CORPORATE FINANCE I: CAPITAL STRUCTURE
WEEK 5
Thomas Noe
SBS/Balliol
OUTLINE
- CAPITAL STRUCTURE NEUTRALITY
- IMPERFECTION: TAXATION
- IMPERFECTION: COST OF FINANCIAL DISTRESS
- IMPERFECTION: UNDERINVESTMENT AND DEBT
- IMPERFECTION: MORAL HAZARD
- IMPERFECTION: ASYMMETRIC INFORMATION
- Framework
- PBE: Example
- Investment and asymmetric information
- Results: Pecking order
- SUMMARY
THE CAPITAL STRUCTURE PROBLEM
- Sources of financing for firms
- Equity (internal; e.g. retained earnings)
- Equity (external)
- Debt (external)
- How should the firm finance its activities?
- Capital structure: the mix between debt and equity resulting from the firm's financing decisions
- Capital structure problem: How does a firm's capital structure affect the wealth of the firm's owners (debt and equity holders)?
- Modigliani and Miller provide a baseline insight that underlies all subsequent research
MODIGLIANI-MILLER THEOREM (1958)
Under the perfect market assumptions:
- Efficient capital markets
- Costless default
- No security issuance transactions costs
- Homogeneous expectations
- Symmetric information
- No taxes
Proposition I: Firm value is independent of capital structure
Intuition:
- Firm value is determined by cash flows.
- How you split up cash flows for distribution to providers of capital (debt or equity) should not affect the total value of the cash flows being split
- "How you slice up a pizza should not affect the value of the pizza"
MODIGLIANI AND MILLER PROPOSITION I (MMI)
- This is a very famous result, both because of its implications, and because of the way in which it is proved
- Arbitrage: risk-free profits obtained by buying one security and selling another
- This should be impossible in a well-functioning market
- MM's proof was the first application of a no-arbitrage condition in financial economics
AN INFORMAL DERIVATION OF MMI
A firm whose cash flows depend upon the state of the world, with two possible capital structures:
| State |
Cash Flow |
Cap Structure 1 |
Cap Structure 2 |
|
|
Equity |
Debt |
Equity |
Debt |
| Good |
1,000 |
1,000 |
0 |
500 |
500 |
| Bad |
300 |
300 |
0 |
0 |
300 |
- What happens with capital structure 2 in the bad state?
- Write $V_1$ and $V_2$ for the firm's value with capital structures 1 and 2
- MM implies that $V_1 = V_2$
MM PROOF (II)
| State |
Cash Flow |
Cap Structure 1: $V_1=E_1$ |
Cap Structure 2: $V_2=E_2+D_2$ |
|
|
Equity |
Debt |
Equity: $E_2$ |
Debt: $D_2$ |
| Good | 1,000 | 1,000 | 0 | 500 | 500 |
| Bad | 300 | 300 | 0 | 0 | 300 |
- Suppose $V_1 < V_2$. We will use home made leverage to derive a contradiction
- Buy $\alpha$ of the equity of a capital structure 1 company
- This will generate cash flows $\alpha \times \binom{1,000}{300}$
- Use the equity as the collateral of a debt issue with face value $\alpha \times 500$
- Debt will repay $\alpha \times \binom{500}{300}$, which has value $\alpha \times D_2$
- Your remaining cash flows will be $\alpha \times \binom{500}{0}$: sell them for $\alpha \times E_2$
- You spent $\alpha V_1$; you received $\alpha D_2 + \alpha E_2 = \alpha V_2 > \alpha V_1$
- There is no such thing as a money pump
MM PROOF (III)
| State |
Cash Flow |
Cap Structure 1: $V_1=E_1$ |
Cap Structure 2: $V_2=E_2+D_2$ |
|
|
Equity |
Debt |
Equity: $E_2$ |
Debt: $D_2$ |
| Good | 1,000 | 1,000 | 0 | 500 | 500 |
| Bad | 300 | 300 | 0 | 0 | 300 |
- Now suppose $V_1 > V_2$
- Buy a fraction $\alpha$ of the debt and equity of capital structure 2
- Cost $\alpha E_2 + \alpha D_2 = \alpha V_2$
- You receive cash flow $=\alpha\binom{500}{0}+\alpha\binom{500}{300}=\alpha\binom{1,000}{300}$; value is $\alpha V_1$
- Sell the cash flow. Your profit is $\alpha(V_1 - V_2)$
- Again, this is an arbitrage: it cannot survive in a competitive market
SIMPLE DERIVATION: MODIGLIANI MILLER PROPOSITION II (1958)
In the MM world, let $\tilde{C}_F$ be the corporation's FCF, and let $\tilde{C}_D$ and $\tilde{C}_E$ be cash flows accruing to debt and equity, respectively. Then:
$$ \tilde{C}_F = \tilde{C}_D + \tilde{C}_E $$
so that:
$$ \frac{\tilde{C}_F}{D+E} = \frac{D}{D+E}\frac{\tilde{C}_D}{D} + \frac{E}{D+E}\frac{\tilde{C}_E}{E} $$
Thus the required return on the levered firm's assets, $r_L$ equals
$$ r_L = \frac{D}{D+E}r_D + \frac{E}{D+E}r_E $$
PROPOSITION II
- Since $D+E$ is not affected by capital structure (MMI)
- And FCF is independent of capital structure,
- Thus,
Proposition II: The cost of capital for the levered firm $(r_L = \tilde{C}_F / (D+E))$ is independent of the firm's capital structure
- Changes in capital structure must result in changes to $r_E$ and $r_D$ that ensure that $r_L$ is unchanged
- Thus $r_L = r_U$, the required return on the assets of an unlevered firm (aka the required return on assets, $r_A$).
EXAMPLE
| Income |
Low |
Medium |
High |
| Unlevered |
| Shares outstanding | 400 | 400 | 400 |
| Earnings | 400 | 1,200 | 2,000 |
| Assets | 8,000 | 8,000 | 8,000 |
| Equity | 8,000 | 8,000 | 8,000 |
| Debt | 0 | 0 | 0 |
| Interest | 0 | 0 | 0 |
| ROE | 0.05 | 0.15 | 0.25 |
| EPS | 1 | 3 | 5 |
| Levered (50%) |
| Shares outstanding | 200 | 200 | 200 |
| Earnings Before Interest | 400 | 1,200 | 2,000 |
| Assets | 8,000 | 8,000 | 8,000 |
| Equity | 4,000 | 4,000 | 4,000 |
| Debt | 4,000 | 4,000 | 4,000 |
| Interest | 400 | 400 | 400 |
| Earnings | 0 | 800 | 1,600 |
| ROE | 0 | 0.2 | 0.4 |
| EPS | 0 | 4 | 8 |
LEVERAGE DOES NOT AFFECT $r_L$, BUT IT INCREASES THE REQUIRED RETURN ON COMMON STOCK
Example:
Unlevered $0.15 = \frac{0}{8,000} \times 0.1 + \frac{8,000}{8,000} \times 0.15$
Levered $0.15 = \frac{4,000}{8,000} \times 0.1 + \frac{4,000}{8,000} \times 0.20$
Description of the Graph:
This is a line graph illustrating Modigliani-Miller Proposition II. The x-axis represents the Debt-to-Equity ratio (D/E), increasing from left to right. The y-axis represents the rate of return, r.
There are three lines plotted:
- A flat horizontal line labeled $r_A$, representing the constant cost of assets (the overall cost of capital), which is unaffected by leverage.
- An upward-sloping line labeled $r_E$, representing the cost of equity. It starts at the same point as $r_A$ when D/E is zero and increases as leverage increases. This shows that as the firm takes on more debt, equity becomes riskier, and shareholders demand a higher return.
- A line labeled $r_D$, representing the cost of debt. It is flat at first, indicating risk-free debt, and then begins to slope upwards at higher levels of leverage, reflecting the increasing risk of default.
The graph shows that while the costs of debt and equity change with leverage, their weighted average, $r_A$, remains constant.
When debtholders demand a higher return on the debt, the rate of increase in $r_E$ slows down.
UNDER WHAT CIRCUMSTANCES DOES THE SLICING MATTER?
Description of the Image:
This is a photograph of a Neapolitan-style pizza on a white plate, set against a light blue background. The pizza is cut into eight slices. The toppings are tomato sauce, melted mozzarella cheese, and a fresh basil leaf on each slice. The image serves as a visual metaphor for the Modigliani-Miller theorem, where the total value of the pizza (the firm) is independent of how it is sliced (its capital structure).
IMPERFECTION: CORPORATION TAX
Corporation tax is typically levied on a firm's profit, after interest payments.
So with a tax rate of 20% (close to UK rate), consider paying £400 on on perpetual risk free bond with face value of £4,000. Assume the risk free rate is 10%.
- The fact that interest payments are tax deductible reduces taxable income by £400
- and thus reduces taxes by (0.20) * 400 = £80
- So the owners (debt&equity holders) cash flows are increased by £80 every year.
- Because the debt is perpetual, the value of this tax reduction to the firm equals, $80/0.10 = £800$
THE TAX SHIELD INCREASES THE VALUE OF THE FIRM RELATIVE TO THE UNLEVERED FIRM
In general, if the only market imperfection is corporate taxation, the firm value equals unlevered firm value plus the present value of the debt tax shield
$$ V_{Levered} = V_{Unlevered} + PV \text{ of debt tax shield} $$
CASH FLOWS OF THE LEVERED AND UNLEVERED FIRM
Description of the Graph:
This is a bar chart with three bars, illustrating how cash flows are distributed. The y-axis represents Cash Flow, from 0 to 1000.
- Assets: The first bar, in green, represents the total Pretax Cash Flow (EBIT) of the firm's assets, which is 1000.
- Unlevered Firm: The second bar shows the distribution for an all-equity firm. A portion at the top is paid in Taxes. The remaining, larger portion goes to Unlevered Equity (Earnings). The total cash paid out to stakeholders is less than 1000 due to the tax payment.
- Levered Firm: The third bar shows the distribution for a levered firm. A bottom portion, in yellow, is paid as Interest to Debt holders. The portion above that goes to Levered Equity (Earnings). A smaller portion at the top goes to Taxes. The key insight is that the tax portion for the levered firm is smaller than for the unlevered firm. The difference is labeled the "Interest Tax Shield". Because less money goes to taxes, more total cash flow is available to be distributed to the firm's investors (both debt and equity holders).
IMPERFECTION: COSTS OF FINANCIAL DISTRESS
Risky debt means default occurs with positive probability; this has costs (the 'bankruptcy cost').
- Direct costs of bankruptcy:
- liquidation cost, business disruption
- administrative costs (lawyers etc)
- In case of default, ownership of assets transferred to creditors.
- What happens to the value of assets when they are sold? Likely reduced!
- More discussion next lecture
INVESTMENT AND DEBT FINANCING
- In the perfect markets world of MM, capital structure does not affect investment policy
- Accept all and positive NPV projects, reject negative NPV projects
- However, it appears that financially distressed firms and individuals frequently reduce investment
- Example: Melzer (2017, Journal of Finance) shows that home owners who are likely to default on their mortgages, substantially reduce investments in home maintenance.
- Why?
DEBT OVERHANG
- Debt overhang (Myers, Journal of Financial Economics, 1977): in the presence of excessive debt, shareholders may forego positive NPV projects.
- Cash constrained firms must typically finance new investment by issuing new equity or new subordinated debt because old (at the time of issue) debtholders have priority claims on cash flows.
- While shareholders fund the new investment, either by providing the requisite cash or selling claims on their portion of the firm's cash flows, part of the benefits from the investment goes to the old debtholders.
MYERS, 1977: DEBT OVERHANG
V: current equilibrium market value of the firm, with $V_D$, $V_E$.
V can be broken down into the PV of assets already in place ($V_A$) and PV of future growth opportunities that the firm may or may not take ($V_G$): $V = V_A + V_G$
Simple case: At $t=0$, firm is all equity financed, and no assets in place ($V_D=0$ and $V_A=0$). If the firm invests an amount I, it obtains an asset worth $V(s)$ at $t=1$.
s is the state of the world. It can be good, bad, ugly or take a distribution of states (will see more on 'distributions' in your QE lectures).
Investment will only be made if $V(s) \ge I$ (there is a threshold state $s_a$ above which this will hold)
THE FIRM'S INVESTMENT DECISION DEPENDS ON THE STATE OF THE WORLD
Description of the Graph (Myers 1977, Figure 1):
This graph illustrates a firm's investment decision based on the future state of the world. The x-axis represents the "State of the World, s". The y-axis represents "Dollars in State s".
There are two lines: a horizontal line at height I, representing the fixed investment cost, and an upward-sloping line labeled V(s), representing the value of the project, which increases as the state of the world improves. The two lines intersect at a point labeled $s_a$. To the left of $s_a$, V(s) is below I, so the project has a negative NPV and the firm does not invest ($x(s)=0$). To the right of $s_a$, V(s) is above I, the project has a positive NPV, and the firm invests ($x(s)=1$). The point $s_a$ is the critical threshold state for the investment decision.
ALL EQUITY-FINANCED FIRM
Balance sheet at $t=0$
Value of growth opportunity $V_G$ | Value of debt 0
Value of firm V | Value of equity $V_E = V$
If the firm invests, new shares need to be issued:
Balance sheet at $t=1$
Value of growth opportunity $V(s)$ | Value of debt 0
Value of firm $V(s)$ | Value of equity $V_E = V(s)$
If the firm does not invest, no new shares issued, and the firm is worthless.
Since the firm will be worth nothing in states $s < s_a$, it cannot issue safe debt. It can issue risky debt with the promised payment P.
First, assume that the debt matures before the investment decision is made, but after the true state of nature is revealed. Then, if $V(s) - I \ge P$, it will be in stockholders' interest to pay back the debt.
If $V(s) - I < P$ the bondholders will take over, and exercise the firm's option to invest if $V(s) \ge I$.
Shareholders can borrow the entire value of the firm if they wish.
THE LINK BETWEEN BORROWING AND THE MARKET VALUE OF THE FIRM
Now, assume that the debt matures after the firm's investment option expires. Then outstanding debt will change the firm's investment decision in some states:
Balance sheet at $t=0$
Value of growth opportunity $V_G$ | Value of debt $V_D$
Value of firm V | Value of equity $V_E$
Proceeds of the debt are used to reduce the required equity investment.
Balance sheet at $t=1$, given investment goes ahead ($s \ge s_a$)
Value of growth opportunity $V(s)$ | Value of debt min[V(s), P]
Value of firm $V(s)$ | Value of equity max[0, V(s)-P]
THERE IS A RANGE OF STATES (BETWEEN $s_a$ AND $s_b$) WHERE INVESTORS WILL NOT INVEST IN A POSITIVE NPV PROJECT
Description of the Graph (Myers 1977, Figure 2):
This graph illustrates the debt overhang problem. It is similar to the previous graph, with the x-axis as the "State of the World, s" and the y-axis as "Dollars in State s". It includes the lines for investment cost (I) and project value (V(s)), intersecting at $s_a$.
A new horizontal line is added at height I + P, where P is the face value of existing debt. This line intersects V(s) at a new point, $s_b$, which is to the right of $s_a$. The issue is that shareholders will only invest if the project's value, V(s), is enough to cover both the new investment I and the old debt P. Therefore, they will only invest for states $s \ge s_b$.
The shaded triangular area between $s_a$ and $s_b$ represents states of the world where the project has a positive NPV (since V(s) > I), but shareholders will not undertake it because the returns would go to the existing debtholders, not them. This is the underinvestment problem caused by debt overhang.
FIRM AND DEBT VALUES AS A FUNCTION OF PAYMENT TO CREDITORS
Description of the Graph (Myers 1977, Figure 3):
This graph shows how the value of the firm and its debt change as the amount of promised payment to creditors (P) increases. The x-axis is "P, Payment Promised to Creditors". The y-axis is "Dollars of Present Value".
There are three curves:
- A flat horizontal line at the top, "V given All-Equity Financing", representing the maximum firm value if there is no debt and thus no underinvestment problem.
- A downward-sloping curve labeled "V", representing the actual value of the levered firm. It starts at the all-equity value when P=0 and declines as P increases, because higher debt leads to a more severe underinvestment problem.
- An inverted U-shaped curve labeled "$V_D$", representing the value of debt. It starts at 0, increases as P increases, reaches a "Maximum Debt Available", and then declines. The decline occurs because at very high levels of promised payments, the underinvestment problem becomes so severe that it reduces the total value of the firm, which in turn reduces the amount that can actually be recovered by debtholders.
PLEDGEABLE FUNDS AND INVESTMENT
- In a perfect market, all positive NPV investments will be undertaken
- The personal wealth of entrepreneurs will not affect their ability to obtain funding
- Only project NPV matters
- Schmalz, Sraer, Thesmar (2017) find that the price of an entrepreneur's house is a significant determinant of the amount of funding the entrepreneur can obtain.
- The house is a pledgable asset that the can be pledged to creditors.
- Why do pledgeable assets seem to affect whether projects will be accepted?
MORAL HAZARD AND CONSTRAINTS ON EXTERNAL FINANCE
Holmstrom and Tirole, Quarterly Journal of Economics, 1997
Consider a world with an entrepreneur (insider) seeking to raise funds (from outsiders) to undertake a risky project.
Entrepreneur:
- has limited pledgeable assets, A, that can be invested in the project
- has an investment project that costs I funds.
Investment project:
- $I > A$
- Outcomes: success w.p. p; failure w.p. $1-p$
- Payoffs: if success, R; if failure, 0.
MODELLING ASSUMPTIONS
Simplifying assumptions:
- Entrepreneur and outsiders are risk-neutral
- No time preference
- Risk-free rate of return $= 0$
- Expected rate of return for outsiders $= 0$ (competitive market in provision of finance by outsiders)
Entrepreneur can affect the probability of success.
- Probability of success and effort
- High enough effort: $p_H$
- Low effort: $p_L < p_H$
- Entrepreneur receives a private benefit from not exerting effort: B.
CONTRACTING
Financial contract between Entrepreneur and outsiders: sharing rule dividing the success cash flow, R. $R_E$ to the entrepreneur and $R_D$ to the outsider.
- Outsider invests I - A, Entrepreneur invests A
- Good outcome: Entrepreneur receives $R_E$; outsider receives $R_D$. Overall return: $R = R_D + R_E$
- Bad outcome: Both receive 0.
EFFORT REQUIRED FOR POSITIVE NPV
- Project has a positive NPV if entrepreneur exerts effort, i.e., $p_H R - I > 0$
- Project has a negative NPV if entrepreneur does not exert effort, i.e., $p_L R - I + B < 0$
OUTSIDER BREAKS EVEN
- The zero-profit constraint for risk-neutral outsider implies that $p R_D = I - A$
- Absent effort, project is negative NPV
- In equilibrium, outsiders profit is 0
- So project will not be undertaken if it cannot be undertaken with a contract that secures entrepreneurial effort.
- Thus, in equilibrium, if the project is financed, the entrepreneur must exert effort
- So outsider must earn 0 profit conditioned on the entrepreneur exerting effort, i.e., $p_H R_D = I - A \quad \text{(Out-BE)}$
INCENTIVE COMPATIBLE EFFORT
- If the entrepreneur exerts effort, the entrepreneur receives $p_H R_E$
- If the entrepreneur does not exert effort, the entrepreneur receives $p_L R_E + B$
- So, for effort to be incentive compatible it must be the case that $p_H R_E \ge p_L R_E + B$
- So $R_E$ must satisfy $R_E \ge \frac{B}{p_H - p_L}$
- Recalling that the benefit to outsiders is $R_D + R_E = R$, we see that $R_D$ must satisfy $R_D \le R - \frac{B}{p_H - p_L} \quad \text{(IC)}$
PLEDGEABLE ASSET CONSTRAINT
- Recall equations (Out-BE) and (IC):
$$ p_H R_D = I - A \quad \text{(Out-BE)}$$
$$ p_H R_D \le p_H(R - \frac{B}{p_H - p_L}) \quad \text{(IC)}$$
- Equations (Out-BE) and (IC) imply that
$$ I - A \le p_H(R - \frac{B}{p_H - p_L}) $$
$$ \Rightarrow A \ge I - p_H(R - \frac{B}{p_H - p_L}) \quad \text{(A-Min)}$$
CREDIT RATIONING
- Thus, if the entrepreneur cannot pledge A satisfying (A-Min), i.e, if
$$ A < I - p_H(R - \frac{B}{p_H - p_L}) $$
- the project cannot be financed
- In this case, credit is rationed: The entrepreneur would like to undertake the positive NPV project by borrowing, but the entrepreneur cannot obtain funding.
- The project's NPV is not affected by A, the wealth the entrepreneur can pledge
- Absent moral hazard, the project would always be undertaken
- Because of moral hazard, a poor (low A) entrepreneur cannot obtain financing.
ANNOUNCEMENT EFFECTS OF EQUITY ISSUE AND RELIANCE ON DEBT FINANCING IN PERFECT MARKETS
- Corporate announcements in perfect markets
- In a perfect market, all information is common knowledge
- Thus, the observed decisions of firms should not affect their stock prices
- Outsiders, having the same information as insiders, can anticipate firm decisions
- In perfect markets, there is no reason for firms to prefer debt issuance to equity issuance
- Or for firms to prefer internal to external financing
IN REALITY
- Announcements of equity issues are typically followed by stock price drops
- Firms seem to prefer to raise external funds through debt rather than equity issues
- Firms seem to prefer internal to external financing
- Why?
ANNOUNCEMENT EFFECTS OF SEASONED EQUITY OFFERINGS
Description of the Graph:
This graph shows the announcement effects of Seasoned Equity Offerings (SEOs) over time. The x-axis is the year, from before 1985 to after 2005. The y-axis is the "%CAR", which stands for Cumulative Abnormal Return, ranging from -4% to over 2%.
Each dot represents the average abnormal stock return for a given year in response to an announcement that a company will issue new shares. The vast majority of the dots are below the zero line, indicating that, on average, a company's stock price falls when it announces an SEO. This is a consistent empirical finding that contradicts the perfect markets assumption.
WHY THE NEGATIVE EFFECT OF SEOS ON STOCK PRICE?
- Perhaps it is just supply/demand, in order to induce investors to hold more shares, you have to lower the price
- But, if this theory is true then,
- Why don't bond issue announcement have significant negative effects on bond prices?
- Why no negative stock price effect when the shares are actually issued?
- Why are the negative effects for regulated utility stocks much smaller? (Eckbo, Masulis, 1995)
EVIDENCE: SOURCES OF EXTERNAL FINANCING
Sources of external financing (1984-1991). Source Rajan and Zingales (1995, p. 1439)
| Composition of External Financing |
External Financing as a Fraction of Total Financing |
Net Debt Issuance |
Net Equity Issuance |
| United States | 0.23 | 1.34 | -0.34 |
| Japan | 0.56 | 0.85 | 0.15 |
| Germany | 0.33 | 0.87 | 0.13 |
| France | 0.35 | 0.39 | 0.61 |
| Italy | 0.33 | 0.65 | 0.35 |
| United Kingdom | 0.49 | 0.72 | 0.28 |
| Canada | 0.42 | 0.72 | 0.28 |
MYERS AND MAJLUF (1984)
Myers, S.C. and Majluf, N.S., 1984. Corporate financing and investment decisions when firms have information that investors do not have. Journal of Financial Economics, 13(2), pp.187-221.
FRAMEWORK: ECONOMY
- All agents are risk neutral wealth maximisers
- All agents are patient (risk free rate is 0)
- One period model with two dates-date 0 and date 1
FRAMEWORK: SETTING
- Managers of a firm have private information
- Firm is currently all equity financed
- Currently, o shares are outstanding
- Firm has access to an investment opportunity
- Manager makes investment decisions and acts to maximise the date 1 payoff of date 0 (old) shareholders
FRAMEWORK: CASH FLOW DISTRIBUTIONS
- The firm has no cash flows at date 0
- At date 1, its old assets pay $a_j, j=G,B$
- $j=G, B$ represents a signal received by the manager about the state of the firm.
- If the firm accepts the investment project, its new assets pay $I+b_j$, $j=G,B$
- If the firm accepts the project, it must issue equity to raise I dollars
- This involves issuing n new shares at date 0, leaving new owners owing the fraction $\alpha = n / (o+n)$ of the firm.
FRAMEWORK: PARAMETERS AND INFORMATION
- $b_j \ge 0$, $j=G,B$ (+ NPV)
- $b_B \le b_G$ & $a_B \le a_G$ (G is really better)
- The mgr. knows whether $j=B$ or G but the market does not (asymmetric information)
- Before observing the firm's action, the market assigns probability p to the event that the signal $j=G$
FRAMEWORK: THE AGENT'S CHOICES
- The firm has two possible actions
- $a = \mathcal{F}$ - accept the project and finance the project with equity
- $a = \mathcal{N}$ - do not accept the project and do not finance.
- In response to the firm's choice of action, the new shareholders, i.e. the "market", compete for the shares of the issue by bidding the faction of the firm, $\alpha$, they will accept in return for financing the investment.
- Bertrand competition implies that the value of the new shareholders' share of the firm equals the value of the funds they provide.
FRAMEWORK: FORMALISATION OF THE GAME
- Let $y_j(a)$ be the firm's total date 1 cash flow given signal j and action a
- $y_j(\mathcal{F}) = a_j + b_j + I$
- $y_j(\mathcal{N}) = a_j$
FRAMEWORK: EQUILIBRIUM
A Perfect Bayesian Equilibrium for this game is a triple consisting of an issue strategy for the manager, $a^*$, a pricing strategy, $\alpha^*$ for the financial market, and beliefs, $\pi^*$ of the financial market, where
- beliefs, $\pi^*(a)$, represent the market's assessment of the probability that the firm has received signal G given it takes action a.
- The issue strategy, $a^*(j)$, represents the action selected by the mgr. given signal j
- and the market pricing strategy, $\alpha^*$, is the fraction of the firm demanded by the market
FRAMEWORK: EQUILIBRIUM CONDITIONS
- Mgr. issues only when issuing is a best response for old owners (Sequential Rationality)
$$ a^*(j) = \mathcal{F} \Rightarrow (1-\alpha^*)y(j,\mathcal{F}) \ge y(j, \mathcal{N}) $$
- The financing terms set by the market, $\alpha^*$, are consistent with Bertrand competition in the capital markets (Bertrand)
$$ \alpha^*(\pi(\mathcal{F})y_G(\mathcal{F}) + (1-\pi(\mathcal{F}))y_B(\mathcal{F})) = I $$
- Whenever possible, market beliefs are generated by applying Bayes rule to the market's prior beliefs, p, given the mgr.'s equilibrium actions, $a^*$ (Belief Consistency)
PBE: EXAMPLE - NUMBERS
- $p = \text{Prob. of signal G} = \text{Prob. of signal B} = \frac{1}{2}$
- Assets in place G: $a_G = 4.875$ Assets in place B: $a_B = 0.875$
- Project NPV (same for G and B): $b_G = b_B = b = 0.125$
- Required investment: $I=1.00$
FINDING AN EQUILIBRIUM: CONJECTURE AND VERIFY
- Conjecture: Market forms a conjecture regarding firm actions. Market sets the fraction of the firm required by outsiders, $\alpha^*$ based on this conjecture
- Verify: Given the $\alpha^*$ determined by the conjecture, will the firm actually do what the market conjectures it will do?
- If YES: Equilibrium
- If NO: Not an equilibrium
PBE: EXAMPLE - CONJECTURE AND BELIEFS
- For strategy #1 (Invest if B, Invest if G), Bayes rule implies that $\pi(\mathcal{F}) = \frac{1}{2}$
- For strategy #2 (Invest if B, Not Invest if G), Bayes rule implies that $\pi(\mathcal{F}) = 0$
- For strategy #3 (Not Invest if B, Invest if G), Bayes rule implies that $\pi(\mathcal{F}) = 1$
- For strategy #4 (Not Invest if B, Not Invest if G), Investing does not occur so Bayes rule cannot be employed, so $\pi(\mathcal{F}) \in [0,1]$
$$ \alpha^* = \frac{I}{\pi(\mathcal{F})(a_G+b_G+I) + (1-\pi(\mathcal{F}))(a_B+b_B+I)} $$
PBE: EXAMPLE - IS STRATEGY #1 THE BEST STRATEGY?
- Conjecture: $\alpha$ based on conjecture solves $\alpha(\frac{1}{2}(a_G+I+b) + \frac{1}{2}(a_B+I+b)) = I \Rightarrow \alpha^* = 0.25$
- Verify:
- Invest if B? $(1-0.25)(0.875+1+0.125) \ge 0.875 \Rightarrow 1.5 \ge 0.875$? YES
- Invest if G? $(1-0.25)(4.875+1+0.125) \ge 4.875 \Rightarrow 4.5 \ge 4.875$? NO
- Conjecture is NOT verified: Not an equilibrium
WHAT ABOUT STRATEGIES #2, #3, #4?
| Strategy | Conjecture | $\alpha^*$ | Conjectured action is a best response? | Equilibrium? |
|---|
| G | B | G | B |
|---|
| #1 | Inv. | Inv. | 0.25 | No | Yes | No |
| #2 | Not Inv. | Inv. | 0.50 | Yes | Yes | Yes |
| #3 | Inv. | Not Inv. | 0.167 | No | Yes | No |
| #4 | Not Inv. | Not Inv. | [0.167, 0.50] | No | No | No |
PBEs IN THIS EXAMPLE
In this example, there is one PBE
- Manager strategy: $a^*(G) = \mathcal{N}$, $a^*(B) = \mathcal{F}$
- Market beliefs: $\pi^*(\mathcal{F})=0$, $\pi^*(\mathcal{N})=1$
- Issue terms: $\alpha^* = 0.50$
COMPUTING THE PRICE OF SHARES AND # OF SHARES ISSUED
- For example, if 10 shares are outstanding before the issue, $o=10$, then, because $n/(o+n) = \alpha^* = 0.50 \Rightarrow n=10$
- All shares have the same claim on cash flows
- If the firm issues, it will have $o+n=20$ shares outstanding and its total value will equal $a_B+b+I = 0.875+0.125+1=2$.
- So when issue is announced, the share price will equal $(a_B+b+I)/(o+n) = 0.10$.
- If the firm does not announce an issue, its share price will equal $a_G/o = 0.4875$
- Because, before the announcement, the market believes that B and G are equally likely, $p=0.50$, the price of the firm's shares before announcement equals $(0.10+0.4875)/2=0.29375$
INVESTMENT RESULTS
RESULT: WHEN MGR. RECEIVES SIGNAL B, THE FIRM NEVER UNDERINVESTS
Why?
- The "worst" belief that the market can have about the firm is that the firm's state is B
- In which case, the terms of the equity issue will be set so that, if the firm's state is B, the equity is correctly priced.
- Given any other market beliefs, conditioned on the state being B, the equity issued to finance the project is worth less than funds raised from new shareholders, i.e., equity is overvalued.
- So, when manager receives signal B, old shareholders sometimes gain and never lose from financing the investment
- The NPV of the project is, by assumption, positive
- Investing in the project is a win-win proposition: positive NPV project + overvaluation
RESULT: POOLING OR SEPARATING
- Because mgr. always invests when signal is B
- Only two equilibrium configurations are possible
- Separating equilibrium: Manager invests if and only if the signal is B. Negative announcement effect from equity issuance
- Pooling equilibrium: Manager always invests (i.e., for both signals G and B). No announcement effect from equity issuance
- Sometimes, for the same parameter choices, both separating and pooling equilibria exist
IN SOME EQUILIBRIA, FIRM SOMETIMES UNDERINVESTS WHEN SIGNAL IS G
Why?
- The "best" belief that the market can have about the firm is that the signal is G, in which case. G-equity is correctly priced
- Otherwise dilution: the equity issued to new shareholders after signal G is worth more than the funds raised, I
- However the NPV of the project is, by assumption, positive
- So, investing in the project is a win-lose proposition when the manager receives the G signal
- win: Positive NPV
- lose: Dilution
INVESTMENT RESULTS
ROLE OF FINANCIAL SLACK
- If the firm had internal funds of at least I (rather than no internal funds),
- The firm would always invest regardless of the signal, Why?
- No dilution effect from external equity issue and positive NPV
- Myers and Majulf call internal funds financial slack
- Enough financial slack $\rightarrow$ No underinvestment
- Cf. Pledgeable assets in Holmstrom and Tirole (1997).
PVT. INFORMATION REGARDING ASSETS IN PLACE REQUIRED FOR UNDERINVESTMENT
- Why?
- Suppose there is no asymmetric information about assets in place
- That is, assets in place are always correctly valued by the market but not new investments
- So a manager receiving signal G knows that mispricing might lead to new shareholder's capturing part of the project's NPV
- Sad for old shareholders; but rejecting the project ensures that old shareholders lose all of the NPV
- Something is better than nothing
- So the firm will still invest in positive NPV projects regardless of the signal
MORE FORMAL DERIVATION: ASSETS IN PLACE
- No asymmetric information about assets in place: $a_B = a_G = a$
- Myers and Majluf assume that the project has a positive NPV
- If the firm invests, firm value is at least $I+a$
- So if we set the outsider's fraction, $\alpha$, equal to, say $\bar{\alpha}$, where $\bar{\alpha} := I/(a+I)$
- then the value of the outsiders share under $\bar{\alpha}$ is
$$ \bar{\alpha}(a+b_j+I) = \frac{I}{I+a}(a+b_j+I) > I, \quad j=G,B $$
- So regardless the signal at terms $\bar{\alpha}$, the value of the outsiders' claim is greater than I
- Not possible (Bertrand condition)
- So in any PBE, $\alpha^* < \bar{\alpha} \Rightarrow 1-\alpha^* > 1-\bar{\alpha}$
- Thus, the payoff from investing satisfies
$$ (1-\alpha^*)(a+b_j+I) > (1-\bar{\alpha})(a+b_j+I) = \frac{a}{a+I}(a+I+b_j) > a $$
- a is the payoff from rejecting the investment
- So the manager will never reject the project
- I.e., no asymmetric information about assets in place $\rightarrow$ no underinvestment
- Corollary: No assets in place $\rightarrow$ no underinvestment in Myers Majluf (1984)
RESULTS: PECKING ORDER
MYERS AND MAJLUF PECKING ORDER ASSERTION
In our model, however, the firm never issues equity. If it issues and invests, it always issues debt, regardless of whether the firm is over- or undervalued... Thus, our model may explain why many firms seem to prefer internal financing to financing by security issues and, when they do issue, why they seem to prefer bonds to stock. (page 208-209)
- Assertion seems reasonable but, actually, it is not quite correct
WHY DOES PECKING ORDER SOMETIMES FAIL
- For some choices of parameters, "Pecking disorder" equilibria exist (Noe, 1988)
- In pecking disorder equilibria, there is a positive probability the manager will prefer equity financing to debt financing
- However, reasonable further restrictions on the permitted distributions of cash flows exist under which the Myers and Majluf pecking order holds (Nachman and Noe, 1994)
- And, even in pecking disorder equilibria, stock prices conditioned on announcing equity issuance are less than stock prices conditioned on announcing debt issuance (Noe, 1988)
SUMMARY: PERFECT AND IMPERFECT CAPITAL MARKETS
- In perfect markets, capital structure is irrelevant Modigliani and Miller, 1958)
- In imperfect markets:
- Capital structure can effect investment decisions
- Debt overhang (Myers, 1977)
- Pledgeable assets constraints (Holmstrom and Tirole, 1997))
- Underinvestment caused by asymmetric information (Myers and Majluf, 1984)
- Availability of internal funds (financial slack, pledgeable assets) affects whether projects will be accepted (Myers and Majluf, 1984; Holmstrom and Tirole, 1997)
SUMMARY: IMPERFECT MARKETS (CONT.)
- Capital structure decisions can signal private information and affect stock prices (Myers, Majluf, 1984)
- Capital structure can affect firm value and owner welfare
- Taxes and financial distress costs
- Dilution when information is asymmetric (Myers and Majluf, 1984)