62 if cash flow is volatile.

Hence, the cost to the shareholders of having the firm bear the gold price risk is $11.90 per ounce

or $11.90M for the firm as a whole.

Let’s look at the cost of having the capital markets bear the gold price risk. If gold price risk

is unsystematic risk, there is no risk premium. The capital markets charge a cost for bearing gold price

risk with our assumptions only if taxes affect the pricing of risky assets. Tax status differs across

investors. For instance, some investors pay no taxes because they are institutional investors; other

investors pay taxes as individuals in the top tax bracket. Let’s suppose that capital markets are

dominated by investors who pay no taxes and that therefore securities are priced ignoring taxes. In

this case, the CAPM applies to pretax returns and the cost of bearing gold price risk for the capital

markets is zero. Hence, the capital markets have a comparative advantage in bearing gold price risk.

If the firm has the capital markets bear gold price risk, it sells gold forward and gets $350m.

Shareholders get less because the firm has to pay taxes. They get $325m or $309.52m in present

value. This is the value of the firm if gold is not random. Hence, capital markets charge nothing for

bearing the risk, but if the firm bears the risk itself, the cost to the firm is $11.90m.

The reason the firm saves taxes through risk management is straightforward. If the firm’s

income is low, the firm pays no taxes. In contrast, if the firm’s income is high, it pays taxes. Shifting

a dollar from when the income is high to when the income is low saves the taxes that would be paid

on that dollar when the income is high. In our example, shifting income of a dollar from when income

is high to when income is low saves $0.50 with probability 0.5.

It should be clear why homemade risk management cannot work in this case. If the firm does

not use risk management to eliminate its cash flow volatility, its expected taxes are higher by $12.5M.

Chapter 3, page 15

This is money that leaves the firm and does not accrue to shareholders. If the firm does not hedge,

shareholders can eliminate the risk from holding the shares. However, through homemade risk

management, shareholders can only guarantee an expected payoff of $312.5M. Let’s figure out how

shareholders would practice homemade risk management. Note that there are only two possible

outcomes: $375 per share or $250 per share with equal probability. Hence, shareholders must take

a forward position per ounce that insures a payoff of $312.5. Let h be the short forward position per

ounce. We then need:

Gold price is $250: $250 - h(350 - 250) = 312.5

Gold price is $450: $375 - h(350 - 450) = 312.5

Solving for h, we get h to be equal to 0.6125. Hence, the investor must sell short 0.6125 ounces to

insure receipt of $312.5 per ounce at the end of the year. If the gold price is $250 an ounce, the

shareholders get $250 per share from the firm and 0.6125*(350 - 250), or $75, from the forward

position. This amounts to $325. The investor is unambiguously better off if the firm hedges directly.

The marginal investor is the one that would not invest in an asset if its expected return was

slightly less. If gold price risk is diversifiable for this investor, this means that the investor does not

expect to make a profit from taking gold price risk net of taxes. So far, we assumed that the marginal

investor pays no taxes. Suppose that, instead, the marginal investor has a positive tax rate. It turns

out that making this different assumption does not change our analysis as long as the marginal

investor’s tax rate is not too different when the gold price is high and when it is low. Since gold price

risk is diversifiable, one would not expect an unexpectedly high or low gold price to change the

Chapter 3, page 16

marginal investor’s tax bracket. Let’s see that this works. Suppose that the tax rate of the marginal

investor is 40% and that this tax rate is the same for the high and the low gold price. Remember that,

since the gold price risk is unsystematic risk for the marginal investor, the investor’s after-tax

expected profit from a forward contract should be zero. In this case, if the investor takes a long

forward position, she expects to receive after tax:

0.5*(1-0.4)*(450 - F) + 0.5*(1-0.4)*(250 - F) = 0

The forward price that makes the expected payoff of a long forward position equal to zero is $350

in this case. Hence, the tax rate does not affect the forward price. This means that when the marginal

investor has a constant positive tax rate, the capital markets still charge nothing to bear unsystematic

gold price risk.

Section 3.2.1. The tax argument for risk management.

The tax argument for risk management is straightforward: By taking a dollar away from a

possible outcome (often called a state of the world in finance) in which it incurs a high tax rate and

shifting it to a possible outcome where it incurs a low tax rate, the taxpayer - a firm or an investor -

reduce the present value of taxes to be paid. The tax rationale for risk management is one that is

extremely broad-based: it applies whenever income is taxed differently at different levels. The tax

code introduces complications in the analysis. Some of these complications decrease the value of

hedging, whereas others increase it. Here are some of these complications:

1. Carry-backs and carry-forwards. If a firm has negative taxable income, it can offset

Chapter 3, page 17

future or past taxable income with a loss this tax year. There are limitations to the ability to carry

losses back or forward. One set of limitations is that losses can be carried back or forward only for

a limited number of years. In addition, no allowance is made for the time-value of money. To see the

importance of the time-value of money, consider a firm which makes a gain of $100,000 this year and

a loss of $100,000 in three years. It has no other income. The tax rate is 30%. Three years from now,

the firm can offset the $100,000 gain of this year with the loss. However, it must pay $30,000 in taxes

this year and only gets back $30,000 in three years, so that it loses the use of the money for three

years.

2. Tax shields. Firms have a wide variety of tax shields. One of these tax shields is the tax

shield on interest paid. Another is the tax shield on depreciation. Firms also have tax credits. As a

result of the complexity of the tax code, the marginal tax rate of firms can be quite variable. Further,

tax laws change so that at various times firms and investors know that taxes will increase or fall. In

such cases, the optimal risk management program is one that increases cash flows when taxes are low

and decreases them when they are high.

3. Personal taxes. In our discussion, we assumed that the tax rate of the marginal investor

on capital markets is uncorrelated with firm cash flow. Even if this is not the case, a general result

holds: As long as the tax rate of investors differs from the tax rate of the corporation, it pays for the

corporation to reallocate cash flow from possible outcomes where the combined tax rate of investors

and the corporation is high to other possible outcomes where it is low.

It is difficult to incorporate all these real life complications in an analytical model to evaluate the

importance of the tax benefits of risk management. To cope with this problem, Graham and Smith

Chapter 3, page 18

(1999) use a simulation approach instead. Their paper does not take into account personal taxes, but

otherwise it incorporates all the relevant features of the tax code. They simulate a firm’s income and

then evaluate the tax benefit of hedging. They find that for about half the firms, there is a tax benefit

from hedging, and for these firms the typical benefit is such that a 1% decrease in the volatility of

taxable income for a given year decreases the present value of taxes by 1%.

Section 3.2.2. The tax benefits of risk management and Homestake

In 1990, Homestake paid taxes of $5.827 million dollars. It made a loss on continuing

operations because it wrote down its investment in North American Metals Corporation. Taxation

in extracting industries is noticeably complicated and hence makes it difficult to understand the extent

to which Homestake could reduce the present value of its taxes with risk management. However, the

annual report is useful in showing why the tax rate of Homestake differs from the statutory tax rate

of 34%. In thousand dollars, the taxes of Homestake differ from the statutory tax as follows:

Homestake made a loss of 13,500. 34% of that loss would yield taxes of (4,600)

Depletion allowance (8,398)

State income taxes, net of Federal benefit (224)

Nondeductible foreign losses 18,191

Other-net 858

Total $ 5,827

It is striking that Homestake paid taxes even though it lost money. The exact details of the

nondeductible foreign losses are not available from the annual report. It seems, however, that part

Chapter 3, page 19

of the problem is due to a non-recurring write-down which may well have been unpredictable.

Although risk management to smooth taxes is valuable, it is unlikely that Homestake could have

devised a risk management program that would have offset this write-down with foreign taxable

gains. At the same time, variations in the price of gold could easily lead to a situation where

Homestake would make losses. Avoiding these losses would smooth out taxes over time and hence

would increase firm value. Based on the information in the annual report, we cannot quantify this

benefit. Petersen and Thiagarajan (1998) compare American Barrick and Homestake in great detail.

In their paper, they find that Homestake has a tendency to time the recognition of expenses when gold

prices are high to smooth income, which may decrease the value of using derivatives to smooth

income.

Section 3.3. Optimal capital structure, risk management, bankruptcy costs and taxes.

Generally, interest paid is deductible from income. A levered firm therefore pays less in taxes

than an unlevered firm for the same operating cash flow. This tax benefit of debt increases the value

of the levered firm relative to the value of the unlevered firm. If a firm’s pretax income is random,

however, there will be circumstances where it cannot take full advantage of the tax benefit of debt

because its operating cash flow is too low. Hence, decreasing the volatility of cash flow can increase

firm value by making it less likely that the operating cash flow is too low to enable the firm to take

advantage of the tax shield of debt.

Let’s consider the impact on the tax shield from debt of a risk management program that

eliminates cash flow volatility. We use the same example as we did in the previous section, in that the

firm pays taxes if its cash flow exceeds $300M. However, now the firm issues debt and pays out the

Chapter 3, page 20

proceeds of debt to the shareholders. Suppose that the shareholders decide to issue debt with face

value of $200M. Since the risk of the firm is diversifiable, the debtholders expect to receive a return

of 5%. Since the firm is never bankrupt with an interest rate of 5%, the debt interest payment will be

5% of $200M, or $10M. At the end of the year, the firm has to make a debt payment of $210M. If

the firm’s cash flow at the end of the year is $250M because the gold price is $250 an ounce, the firm

pays no taxes. Hence, it does not get a tax benefit from having to pay $10M in interest. In contrast,

if the firm’s cash flow is $450M, the firm gets to offset $10M against taxable income of $150M and

hence pays taxes only on $140M. This means that the value of the firm is:

Value of levered firm = PV(Cash flow - taxes paid)

= PV(Cash flow) - PV(Taxes paid)

= 333.33M - 0.5*0.5*(450M - 300M - 10M)/1.05

= 333.33M - 33.33M

= 300M

The value of the firm is higher than in the previous section because the firm benefits from a tax shield

of $10m if the gold price is $450 per ounce. The expected value of that tax shield is 0.5*0.5*10M,

or $2.50M. The present value of that amount is $2.38M using the risk-free rate of 5% as the discount

rate since gold price risk is unsystematic risk. In the previous section, the value of the firm in the

absence of risk management was $297.62M, which is exactly $2.38M less than it is now. The

difference between $300M and $297.62M represents the benefit of the tax shield of debt. However,

when the cash flow is risky, the firm gets the benefit only when the price of gold is $450 an ounce.

1If the funds were kept within the firm, they would have to be invested which wouldcomplicate the analysis because taxes would have to be paid on the investment income.

Chapter 3, page 21

Consider the situation where the firm eliminates the volatility of cash flow. We know that in

this case the firm insures a cash flow pre-tax of $350M. Its taxable income with debt is $350M -

$10M - $300M, or $40M, so that it pays taxes of $20M for sure. Firm value is therefore the present

value of $350M - $20M, or $314.286M. In the absence of debt, hedged firm value is instead

$309.524M. Shareholders therefore gain $4.762M by issuing debt and hedging. The benefit from

hedging in this example comes solely from the increase in the tax shield of debt. Since the firm issues

risk-free debt, the interest rate on the debt does not depend on whether the firm hedges or not in our

example.

In our analysis so far, we took the firm’s debt as given. With a promised payment to

debtholders of $210M, the firm is never bankrupt yet benefits from the tax shield of debt. Let’s now

extend the analysis so that the tax shield of debt is maximized. If this involves increasing the firm’s

debt, we assume that the funds raised are paid out to shareholders in the form of a dividend so that

the firm’s investment policy is unaffected.1 Let’s start with the case where the firm eliminates gold

price risk and can guarantee to the debtholders that it will do so. Since in that case the firm has no

risk, it either never defaults or always defaults. One would expect the IRS to disallow a deduction

for debt that always defaults, so that the total debt and tax payments cannot exceed $350M for the

firm to benefit from a tax shield of debt. Since the firm never defaults with hedging, it can sell the new

debt so that it earns the risk-free rate of 5% since it is risk-free. To maximize firm value, we maximize

the expected cash flow minus taxes paid:

Chapter 3, page 22

Firm cash flow = 350M - 0.5Max(50M - 0.05F,0)

where F is the amount borrowed. Since the firm has no volatility, it is never bankrupt. Figure 3.6.

plots firm value imposing the constraint that total debt and tax payments cannot exceed $350M. Since

the tax shield increases with debt payments, the firm wants to issue as much debt as it can without

being bankrupt. This means that taxes plus debt payments have to equal $350M. Solving for F, we

get $317.073M. To see that this works, note that the firm has to pay taxes on 50M - 10M -

0.05*117.073M, corresponding to taxes of $17.073M. The debt payments amount to $210M plus

1.05*$117.073, or $332.927M. The sum of debt payments and taxes is therefore exactly $350M. The

shareholders get nothing at maturity, so that the firm is an all-debt firm after the additional debt issue

(one could always have the shareholders hold a small amount of equity so that the firm is not an all-

debt firm). They benefit from the increase in leverage because they receive a dividend worth

$317.073M when the debt is issued. If the firm issues only debt with principal of $200M, the

shareholders own a firm worth $314.286M in the form of a dividend of $200M and shares worth

$114.286. Hence, by issuing more debt, shareholders increased their wealth by a further $2.787M.

To check that the shareholders have chosen the right amount of debt, let’s see what happens

if they issue an additional $1M of debt that they pay out as a dividend. This would lead to an

additional debt payment of $1.05M. Taxes would fall by $0.025M because of the addition $0.05M

of interest payment, so that the firm would have to pay net an additional $1.025M. As a result of this

additional promised payment, the firm would always bankrupt. Suppose next that the firm issues $1M

less of debt. In this case, the dividend falls by $1M and the firm has $1.05M less of debt payments

at the end of the year. This has the effect of increasing taxes by $0.025M, so that shareholders get

0 5 230 0 5 1. * . ( )+ +=

x F

1.05F

450 - 0.5(150 - xF) - (1 + x)F = 0

2 Let x be the promised interest rate on debt and F be the amount borrowed in millions. Tosolve for x and F, we have to solve two equations:

The first equation states that the present value of the debt payoffs has to be equal to the principal.The second equation states that the cash flow if the gold price is $450 an ounce has to be equal tothe debt payment and taxes.

Chapter 3, page 23

$1.025M at the end of the year. The present value of $1.025M is less than $1M, so that shareholder

equity falls as a results of decreasing debt.

Suppose now that the firm wants to maximize its value without using risk management. In this

case, if the optimum amount of debt is such that the debt payment exceeds $250M, the firm is

bankrupt with probability 0.5. Since, in this case, increasing the principal amount of debt further does

not affect bankruptcy costs, the firm’s best strategy would be to issue a sufficient amount of debt so

that it minimizes taxes paid when the gold price is $450 an ounce since it pays no taxes when the gold

price is $250 an ounce. Consequently, the firm chooses debt so that the debt payment plus taxes paid

are equal to the before-tax cash flow of $450M. If the firm does that, it will be bankrupt if the gold

price is $250 an ounce. If bankruptcy takes place, the firm incurs a bankruptcy cost which we assume

to be $20M as before so that bondholders get $230M in that case. Since the firm defaults when the

gold price is $250 an ounce, the yield of the debt has to exceed the risk-free rate so that the expected

return of the bondholders is the risk-free rate. The bondholders require an expected return equal to

the risk-free rate because we assumed that gold price risk is nonsystematic risk. Solving for the

promised interest rate and the amount borrowed, we find that the firm borrows a total amount of

316.29M promising to pay interest at the rate of 37.25%.2 The value of the firm to its shareholders

Chapter 3, page 24

corresponds to the amount borrowed of 316.29M, so that the value of the firm is lower in the absence

of risk management.

The difference between firm value with risk management and firm value without risk

management depends crucially on the bankruptcy cost. As the bankruptcy cost increases, the risk

management solution becomes more advantageous. If the bankruptcy cost is $100M, the value of the

firm without risk management falls to $290.323. In this case, the firm has a higher value with no debt.

If there is no bankruptcy cost, the solution that involves no risk management has higher value than

the solution with risk management because it eliminates more taxes when the firm is profitable. In this

case, firm value is $322.581M. The problem with the solution without risk management is that it may

well not be possible to implement it: It involves the firm going bankrupt half the time in this example,

so that the IRS would probably disallow the deduction of the interest payment from taxable income,

viewing the debt as disguised equity.

It is important to note that if the firm engages in risk management but debtholders do not

believe that it will do so, then the debt is sold at a price that reflects the absence of risk management.

In this case, the yield on debt where there is a probability of default is higher to reflect the losses

bondholders make if the firm defaults. If shareholders are paying the bondholders for the risk of

bankruptcy, it may not make sense to remove that risk through risk management because doing so

might benefit mostly bondholders. If the firm issues debt so that there is no significant risk of

bankruptcy, it matters little whether bondholders believe that the firm will hedge or not. However,

many firms could increase their leverage without significantly affecting their probability of

bankruptcy. For such firms, risk management would be valuable because it implies that firms capture

Chapter 3, page 25

more of the tax shield of debt.

In the example discussed here, firm value depends on leverage because of the existence of

corporate taxes. If there is a tax shield of debt, more leverage decreases taxes to be paid. However,

with bankruptcy costs, there is an offsetting effect to the tax benefit of debt. As leverage increases,

it becomes more likely that the firm will be bankrupt and hence that bankruptcy costs will have to be

paid. This reasoning leads to an optimal capital structure for a firm. Without bankruptcy costs but a

tax shield of debt, the optimal capital structure would be for the firm to be all debt since this would

maximize the tax shield of debt. With bankruptcy costs but without a tax shield of debt, the firm

would not want any debt since there is no benefit to debt but only a cost. With bankruptcy costs and

with a tax shield of debt, the firm chooses its capital structure so that the tax benefit of an additional

dollar of debt equals the increase in bankruptcy costs. When bankruptcy costs are nontrivial, the firm

finds it worthwhile to decrease risk through risk management so that it can increase leverage. In

general, the firm cannot eliminate all risk through risk management so that there is still some

possibility of bankruptcy. As a result, the optimal solution is generally far from having only debt.

Further, as we will see later, there are other reasons for firms not to have too much debt.

All our tax discussion has taken place assuming a very simple tax code. One complication we

have ignored is that investors pay taxes too. Miller (1978) has emphasized that this complication can

change the analysis. Suppose investors pay taxes on coupon income but not on capital gains. In this

case, the required expected return on debt will be higher than on equity to account for the fact that

debt is taxed more highly than equity at the investor level. In this case, the tax benefit at the

corporation level of debt could be decreased because of the higher yield of debt. At this point,

though, the consensus among financial economists is that personal taxes limit the corporate benefits

Chapter 3, page 26

from debt but do not eliminate them. In any case, if the firm has tax shields, whether there are

personal taxes or not, the corporation will want to maximize their value.

Section 3.3.1. Does Homestake have too little debt?

The answer to this question is undoubtedly yes. Homestake is paying taxes every year. Most

years, its tax rate is close to the statutory rate of 34%. In 1990, as we saw, Homestake pays taxes at

a rate that even exceeds the statutory rate. Yet, we also saw that Homestake has almost no debt and

that its long-term debt is dwarfed by its cash balances. By increasing its debt, Homestake would

increase its tax shield of debt and reduce its taxes. Doing so, however, it would increase the

importance of risk management to avoid wasting the tax shield of debt when the price of gold moves

unfavorably.

Section 3.4. Poorly diversified stakeholders.

So far, we assumed that risk management involves no transaction costs. Suppose, however,

that homemade risk management is more expensive than risk management by the firm. In this case,

investors might care about the risks that the firm bears. However, investors who own large diversified

portfolios are relatively unaffected by the choices of an individual firm. On average, the risks balance

out except for systematic risks that have to be born by the economy as a whole and can easily be

controlled by an investor through her asset allocation. There are, however, investors for whom these

risks do not balance out because they have a large position in a firm relative to their wealth. These

investors might be large investors who value a control position. They might also be management who

has a large stake in the firm for control reasons or because of a compensation plan. Investors who

Chapter 3, page 27

cannot diversify away firm-specific risk want the firm to decrease it unless they can reduce risk more

cheaply through homemade risk management.

Consider the case of our gold producing firm. Now, this firm has one big shareholder whose

only investment is her holding of 10% of the shares of the firm. The shareholder is not diversified and

consequently cares about the diversifiable risk of the gold mining firm. Unless she strongly expects

the price of gold to be high at the end of the year, she wants to reduce the risk of her investment. To

do that, she could sell her stake and invest in a diversified portfolio and the risk-free asset. Second,

she could keep her stake but use homemade hedging. Third, she could try to convince the firm to

hedge.

Let’s assume that the investor wants to keep her stake intact. There are circumstances such

that the investor might prefer the firm to hedge instead of having to do it herself. This will be the case

when there are large setup costs for trading in financial instruments used to hedge and the firm has

already paid these costs. For instance, suppose that a banking relationship is required to set up the

appropriate hedge. The firm has such a relationship and the investor does not. In such a situation, the

investor would want the firm to hedge because homemade hedging is not possible. It is therefore

possible for the firm to have a comparative advantage in hedging. It is not clear, though, why the firm

would expend resources to hedge to please that large investor. If the only benefit of hedging is that

this large investor does not have to hedge on her own, the firm uses resources to hedge without

increasing firm value. If the large shareholder cannot hedge and sells her shares, she is likely to be

replaced by well-diversified shareholders who would not want the firm to pay to hedge and thereby

decrease its value. There is no clear benefit for the firm from having the large shareholder in our

example. If the firm gains from having the large shareholder, then it can make sense to hedge to make

Chapter 3, page 28

it possible for the large shareholder to keep her investment in the firm.

Having large shareholders can increase firm value. Small, highly diversified, shareholders have

little reason to pay much attention to what the firm is doing. Such shareholders hold the market

portfolio and cannot acquire easily information that allows them to beat the market. Evaluating the

actions of management takes time. Suppose that by spending one month of her time a shareholder has

a 10% chance of finding a way to increase the value of a firm by 5% and that, if this happens,

spending a month to convince management has a 20% chance of success. With these odds, a

shareholder whose time is worth $10,000 a month would need an investment in the firm of at least

$500,000 to justify starting the process of studying the firm. One might argue about the odds we give

the shareholder of finding something useful and of convincing management that she did. Most likely,

however, the true odds are much worse for the shareholder. Further, most diversified shareholders

have a smaller stake in a firm than $500,000. Hence, most diversified shareholders get no benefit

from evaluating carefully the actions of managers. A shareholder who has a stake of $10M in a firm

will follow the actions of management carefully even if the odds against her finding something that

would increase the value of the firm are worse than we assumed. The action of evaluating

management and trying to improve what it does is called monitoring management. Large

shareholders get greater financial benefits from monitoring management than small ones.

There are two reasons why monitoring by shareholders can increase firm value. First, an

investor might become a large shareholder because she has some ability in evaluating the actions of

management in a particular firm. Such an investor has knowledge and skills that are valuable to the

firm. If management chooses to maximize firm value, management welcomes such an investor and

listens to her carefully. Second, management does not necessarily maximize firm value. Managers

Chapter 3, page 29

maximize their welfare like all economic agents. Doing so sometimes involves maximizing firm value,

but other times it does not. What a manager does depends on his incentives. A manager whose only

income is a fixed salary from the firm wants to make sure that the firm can pay his salary. If an action

increases firm value but has much risk, that manager may decide against it because a firm that is

bankrupt cannot pay his salary. A large shareholder can make it more likely that management

maximizes firm value by monitoring management. For instance, a large shareholder might find that

management failed to take an action that maximizes firm value and might draw the attention of other

shareholders to her discovery. In some cases, a large shareholder might even convince another firm

to try to make a takeover attempt to remove management and take actions that maximize firm value.

A firm’s risk generally makes it unattractive for a shareholder to have a stake large enough that it is

worthwhile for him to monitor a firm. By hedging, a firm can make it more attractive for a

shareholder that has some advantage in monitoring management to take a large stake. As the large

shareholder takes such a stake, all other shareholders benefit from his monitoring.

Section 3.4.1. Risk and the incentives of managers.

Since managers, like all other individuals associated with the firm, pursue their own interests,

it is important for shareholders to find ways to insure that managers’ interests are to maximize the

value of the shares. One device at the disposal of shareholders for this purpose is the managerial

compensation contract. By choosing a managerial contract which gives managers a stake in how well

the firm does, shareholders help insure that managers are made better off by making shareholders

richer. If managers earn more when the firm does better, this induces them to work harder since they

benefit more directly from their work. However, managerial compensation related to the stock price

Chapter 3, page 30

has adverse implications for managers also. It forces them to bear risks that have nothing to do with

their performance. For instance, a firm may have large stocks of raw materials that are required for

production. In the absence of a risk management program, the value of these raw materials fluctuates

over time. Random changes in the value of raw materials may be the main contributors to the

volatility of a firm’s stock price, yet management has no impact on the price of raw materials. Making

managerial compensation depend strongly on the stock price in this case forces management to bear

risks, but provides no incentive effects and does not align management’s incentives with those of

shareholders. In fact, making managerial compensation depend strongly on the part of the stock

return which is not under control of management could be counterproductive. For instance, if the

value of raw materials in stock strongly affects the riskiness of managerial compensation, managers

might be tempted to have too little raw materials in stock.

If it is easy to know how variables that managers do not control affect firm value, then it

would be possible to have a management compensation contract that depends only on the part of the

stock return that is directly affected by managerial effort. Generally, however, it will be difficult for

outsiders to find out exactly which variables affect firm value. Hence, in general it will make sense

to tie managerial compensation to some measure of value created without trying to figure out what

was and what was not under management’s control. Management knows what is under its control.

It could reduce risk through homemade hedging, but it might be more cost effective to have the firm

hedge rather than having managers trying to do it on their own. If the firm can reduce its risk through

hedging, firm value depends on variables that management controls, so that having compensation

closely related to firm value does not force management to bear too much risk and does not induce

management to take decisions that are not in the interest of shareholders to eliminate this risk. This

Chapter 3, page 31

makes it possible to have managerial compensation closely tied to firm value, which means that when

managers work hard to increase their compensation, they also work hard to increase shareholder

wealth.

Having management own shares in the firm they manage ties their welfare more closely to the

welfare of the shareholders. Again, if management owns shares, they bear risk. Since managers are

not diversified shareholders, they care about the firm’s total risk. This may lead them to be

conservative in their actions. If the firm reduces risk through risk management, the total risk of the

firm falls. Consequently, managers become more willing to take risks. This means that firm-wide

hedging makes managerial stock ownership a more effective device to induce management to

maximize firm value.

Another argument can be made to let management implement a risk management program

within the firm. Suppose that instead of having compensation depend directly on firm value, it

depends on firm value indirectly in the sense that management’s employment opportunities depend

on the performance of the firm ‘s stock. In this case, in the absence of firm-made risk management,

firm value fluctuates for reasons unrelated to managerial performance. As a result, the market’s

perception of managers can fall even when managers perform well. This is a risk that managers cannot

diversify. Having a risk management program eliminates sources of fluctuation of the firm’s market

value that are due to forces that are not under control of management. This reduces the risk attached

to management’s human capital. Again, management is willing to have a lower expected

compensation if the risk attached to its human capital is lower. Hence, allowing management to have

a risk management program has a benefit in the form of expected compensation saved which increases

firm value. Possibly the greater benefit from allowing management to have a risk management

Chapter 3, page 32

program is that this makes it less likely that management undertakes risk reducing activities that

decrease firm value but also decrease the risks that management bears.

Not every form of compensation that depends on firm value induces management to try to

reduce firm risk. Suppose that management receives a large payment if firm value exceeds some

threshold. For instance, in our gold producing firm, suppose that management receives a $20m bonus

if firm value before management compensation exceeds $400m at the end of the year. In this case,

management receives no bonus if the firm hedges and has a 50% chance of getting a bonus if the firm

does not hedge. Obviously, management will not hedge. Management compensation contracts of this

types make management’s compensation a nonlinear function of firm value. If management owns call

options on the firm’s stock, it has incentives to take risks. Call options pay off only when the stock

price exceeds the exercise price. They pay more for large gains in the stock price. An option pays

nothing if the stock price is below the exercise price, no matter how low the stock price is. Hence,

managerial compensation in the form of options encourages management to take risks so that the

stock price increases sufficiently for the options to have value. In fact, management’s incentives might

be to take more risk than is required to maximize firm value.

To see how options might induce management to not hedge when hedging would maximize

firm value, let’s consider our gold firm example. Suppose that management owns a call option on

1,000 shares with exercise price of $350 a share. For simplicity, let’s assume that management

received these options in the past and that exercise of the options does not affect firm value. In our

gold firm example, suppose that there is a tax advantage to hedging as discussed in section 2. In this

case, firm value before managerial compensation is maximized if the firm hedges. Hedging locks in

a firm value before managerial compensation of $309.52. In this case, the options management has

Chapter 3, page 33

are worthless. If the firm does not hedge, there is a 50% chance that the shares will be worth $375

and hence a 50% chance that the options will pay off.

Section 3.4.2. Managerial incentives and Homestake.

The Homestake proxy statement for 1990 shows that the directors own 1.1% of the shares.

As mentioned earlier, two of the directors are executives of a company which owns 8.2% of

Homestake. The CEO of Homestake, Mr. Harry Conger, owns 137,004 shares directly and has the

right to acquire 243,542 shares through an option plan. The shares in the option plan have an average

exercise price of $14.43, but the share price in 1990 has a high of 23.6 and a low of 15.3.

Management holds few shares directly and much less than is typical for a firm of that size. Most of

management’s ownership is in the form of options. There is not much incentive for management to

protect its stake in the firm through hedging and management might benefit some from volatility

through its option holdings.

Section 3.4.3. Stakeholders.

So far in this section, we have considered individuals - large shareholders and managers - for

whom it was costly to be exposed to firm risk. We saw that the firm could benefit by reducing the

firm risk that these individuals are exposed to. The reason these individuals were exposed to firm risk

was that they could not diversify this risk away in their portfolio or use homemade hedging

effectively. There are other individuals associated with corporations that are in a similar situation. All

individuals or firms whose welfare depends on how well the firm is doing and who cannot diversify

the impact of firm risks on their welfare are in that situation. Such individuals and firms are often

Chapter 3, page 34

called stakeholders. It can be advantageous for a firm to reduce the risks that its stakeholders bear.

Often, it is important for the firm to have its stakeholders make long-term firm-specific investments.

For instance, the firm might want workers to learn skills that are worthless outside the firm. Another

example might be a situation where a firm wants a supplier to devote R&D to design parts that only

that firm will use. A final example is one where customers have to buy a product whose value

depends strongly on a warranty issued by the firm. In all these cases, the stakeholders will be reluctant

to make the investments if they doubt that the firm will be financially healthy. If the firm gets in

financial trouble, it may not be able to live up to its part of the bargain with the stakeholders. This

bargain is that the stakeholders invest in exchange for benefits from the firm over the long-term.

Hedging makes it easier for the firm to honor its bargain with the stakeholders.

If the firm does not reduce its risk, it may only be able to get the stakeholders to make the

requisite investments by bribing them to do so. This would mean paying workers more so that they

will learn the requisite skills, paying the suppliers directly to invest in R&D, and selling the products

more cheaply to compensate for the risks associated with the warranty. Such economic incentives can

be extremely costly. If hedging has low costs, it obviously makes more economic sense for the firm

to hedge rather than to use monetary incentives with its stakeholders.

Section 3.4.4. Are stakeholders important for Homestake?

No. The firm is financially healthy so that there is no risk of bankruptcy. The firm could suffer

large losses before bankruptcy would become an issue. Hence, those having relationships with the

firm have no good reason to worry about getting paid.

Homestake has one large shareholder, Case, Pomeroy and Co. This company owns 8.1% of

Chapter 3, page 35

the shares. Two executives of that company are represented on the board of directors. Case has been

decreasing its stake in Homestake and has a standstill agreement with Homestake that prevents it

from buying more shares and gives Homestake rights of first refusal when Case sells shares. This

large shareholder can hedge on its own if it chooses to do so.

Section 3.5. Risk management, financial distress and investment.

So far, we have paid little attention to the fact that firms have opportunities to invest in

valuable projects. For instance, suppose that the gold firm we focused on does not liquidate next

period but instead keeps producing gold. Now, this firm has an opportunity to open a new mine a

year from now. This mine will be profitable, but to open it a large investment has to be made. If the

firm does not have sufficient internal resources, it has to borrow or sell equity to finance the opening

of the mine. There are circumstances where a firm’s lack of internal resources makes it impossible

for the firm to take advantage of projects that it would invest in if it had more internal resources

because the costs of external financing are too high. In other words, it could be that the gold mining

firm in our example might not be able to open the mine because of a lack of internal resources. In this

case, the shareholders would lose the profits that would have accrued to them if the mine had been

opened. Firm value would have been higher had the firm managed its affairs so that it would not have

gotten itself into a situation where it cannot invest in profitable projects. In the remainder of this

section, we investigate the main reasons why firms might not be able to invest in profitable projects

and show how risk management can help firms avoid such situations.

Chapter 3, page 36

Section 3.5.1. Debt overhang.

Consider a firm with debt obligations that are sufficiently high that if the firm had to pay off

the debt today it could not do so and normal growth will not allow it to do so when the debt matures.

Such a situation creates a conflict between the firm’s creditors and the firm’s shareholders.

Shareholders want to maximize the value of their shares, but doing so can be inconsistent with

maximizing firm value and can reduce the value of the firm’s debt. First, shareholders may want to

take risks that are not beneficial to the firm as a whole. Second, they may be unwilling to raise funds

to invest in valuable projects. We look at these problems in turn.

We assumed that the firm cannot pay off its debt today. If the firm does not receive good

news, when the debt has to be paid off, shareholders will receive nothing and the creditors will own

the firm. Consequently, shareholders want to make it more likely that the firm will receive good news.

To see the difficulty this creates, consider the extreme case where the firm has no risk with its current

investment policies. In this case, unless shareholders do something, their equity is worthless. Suppose

however that they liquidate existing investments and go to Las Vegas with the cash they have

generated. They bet the firm at a game of chance. If they lose, the cash is gone. The loss is the

creditors’ loss since equityholders were not going to get anything anyway. If they win, the firm can

pay off the creditors and something is left for the equityholders. This strategy has a positive expected

profit for the shareholders so they want to undertake it - if they can. In contrast, this strategy has a

negative expected profit for the firm. This is because betting in Las Vegas is not a fair gamble - the

house has to make money on average. Excess leverage resulting from adverse shocks to firm value

therefore leads shareholders to do things that hurt firm value but help them. The possibility that there

is some chance that the firm might be in such a situation therefore reduces its value today. If low cost

Chapter 3, page 37

risk management can decrease the probability that the firm might ever find itself in such a situation,

it necessarily increases firm value. Unfortunately, if the firm reduces risk through risk management

but nevertheless finds itself in a situation where shareholders believe that gambling would benefit

them, they may choose to give up on risk management. Since they would give up on risk management

precisely when bondholders would value it the most -- because any loss is a loss for the bondholders

-- this possibility can make it harder to convince bondholders that the firm will consistently reduce

risk.

Consider again a firm with large amounts of debt that it could not repay if it had to do so

today. In contrast to the previous paragraph, we now assume that the firm cannot sell its assets. This

could be because bond covenants prohibit it from doing so or because the market for the firm’s assets

is too illiquid. Now, suppose that this firm has an investment opportunity. By investing $10m., the

firm acquires a project that has a positive net present value of $5m. This project is small enough that

the firm still could not repay its debt if it took the project and had to repay the debt today. The firm

does not have the cash. The only way it can invest is by raising funds. In this situation, shareholders

may choose not to raise the funds.

In our scenario, the firm could raise funds in two ways: It could borrow or issue equity. Since

the firm cannot repay its existing debt in its current circumstances, it cannot raise debt. Any debt

raised would be junior to the existing debt and would not be repaid unless the value of the firm

increases unexpectedly. Consequently, the firm would have to sell equity. Consider the impact of

having an investor invest one dollar in a new share. Since the firm is expected to default, that dollar

will most likely end up in the pockets of the creditors. If something good happens to the firm so that

equity has value, there will be more shareholders and the existing shareholders will have to share the

Chapter 3, page 38

payoff to equity with the new shareholders. This is most likely a no-win situation for the existing

shareholders: They do not benefit from the new equity if the firm is in default but have to share with

the new equity if the firm is not in default. Hence, even though the project would increase firm value,

existing shareholders will not want the firm to take it because it will not benefit them. The only way

the firm would take the project is if shareholders can renegotiate with creditors so that they get more

of the payoff of the project. If such a renegotiation is possible, it is often difficult and costly.

Sometimes, however, no such renegotiation succeeds. When the firm is valued by the capital markets,

its value is discounted because of the probability that it might not take valuable projects because its

financial health might be poor. Hence, reducing this probability through risk management increases

firm value as long as risk management is cheap.

Both situations we discussed in this section arise because the firm has too much debt. Not

surprisingly, in such cases the firm is said to have a debt overhang. A debt overhang induces

shareholders to increase risk and to avoid investing in valuable projects. The probability that the firm

might end up having a debt overhang in the future reduces its value today. Consequently, risk

management that reduces this probability increases firm value today. The costs associated with a debt

overhang are costs of financial distress. As with the costs of financial distress, the present value of

these costs could be reduced by having less debt. We saw, however, that debt has value and that it

is generally not an optimal strategy for a firm to be an all-equity firm. As long as a firm has some debt

and some risk, there is some possibility that it might end up having a debt overhang.

Section 3.5.2. Information asymmetries and agency costs of managerial discretion.

Most of our analysis derives benefits from risk management that depend on the existence of

Chapter 3, page 39

debt. Without debt of some sort, there are no bankruptcy costs and no tax benefits of debt to protect.

Generally, one thinks of costs of financial distress as costs resulting from difficulties the firm has to

cope with its debt service. In section 3.4., we saw that the existence of valuable stakeholders could

lead a firm to want to reduce risk. That argument for risk management does not depend on the

existence of debt. Let’s consider here another situation where risk management creates value even

for a firm that has no debt. Firm value fluctuates randomly. Hence, sometimes it will fall

unexpectedly. The problem with a low firm value is that it limits the firm’s ability to invest. Firms with

limited net worth can sometimes raise extremely large amounts of money, but typically they cannot.

Hence, if such firms want to invest massively, they may have trouble to do so.

The key problem management faces when trying to raise funds is that it knows more about

the firm’s projects than the outsiders it is dealing with. A situation where one party to a deal knows

more than the other is called a situation with an information asymmetry. Suppose that the firm’s

net worth with its existing projects is $10M. Management knows that by investing $100M the firm

can double its net worth. All management has to do then is find investors who will put up $100M.

If you are such an investor, you have to figure out the distribution of the return on your investment

based on the information provided to you by management. Generally, management has much to gain

by investing in the project. For instance, management compensation and perquisites increase with firm

size. Small firms do not have planes for managers; large firms do. As a result, management will be

enthusiastic about the project. This may lead to biases in its assessment and a tendency to ignore

problems. Even if management is completely unbiased and reveals all of the information it has to

potential investors, the potential investors cannot easily assess that management is behaving this way.

Potential investors know that often, management has enough to gain from undertaking the project

Chapter 3, page 40

that it might want to do so even if the chance of success is low enough that the project is a negative

net present value project. The costs associated with management’s opportunity to undertake projects

that have a negative net present value when it is advantageous for it to do so are called the agency

costs of managerial discretion. In the absence of managerial discretion, management would not have

this opportunity. Managerial discretion has benefits - without it, management cannot manage. It has

costs also, however. With managerial discretion, management pursues its own objectives, which

creates agency costs - the agent’s interests, management, are not aligned with the interests of those

who hire management, the principals, namely the shareholders.

Agency costs of managerial discretion make it harder for the firm to raise funds and increase

the costs of funds. If outsiders are not sure that the project is as likely to pay off as management

claims, they require a higher expected compensation for providing the funds. Clearly, if management

was truthful about the project, having to pay a higher expected compensation reduces the profits from

the project. This higher expected compensation could lead to a situation where the project is not

profitable because the cost of capital for the firm is too high because of costs of managerial discretion.

The firm could use a number of approaches to try to reduce the costs of managerial discretion

and hence reduce the costs of the funds raised. For instance, it could entice a large shareholder to

come on board. This shareholder would see the company from the inside and would be better able

to assess whether the project is valuable. However, if the firm could have invested in the project in

normal times more easily but has a low value now because of adverse developments unrelated to the

value of the project, a risk management strategy might have succeeded in avoiding the low firm value

and hence might have enabled the firm to take the project. For instance, if the firm’s value is much

larger, it might be able to borrow against existing assets rather than having to try to borrow against

Chapter 3, page 41

the project.

A risk management strategy that avoids bad outcomes for firm value might help the firm to

finance the project for another reason. Investors who look at the evolution of firm value have to

figure out what a loss in firm value implies. There could be many possible explanations for a loss in

firm value. For instance, firm value could fall because its stock of raw materials fell in value, because

the economy is in a recession, because a plant burned down, or because management is incompetent.

In general, it will be difficult for outsiders to figure out exactly what is going on. They will therefore

always worry that the true explanation for the losses is that management lacks competence.

Obviously, the possibility that management is incompetent makes it more difficult for management

to raise funds if is competent but outsiders cannot be sure. By reducing risk through risk

management, the firm becomes less likely to be in a situation where outsiders doubt the ability of

management.

Section 3.5.3. The cost of external funding and Homestake.

Our analysis shows that external funding can be more expensive than predicted by the CAPM

because of agency costs and information asymmetries. Agency costs and information asymmetries

create a wedge between the costs of internal funds and the costs of external funds. This wedge can

sometimes be extremely large. The box on “Warren Buffet and Catastrophe Insurance” provides an

example where taking on diversifiable risk is extremely rewarding. For Homestake, however, this is

not an issue. It turns out that Homestake could repay all its debt with its cash reserves, so that debt

overhang is not an issue. The firm also has enough cash that it could finance large investments out

of internal resources.

Chapter 3, page 42

Section 3.6. Summary.

In this chapter, we have investigated four ways in which firms without risk management can

leave money on the table:

1. These firms bear more direct bankruptcy costs than they should.

2. These firms pay more taxes than they should.

3. These firms pay more to stakeholders than they should.

4. These firms sometimes are unable to invest in valuable projects.

In this chapter, we have identified benefits from risk management that can increase firm value. In the

next chapter, we move on to the question of whether and how these benefits can provide the basis

for the design of a risk management program.

Chapter 3, page 43

Key concepts

Bankruptcy costs, financial distress costs, tax shield of debt, optimal capital structure, stakeholders,

debt overhang, agency costs of managerial discretion, costs of external funding.

Chapter 3, page 44

Review questions

1. How does risk management affects the present value of bankruptcy costs?

2. Why do the tax benefits of risk management depend on the firm having a tax rate that depends on

cash flow?

3. How do carry-back and carry-forwards affect the tax benefits of risk management?

4. How does risk management affect the tax shield of debt?

5. Does risk management affect the optimal capital structure of a firm? Why?

6. When does it pay to reduce firm risk because a large shareholder wants the firm to do it?

7. How does the impact of risk management on managerial incentives depend on the nature of

management’s compensation contract?

8. Is risk management profitable for the shareholders of a firm that has a debt overhang?

9. How do costs of external funding affect the benefits of risk management?

Chapter 3, page 45

Literature note

Smith and Stulz (1985) provide an analysis of the determinants of hedging policies that covers the

issues of bankruptcy costs, costs of financial distress, stakeholders, and managerial compensation.

Stulz (1983) examines optimal hedging policies in a continuous-time model when management is risk-

averse. Diamond (1981) shows how hedging makes it possible for investors to evaluate managerial

performance more effectively. DeMarzo and Duffie (1991) and Breeden and Viswanathan (1998)

develop models where hedging is valuable because of information asymmetries between managers and

investors. Froot, Scharfstein and Stein (1993) construct a model that enables them to derive explicit

hedging policies when firms would have to invest suboptimally in the absence of hedging because of

difficulties in securing funds to finance investment. Stulz (1990,1996) discusses how hedging can

enable firms to have higher leverage. Stulz (1990) focuses on the agency costs of managerial

discretion. In that paper, hedging makes it less likely that the firm will not be able to invest in valuable

projects, so that the firm can support higher leverage. In that paper, debt is valuable because it

prevents managers from making bad investments. Tufano (1998) makes the point that reducing the

need of firms to go to the external market also enables managers to avoid the scrutiny of the capital

markets. This will be the case if greater hedging is not accompanied by greater leverage.

Bessembinder (1991) and Mayers and Smith (1987) also analyze how hedging can reduce the

underinvestment problem. Leland (1998) provides a continuous-time model where hedging increases

firm value because (a) it increases the tax benefits from debt and (b) it reduces the probability of

default and the probability of incurring distress costs. Ross (1997) also models the tax benefits of

hedging in a continuous-time setting. Petersen and Thiagarajan (1998) provide a detailed comparison

of how hedging theories apply to Homestake and American Barrick.

3The source is Kenneth Froot, The limited financing of catastrophe risk: An overview, in“The Financing of Property Casualty risks”, University of Chicago Press, 1997.

Chapter 3, page 46

BOX

Warren Buffet and the Catastrophe Insurance3

Let’s look at an interesting example where the costs of external finance can be computed directly and

turn out to be much larger than predicted by the CAPM. There exists a market for catastrophe

insurance. In this market, insurers provide insurance contracts that pay off in the event of events such

as earthquakes, tornadoes, and so on. Insurance companies hedge some of their exposure to

catastrophes by insuring themselves with re-insurers. A typical re-insurance contract promises to

reimburse an insurance company for claims due to a catastrophe within some range. For instance, an

insurance company could be reimbursed for up to $1 billion of Californian earthquake claims in excess

of $2 billion. Catastrophe insurance risks are diversifiable risks, so that bearing these risks should not

earn a risk premium. This means that the price of insurance should be the expected losses discounted

at the risk-free rate. Yet, in practice, the pricing of re-insurance does not work this way.

Let’s look at an example. In the Fall of 1996, Berkshire Hattaway, Warren Buffet’s company,

sold re-insurance to the California Earthquake Authority. The contract was for a tranche of $1.05

billion insured for four years. The annual premium was 10.75% of the annual limit, or $113M. The

probability that the reinsurance would be triggered was estimated at 1.7% at inception by EQE

International, a catastrophe risk modeling firm. Ignoring discounting, the annual premium was

therefore 530% the expected loss (530% is (0.1075/0.017) - 1 in percent). If the capital asset pricing

Chapter 3, page 47

model had been used to price the reinsurance contract, the premium would have been $17.85M in the

absence of discounting and somewhat less with discounting.

How can we make sense of this huge difference between the actual premium and the premium

predicted by the capital asset pricing model? A re-insurance contract is useless if there is credit risk.

Consequently, the re-insurer essentially has to have liquid assets that enable it to pay the claims. The

problem is that holding liquid assets creates agency problems. It is difficult to make sure that the re-

insurer will indeed have the money when needed. Once the catastrophe has occurred, the under-

investment problem would prevent the re-insurer from raising the funds because the benefit from

raising the funds would accrue to the policy holders rather than to the investors. The re-insurer

therefore has to raise funds when the policy is agreed upon. Hence, in the case of this example, the

re-insurer would need - if it did not have the capital - to raise $1.05 billion minus the premium. The

investors would have to be convinced that the re-insurer will not take the money and run or take the

money and invests it in risky securities. Yet, because of the asset substitution problem, the re-insurer

has strong incentives to take risks unless its reputational capital is extremely valuable. In the absence

of valuable reputational capital, the re-insurer can gamble with the investors’ money. If the re-insurer

wins, it makes an additional profit. If it loses, the investors or the insurer’s clients lose.

There is another problem with re-insurance which is due to the information asymmetries and

agency costs in the investment industry. The re-insurer has to raise money from investors, but the

funds provided would be lost if a catastrophe occurs. Most investment takes place through money

managers that act as agents for individual investors. In the case of funds raised by re-insurance

companies, the money managers is in a difficult position. Suppose that he decides that investing with

a re-insurance firm is a superb investment. How can the individual investors who hire the money

Chapter 3, page 48

manager know that he acted in their interest if a catastrophe occurs? They will have a difficult time

deciding whether the money manager was right and they were unlucky or the money manager was

wrong. The possibility of such a problem will lead the money manager to require a much larger

compensation for investing with the re-insurance firm.

Berkshire Hataway has the reputational capital that makes it unprofitable to gamble with

investors’ money. Consequently, it does not have to write complicated contract to insure that there

will not be credit risk. Since it has already large reserves, it does not have to deal with the problems

of raising large amounts of funds for re-insurance purpose. Could these advantages be worth as much

as they appeared to be worth in the case of our example? Maybe not. However, there is no evidence

that there were credible re-insurers willing to enter cheaper contracts. With perfect markets, such re-

insurers would have been too numerous to count.

Chapter 3, page 49

Figure 3.1. Cash flow to shareholders and operating cash flow.

The firm sells 1M ounces of gold at the end of the year and liquidates. There are no costs. Theexpected gold price is $350.

Chapter 3, page 50

Figure 3.2. Creating the unhedged firm out of the hedged firm.The firm produces 100M ounces of gold. It can hedge by selling 100M ounces of gold forward. Theexpected gold price and the forward price are $350 per ounce. If the firm hedges and shareholdersdo not want the firm to hedge, they can recreate the unhedged firm by taking a long position forwardin100M ounces of gold.

Chapter 3, page 51

Figure 3.3. Cash flow to shareholders and bankruptcy costs. The firm sells 1m ounces of goldat the end of the year and liquidates. There are no costs. The expected gold price is $350.Bankruptcycosts are $20M if cash flow to the firm is $250M. Expected cash flow to shareholders for unhedgedfirm is 0.5 times cash flow if gold price is $250 plus 0.5 times cash flow if gold price is $450.

Chapter 3, page 52

Figure 3.4. Expected bankruptcy cost as a function of volatility. The firm produces 100M ounces of gold and then liquidates. It is bankrupt if the price of gold isbelow $250 per ounce. The bankruptcy costs are $20 per ounce. The gold price is distributednormally with expected value of $350. The volatility is in dollars per ounce.

Chapter 3, page 53

Figure 3.5. Taxes and cash flow to shareholders. The firm pays taxes at the rate of 50% on cash flow in excess of $300 per ounce. For simplicity, theprice of gold is either $250 or $450 with equal probability. The forward price is $350.

Chapter 3, page 54

100 200 300 400

305

310

315

320

325

330

Figure 3.6. Firm after-tax cash flow and debt issue. The firm has an expected pre-tax cash flow of $350M. The tax rate is 0.5 and the risk-free rate is 5%.The figure shows the impact on after-tax cash flow of issuing more debt, assuming that the IRSdisallows a deduction for interest of debt when the firm is highly likely to default.

After tax cash flow of hedged firm

Optimal amount ofdebt, $317.073M

Principal amount of debt