This lecture is mainly based the following textbooks:
Study review and practice: I strongly recommend using Prof. Henrique Castro (FGV-EAESP) materials. Below you can find the links to the corresponding exercises related to this lecture:
\(\rightarrow\) For coding replications, whenever applicable, please follow this page or hover on the specific slides with coding chunks.
An important consequence of leverage is the risk of bankruptcy:
When a firm has difficulty meeting its debt obligations, we say that it is in Financial Distress:
\(\rightarrow\) After the firm defaults, debtholders are given certain rights to the assets of the firm and may even take legal ownership of the firm’s assets through bankruptcy
\(\rightarrow\) The next slides will show how the funding structure affect the value of Armin in both states of the economy
All-Equity | All-Equity | Leverage | Leverage | |
---|---|---|---|---|
Success | Failure | Success | Failure | |
Debt Value | - | - | $100 | $80 |
Equity Value | $150 | $80 | $50 | $0 |
All Investors | $150 | $80 | $150 | $80 |
Both debt and equity holders are worse off if the product fails rather than succeeds:
Importantly, since the firms is worth \(\small \$80\) and debt is \(\small \$100\), the firm is in default if the project fails with leverage!
\[ \small V^U= \dfrac{\dfrac{1}{2}\times 150 + \dfrac{1}{2}\times80}{(1+5\%)}=109.52\\ \]
\[ \small V^L= \dfrac{\overbrace{\dfrac{1}{2}\times 100 + \dfrac{1}{2}\times80}^{\text{Debtholders}}+ \overbrace{\dfrac{1}{2}\times 50 + \dfrac{1}{2}\times0}^{\text{Equityholders}}}{(1+5\%)}=\dfrac{115}{(1+5\%)}=109.52 \]
\(\rightarrow\) With perfect capital markets, Modigliani and Miller (MM) Proposition I applies: the total value to all investors does not depend on the firm’s capital structure
With perfect capital markets, we saw that the risk of bankruptcy is not a disadvantage of debt:
In reality, however, a bankruptcy process is a complex, time-consuming, and costly process:
We refer to these costs as the direct costs of bankruptcy, as they reduce the value of the assets that the firm’s investors will ultimately receive: it is estimated that the average direct costs of bankruptcy are approximately \(\small 3\%-4\%\) of the pre-bankruptcy market value of total assets
On top of the direct costs associated due bankruptcy and financial distress, a firm can also suffer from the indirect costs of bankruptcy
Due to its nature, although indirect costs are difficult to measure accurately, they are often much larger than the direct costs of bankruptcy
The estimated potential loss due to financial distress is around \(\small 10\%-20\%\) of firm value
Let’s go back to our previous example on Armin. How do bankruptcy costs fit into that situation?
Say that, after some calculations, Armin has estimated financial distress costs of \(\small \$20\) million
\(\rightarrow\) As a result, debtholders will receive less than 80 million!
In this case, debtholders receive only \(\small \$80-\$20=\$60\) million after accounting for the costs of financial distress
These costs will lower the total value of the firm with leverage, \(\small V^L\) and Modigliani and Miller’s Proposition I will no longer hold: the total value to all investors is less with leverage than it is without leverage when the new product fails!
All-Equity | All-Equity | With Leverage | With Leverage | |
---|---|---|---|---|
Success | Fail | Success | Fail | |
Debt Value | - | - | $100 | $60 |
Equity Value | $150 | $80 | $50 | $0 |
All Investors | $150 | $80 | $150 | $60 |
\[ \small V^U = \dfrac{\dfrac{1}{2} \times 150 + \dfrac{1}{2} \times 80}{(1+5\%)}= \dfrac{115}{(1+5\%)}= 109.52\\ \]
\[ \small V^L= \dfrac{\overbrace{\dfrac{1}{2} \times 100+\dfrac{1}{2}\times60}^{\text{Debtholders}}+\overbrace{\dfrac{1}{2} \times 50+\dfrac{1}{2}\times 0 }^{\text{Equityholders}}}{(1+5\%)}= \dfrac{105}{(1+5\%)}=100 \]
We saw that the value of the levered firm, \(\small V^L\), was lower due to the financial distress costs. An important question regarding financial distress costs is who ultimately bears it:
As a result, debtholders will require to pay less for the debt:
\(\rightarrow\) When securities are fairly priced, the original shareholders of a firm pay the present value of the costs associated with bankruptcy and financial distress!
If debtholders pay less for the debt initially, by how much precisely is this difference? To see that, that at the beginning of the year, Armin Industries has \(\small 10\) million shares outstanding and no debt. Armin then announces plans to issue one-year debt with a face value of \(\small \$100\) million and to use the proceeds to repurchase shares
Due to financial distress costs, the present value of debt is:
\[ D=\small \dfrac{\small 1/2\times100+1/2\times 60}{(1+5\%)}=76.19 \text{ million} \]
From the data in the previous slide, Armin will be able to issue \(\small\$76.19\), instead of \(\small \$80\), and this translates to buying \(\small 7,619\) shares, leaving \(\small 2,381\) outstanding shares
As the value of the levered equity is \(\small \$23.81\) million, the share price is now only \(\$10\) per share. All in all, all shareholders1 are worse off by:
\[ \small \underbrace{(10.952-10.00)}_{\text{Unlevered - Levered Equity}}\times \underbrace{10,000,000}_{\text{Shares outstanding}}=9.52 \text{ million} \]
\(\rightarrow\) Although debt holders bear these costs in the end, shareholders pay the present value of the costs of financial distress up front, and ultimately born the costs of financial distress!
Let’s take a step back and recall what we have defined in earlier classes:
\[ \small V^L= V^U+PV(ITS) \]
Definition
The Trade-off Theory states that the firm picks its capital structure by trading off the benefits of the tax shield from debt against the costs of financial distress and agency costs.
According to the theory, the total value of a levered firm, \(\small V^L\) equals the value of the firm without leverage plus the present value of the tax savings from debt, less the present value of financial distress costs:
\[ V^L = V^U + PV(ITS) - PV(\text{Financial Distress Costs}) \]
There are basically three key factors determine the present value of financial distress costs:
There are basically three key factors determine the present value of financial distress costs:
An implication of the Trade-Off Theory is that each firm will have an optimal leverage level:
\[ \small \max V^L_{\{\%E,\%D\}} = V^U + PV(ITS) - PV(\text{Financial Distress Costs}) \]
Holland is considering adding leverage to its capital structure. Holland’s managers believe they can add as much as \(\small \$50\) million in debt and exploit the benefits of the tax shield. They estimate that the corporate tax rate is \(\tau_c = 39\%\). However, they also recognize that higher debt increases the risk of financial distress. Based on simulations of the firm’s future cash flows, the CFO has made the following estimates (in millions of dollars):
Debt-to-Value | 0% | 10% | 20% | 30% | 40% | 50% |
---|---|---|---|---|---|---|
PV(Int. Tax. Shield) | - | $3.9 | $7.8 | $11.7 | $15.6 | $19.5 |
PV(Fin. Dis. Costs) | - | $0 | $0 | $3.38 | $19.23 | $23.47 |
Question: what of debt should the firm choose?
Holland is considering adding leverage to its capital structure. Holland’s managers believe they can add as much as \(\small \$50\) million in debt and exploit the benefits of the tax shield. They estimate that the corporate tax rate is \(\tau_c = 39\%\). However, they also recognize that higher debt increases the risk of financial distress. Based on simulations of the firm’s future cash flows, the CFO has made the following estimates (in millions of dollars):
Debt-to-Value | 0% | 10% | 20% | 30% | 40% | 50% |
---|---|---|---|---|---|---|
PV(Int. Tax. Shield) | - | $3.9 | $7.8 | $11.7 | $15.6 | $19.5 |
PV(Fin. Dis. Costs) | - | $0 | $0 | $3.38 | $19.23 | $23.47 |
Net Benefit | - | $3.9 | $7.8 | $8.32 | $-3.63 | $-3.97 |
\(\rightarrow\) Solution: the level of debt that leads to the highest net benefit is 30 million. Holland will gain \(\small\$11.7\) million due to tax shields and lose \(\small \$3.38\) million due to the present value of financial distress costs, for a net gain of \(\small \$8.32\) million.
Apart from any direct costs and benefits from increased leverage, debtholders may also be concerned around which managerial actions will be taken after debt is in place - and whether it will ultimately lead to increasing indirect costs to them
The potential costs due to misalignment between different stakholders of the firm are called Agency Costs
Definition
Agency Costs are costs that arise when there are conflicts of interest between the firm’s stakeholders:
Although not directly measurable, Agency Costs can vary significantly and have a substantial impact on the value of the levered firm
Under Modigliani and Miller’s hypotheses for Perfect Capital Markets, there are no Agency Costs - this is embedded in the assumption that there are no transaction costs and/or information asymmetry
Examples of managerial actions that are supposedly costly for debtholders are:
Definition
When a firm faces financial distress, shareholders can gain at the expense of debt holders by taking a negative-NPV project if it is sufficiently risky - also called risk-shifting problem
Question: should Baxter execute this strategy?
\[ \small V^L_{\text{New}}=\small 50\% \times 1.3 + 50\% \times 0.3 = 0.8 \text{ million} \]
Why managers would even consider this strategy? It is important to note that, if Baxter does nothing, it will ultimately default and equity holders will get nothing with certainty:
\[ \small E^L_{\text{New}}=50\% \times 0 + 50\% \times 300,000 = 150,000 \]
Old Strategy | New - Success | New - Failure | New - Exp. | |
---|---|---|---|---|
\(V^L\) | $900 | $1,300 | $300 | $800 |
Debt | $900 | $1,000 | $300 | $650 |
Equity | $0 | $300 | $0 | $150 |
\[ \small 50\% \times 1,000,000 + 50\% \times 300,000 = 650,000 \text{ million} \]
\(\rightarrow\) This loss corresponds to the 100,000 expected decline in firm value due to the risky strategy and the equityholder’s 150,000 gain
As we saw before, if managers are acting on behalf of shareholders, they may choose to gamble with debtholder’s money by choosing projects that with asymmetrical payoffs (in expectation, benefits shareholders at the expense of debtholders)
A way to materialize this is to choose projects that are risky enough so that shareholders are better-off if the project is succesfull:
The previous example has shown how potential a misalignment between shareholders and debtholders may result in a move towards more risky projects
What if there are actually projects less risky projects that would otherwise increase the firm’s NPV?
Definition
Debt Overhang (or simply Under-Investment) is a situation in which equity holders choose not to invest in a positive NPV project because the firm is in financial distress and the value of undertaking the investment opportunity will accrue to bondholders rather than themselves
\(\rightarrow\) As a result, when a firm faces financial distress, it may choose not to finance new, positive-NPV projects!
Assume that Baxter does not pursue the risky strategy, but instead the firm is considering an investment opportunity that requires an initial investment of \(\small\$100,000\) and will generate a risk-free return of \(\small50\%\)
If the current risk-free rate is \(\small5\%\), this investment clearly has a positive NPV
Question: would managers, acting on behalf of the shareholders, be willing to raise funding and invest in this project?
Without project | With new project | |
---|---|---|
Existing assets | $900,000 | $900,000 |
New project | - | $150,000 |
Total firm value | $900,000 | $1,050,000 |
Debt | $900,000 | $1,000,000 |
Equity | $0 | $50,000 |
\(\rightarrow\) As debtholders receive most of the benefit, thus this project is a negative-NPV investment opportunity for equityholders, even though it offers a positive NPV for the firm!
Definition
Cashing out is a situation where shareholders are more likely to liquidate assets and return back to shareholders, even if this is a negative-NPV transaction. When in financial distress, shareholders have an incentive to withdraw money from the firm, if possible.
Ultimately, if the firm defaults, as debtholders seize the assets, they may have even more difficulties in liquidating them as they do not understand the business:
For example, Tiffany is worth more in the hands of LVMH rather than a bank due to the potential synergy benefits
This helps explaining why, in some cases, a takeover from another firm within the same industry may preserve more value than an asset liquidation by banks!
As shown before, when an unlevered firm issues new debt, equityholders will bear any anticipated agency/bankruptcy costs that might affect the firm
A different story arises when our starting point is a levered firm: once a firm has debt already in place, some of the agency or bankruptcy costs that result from taking on additional leverage will fall on existing debtholders:
While it will induce firms to borrow less initially in order to avoid these costs, over time it may lead to excessive leverage as shareholders prefer to increase, but not decrease, the firm’s debt
For instance, by reducing debt, equity holders lose their incentive to take on a risky negative NPV investment
How to prevent bankruptcy events from the perspective of a debtholder? One way of doing so is establishing debt covenants:
Debt covenants are conditions (both positive or negative) that lenders (creditors, debt holders, investors) put on lending agreements to limit the actions of the borrower (debtor)
In other words, debt covenants are agreements between a company and its lenders that the company will operate within certain rules set by the lenders
When a debt covenant is violated, depending on the severity, the lender can do several things:
Positive Debt Covenants are covenants that state what the borrower must do:
Negative Debt Covenants are covenants that state what the borrower cannot do:
\(\rightarrow\) See “Succession” on IMBd - access here
So far, we assumed that managers act in the interests of the firm’s equityholders, and we considered the potential conflicts of interest between debtholders and equityholders when a firm has leverage
Notwithstanding, managers also have their own personal interests, which may differ from those of both equity and debtholders - also known as management entrenchment:
How can a firm insulate from this issue? In what follows, we will see that leverage can provide incentives for managers to run the firm more efficiently and effectively
Together with other benefits we will describe, in addition to the tax benefits of leverage, give the firm an incentive to use debt rather than equity!
Definition
Management Entrenchment is a situation arising as the result of the separation of ownership and control in which managers may make decisions that benefit themselves at investors’ expenses
How can leverage prevent this issue?
Leverage can reduce the degree of managerial entrenchment because managers are more likely to be fired when a firm faces financial distress
In addition, when the firm is highly levered, creditors themselves will closely monitor the actions of managers, providing an additional layer of management oversight
Another advantage of using leverage is that it allows the original owners of the firm to maintain their equity stake in the company (i.e, avoids the dilution of their participation)
With more “skin in the game”, they are likely having more interest in doing what is best for the firm overall
To see that, assume that you are the owner of a firm and plans to expand. You can either borrow the funds needed for expansion or raise the money by selling shares in the firm:
As we will see, having higher ownership will provide additional incentives to run the firm more efficiently
Without leverage
If you sell new shares, you will only retain \(\small60\%\) ownership and thereby receive \(\small60\%\) of the increase in firm value: if the value largely depends on your personal effort, you’d have more incentives if you kept \(\small100\%\) of the firm
Having \(\small60\%\), you would be more tempted to overspend in perks: by selling equity, you bear only \(\small60\%\) of the perks costs, while the other \(\small40\%\) will be paid for by the new equityholders
How can leverage prevent this issue?
As a consequence, managers may expand unprofitable divisions, pay too much for acquisitions, make unnecessary capital expenditures, or hire unnecessary employees
Having leverage limits these actions as debtholders may prevent empire building through covenants - note that this can also benefit equityholders
Managers may over-invest because they are overconfident: they tend to be bullish on the firm’s prospects and may believe that new opportunities are better than they actually are
Debt forces managers to be more realistic with the true prospects of the firm because they have the commitment to pay back debtholders
The occurrence of wasteful investments and room for managerial overconfidence is fueled by the fact that a firm has resources (cash) to invest
However, when cash is tight, managers may be motivated to run the firm more efficiently:
Definition
The Free Cash Flow Hypothesis is the view that wasteful spending is more likely to occur when firms have high levels of cash flow in excess of what is needed after making all positive-NPV investments and payments to debt holders
Question: how would you estimate net effect of leverage on the firm value?
\[ \small V^L = V^U + PV(ITS) - PV(\text{Financial Distress Costs})- PV(\text{Agency Costs}) + PV(\text{Agency Benefits}) \]
R&D-Intensive Firms
Low-Growth, Mature Firms
Definition
Asymmetric Information is a situation in which parties have different information. For example, when managers have superior information to investors regarding the firm’s future cash flows.
If we depart from this assumption, can asymmetric information be related to leverage? The Signaling Theory of Debt implies a relationship between the degree of information asymmetry and the level of debt:
Whenever we allow for information asymmetry, we no longer guarantee that all agents operate on the same level of information: for example, there might be more informed traders (such as insider traders) that have a different estimate for a firm’s value
What happens if one party anticipates that the other party has different information?
Adverse Selection is the idea that when the buyers and sellers have different information, the average quality of assets in the market will differ from the average quality overall
The Lemons Principle is widely used to depict a situation of adverse selection. There are implications for both high and low quality cars:
Notwithstanding, this same principle can be applied to the market for equity:
In other words:
As a consequence, due to the fact that managers and potential investors have different levels of information regarding the firm’s prospects, issuing/repurchasing equity can be seen as a signal from managers about their assessment
This helps explaining why startups tend to rely more on internal funding before going through an external funding process:
You are an analyst who follows Great Windows’ stock. Although the current stock price is \(\small \$37.50\), you believe the stock is worth either \(\small \$25\) or \(\small \$50\), depending on the success of a new product launch. If Great Windows’ CEO announces that she plans to buy \(\small 10,000\) additional shares in the company, how will the share price change?
\(\rightarrow\) Solution
What does information asymmetry tells us when it comes to all the financing options we’ve studied so far? It is important to note that these options have different degrees of information asymmetry
For example, managers who perceive the firm’s equity is underpriced will have a preference to fund investment using retained earnings, or debt, rather than equity.
Therefore, the Pecking-Order Theory of financing choices states a rank-ordering in terms of the preferable funding options for a firm:
Nesbat Industries needs to raise \(\small \$25\) million for a new investment project. If the firm issues one year debt, it may have to pay an interest rate of \(\small 10\%\), although Nesbat’s managers believe that \(\small 8\%\) would be a fair rate given the level of risk. However, if the firm issues equity, they believe the equity may be underpriced by \(\small 7.5\%\). What is the cost to current shareholders of financing the project out of retained earnings, debt, and equity?
\(\rightarrow\) Solution
If the firm spends \(\small \$25\) million out of retained earnings, rather than paying that money out to shareholders as a dividend, the cost to shareholders is \(\small \$25\) million
Using debt costs the firm pays \(\small \$25 \times (1+10\%) = \$27.5\) million in one year, which has a present value based on management’s view of the firm’s risk of \(\small \$27.5/(1+8\%)= \$25.46\) million
Finally, if equity is underpriced by \(\small 7.5\%\), then to raise \(\small \$25\) million, the firm will need to issue \(\small 25/(1-7.5\%) = \small \$27.03\) million of new equity. Thus, the cost to existing shareholders will be \(\small \$27.03\) million
Important
Practice using the following links: