Logic & Summaries Flashcards
Game theory
Equilibrium Concepts
The basic idea of an equilibrium is that each player’s strategy makes sense given the other players’ strategies. So all players have plans that are sensible given what the other players’ plans are.
- A dominant strategy equilibrium is a strategy profile consisting of a dominant strategy for each player.
- A strategy profile s* is a Nash equilibrium if no player has incentives to deviate from her strategy given that the other players do not deviate.
Some key properties of the equilibrium concepts:
- A dominant strategy equilibrium is also a Nash equilibrium.
- A game has at most one dominant strategy equilibrium.
- A game may have more than one Nash equilibrium.
- There are games that do not have a Nash equilibrium (in pure strategies).
Sequential games
In a sequential game, at least one player move after having observed a move made by another player. SEE IMAGE
Bayesian equilibrium and PBE (perfect Bayesian eq)
–> Nash equilibrium when the players update their beliefs according to Bayers’ rule. When moving from Bash to Bayesian, our procedure goes from two to three steps.
- Propose a strategy profile
- See what beliefs the strategy profile generates (this is where Bayes comes in)
- Check that given those beliefs and the strategies of the other players, each players is choosing a best response
The players’ beliefs are now an integral part of an equilibrium. This is recognized formally in e.g. the perfect Bayesian equilibrium concept by requiring that an equilibrium is not just a strategy profile, but also consists of the player’s beliefs.
A perfect Bayesian equilibrium (PBE) adds the requirements that (I) every players’ beliefs must be specified at all points the player makes a move, and (II) all moves specified by a player’s strategy must be best responses given the player’s beliefs (at the node the move is made). Thus, a PBE adds the requirement that beliefs also be specified off the equilibrium path while a Bayesian equilibrium only constrains beliefs on the equilibrium path. A PBE thus requires that the actions off the equilibrium path are rational given the beliefs there, which goes some wat towards eliminating non-credible threats (think Mayers and Majluf [DN,DN] valuation of issue and invest can’t be worse than bad state)
EXAM2017
Grossman & Hart
Formal Dilution Modal
Problem
- Incumbent mangement is inefficient
- A corporate raider may—at a cost—raid the firm
- Shareholders may free-ride on the corporate raider by retaining their shares in the firm and thus share in the profits generated by the raid
The social benefit of a takeover equals the resulting increase in value less the cost of carrying out the takeover. The raider bears all the costs of the raid, but does not capture all of the benefits due to the hold-out problem. Thus, free-riding by minority shareholders may prevent (socially and/or privately) beneficial takeovers.
Possible solution: Voluntary dilution; shareholder may include porvisions in corp. charter that allows a raider to dillute the value that holdout minority shareholders obtain after take-over
This result in a decrease of profit from free-riding, and therefore makes the raid more likely to be profitable for raider. This may be in shareholders interest for two reason, 1) managment is more incentivized due to higher threat of raid, 2) higher likelihood og takober which increases share value because raiders usually pay a takeover premium.
Formal model
q=f(a0)=current value of the firm
p=tender price announced by raider
v=max f(a) + £ = value of the firm under raiders managment, wher £ is the diff in ability between raider and current mgmt
All of the above is common knowledge. We also assume many shareholders.
See first image for choice faing shareholders. Investors are rational, in the sense that for a given p, they correctly anticipate the outcome of the bid (i.e. we are looking at PBE). So if the tender offer is successful, then this is anbticipated in eq, hence the case must be that p>=v, or no one would tender.
==> But this measn raider would make a loss form all successful tenders offers. Thus there will be no takovers, and profit from takovers are foregone. (in q
Suppose raider can dillute, now image two holds! If p<q></q>
<p>Let c denote cost of raid. Leaving raider a profit of v-p-c = v-max(v-ø,q)-c = min(ø,v-q)-c. <br></br>--> If both ø and v-q exceed c, then raider makes a profit and the firm is raided. <br></br>The raiders ability to dilute minority stock value reduces profit from free-riding, so that the takeover becomes profitable for raider.</p>
<p>If v-ø>q, then p=v-ø, and existing shareholders make a profit equal to v-ø-q>0. </p>
<p><u>Optimal dilution</u></p>
<p>Increasing diltuion (ø) has four implications for shareholders<br></br>(bad)1. Raider suceeds with lower p, so in the event of raid p=max(v-ø,q) decreases<br></br>(good)2. The probability of raids increase, which is good since p typically will be bigger than q<br></br>(good) 3. Influences managers to achieve higher q to prevent raids, so current share value q increases</p>
<p>--> Consequence, It may be in the shareholders interests to set up a corporate charter that permits (not completely prevents) dilution of minority shareholders in the event of a takeover.</p>
<p>PS! The ex ante social benefit from a takeover equals the takeover’s impact on the current stock value plus the expected profit of the raider. Thus the social benefit of dilution is greater than the private benefit to the current shareholders, so the socially optimal dilution is at least as high as the privately optimum, and in general it is larger.</p>
<p> </p>
</q>
The agency cost of equity
Jensen & Meckling Model
Outside equity financing introduces a conflict of interests between (outside) shareholders and the manager (owner). Consider a 100% equity financed firm in which the manager initially owns all the equity. The manager maximizes his utility by choosing optimal combinations of the total value of the firm and the cost of perquisites he consumes. Increased spending on perquisites decreases the value of the firm, but increases the manager’s utility from consumption of such benefits. As long as the manager owns 100% of the firm, the manager’s wealth is reduced by the full cost of his perquisites. Suppose the manager sells a fraction (1- ∝) of the equity to outside investors and retains ∝ fraction a of the equity himself. In this case, the manager’s wealth is reduced only by a times the cost of the perquisites. In other words, the manager obtains his perquisites at a lower cost and therefore increases his consumption of them. This leads to agency costs (residual loss) since there is now sub-optimal consumption of perquisites.
When the manager of the firm owns 100% of the equity, the value of the firm and the level of perks is given by point D. Where the indifference curve of the manager U2 is tangent with the managers budget constraint (slope of -1), giving V* and F* respectively. However if the manager sells a share of the firm (1- ∝), and retain share ∝ for himself his incentive to consume perks increases.
If the buyer believes that the managers consumption of perks will not change, the buyer will be willing to pay(1- ∝)V* for the fraction 1- ∝ of the firms equity. The manager does of course wish to maximize his own utility, and as his share of the firm decreases the cost of consuming perks decreases as well. This leads to the owner wanting to consumer more perks after the outsider buys 1- ∝ of the firms equity if he is allowed. His new budget constraint (from V1 to P1) will have a slope of - ∝ (cost of consuming $1 of perks is ∝ x $1, where 0< ∝). The manager will now move to point A where his utility is maximized, this leads to the firms value decreasing to V0 , while the owner now consume F0 of perks.
However, a rational outside buyer will take into account this rational expectation in the equity market, and will therefore be aware that the managers consumption of perks will increase after he sells 1- ∝ of the firms equity. The outsider will therefore not pay (1- ∝)xV*, he will instead pay 1- ∝ times the value he expects the firm to have given the change in the managers consumption of perks. The budget constraint from V2 to P2 represents the new budget constraint the owner will face given the reduction in price. The manager wealth will be maximized when a indifference curve such as U3 is tangent with the budget constraint. The price for 1-∝ of the firms equity that is acceptable to both parties must be along the original budget constraint. Therefore, the value of the firm must be given from the point B, which is V’.
In conclusion, when the manager sells 1-∝ of the firm, the outside buyer will pay (1-∝)xV’ for the equity, which leads to the manager consuming F’ perks. The consumption of perks will increase when the manager sells a share of the firm, but not so much as it would if the equity market was without rational expectations of the managers perks consumption.
We see that in the figure this leads to the manager obtaining a lower utility. This is in favor of the manager keeping 100% of his assets inside the firm, because he avoids paying for the agency cost. Therefore if the manager chooses to sell equity the reason must come from outside the model. Such as the managers gain from diversification is big enough that the manager chooses to diversify (given optimal outside financing the diversification is equal to the agency cost).
Monitoring and bonding activities
Monitoring by the outside investors and bonding by the manager have two separate effects on the manager’s opportunity set (set of available combinations of firm value and perquisite expenditure). First, as more monitoring and bonding costs are incurred, the manager’s expenditure on perquisites will decrease. This increases the value of the firm. Secondly, as the cost of monitoring and bonding increases, the value of the firm is reduced by the amount of these costs. The net effect will be an increase in firm value if the benefit from monitoring and bonding is higher than the cost of these activities.
That is, monitoring and bonding may be desirable if the resulting reduction in agency costs is higher than the incurred monitoring and bonding costs. Note that it may be in the owner-manager’s interest to facilitate monitoring by the outside shareholders since it is the manager that suffers the entire agency cost. However, the manager will also have to pay the monitoring costs since the outside investors will not pay more than the value of their equity share net of monitoring and agency costs. It will in general be desirable for the manager to restrict the maximum level of monitoring because the outside shareholders want to restrict the manager’s expenditure on perquisites by more than the optimal restriction from the manager’s point of view genereally.
(Perks could also include efforts, or stuff such as private jet, nice HQ, etc..)
PS! Solution for manager if he is able to freeze assets when selling (the reason for selling is not that he needs to be liquid:
Suppose the manager sets aside the cash generated by the sold equity and writes a put to the outside shareholders allowing these to sell their shares back to the manager at the price they paid for their shares.
–> Guess clawbak could also work, but harder to enforce!
Modigliani & Miller’s
Take aways
M&MI:
If tc = 0, then VL = VU. That is, in the absence of taxes, and other frictions, the market value of any firm is independent of its capital structure and is given by capitalizing its expected cash flows at the discount rate r appropriate for the firm’s risk.
Consider the net cash inflow of a firm. The capital structure determines how this inflow is distributed among the claimants on the firm. Suppose the firm can alter its capital structure without causing frictions, i.e. the total cash outflow of the firm is the same regardless of the capital structure. The capital structure choice is in that case irrelevant for firm value and cost of capital.
However, if the key assumptions are relaxed, the firm’s value depends on the firm’s capital structure. Seen in this light, M&MI identifies the reasons why capital structure affects firm value (violations of key assumptions)
M&MII:
The fact that debt is cheaper than equity ( rf < p), is not a reason why capital structure is important because the cost of equity increases linearly with the firm’s leverage. This is logical, because increased leverage makes the residual cash flow (to equity) riskier, even when there is now default risk. Equity holders will therefore require a higher return on capital invested as leverage increases.
Note: Obvious weakness in the presence of taxes, tc > 0 would imply 100% debt financing. Two reasons why this doesn’t hold in real world: Othre frictions such as bankruptcy cost or Miller (1977). Also there may be a maximum tax shield, this limit is equal to the value of gov’s entitlement to tax payments (in the absence of TS)
Straightforward lessons:
I) the fact that cost of capital for debt is typically less than that of equity is not a reason to employ debt.
II) WACC is still independent of the capital structure in the absence of tax effects
(and III) under M&M assumptions, with corporate taxes, WACC declines (firm value increases) in the debt/equity ratio.
Indirect (main) lesson: capital structure is relevant to the extent that the assumptions (implicit or explicit) in M&M are violated (counting for this purpose “no tax” as an assumption).
Miller (1977)
Initial idea
Miller [1977] modifies Modigliani and Miller’s model by relaxing the assumption that there are no personal taxes. With this Miller captures the effect of equilibrium usage of debt in the economy. He explains this as a reason for why de wo not see 100% debt financed firms, and argues that this is relevant since bankruptcy cost etc empirically is nowhere close to big enough to outweigh the advantage of debt financing.
Model
In the case that the equilibrium personal income tax for buyers of small amount bonds are less than corporate tax rate, all firms want to issue more bonds in order to increase firm value as there is an advantage to be had from debt financing (each firm wil issue as many riskless bonds as possible at r(se)). However, the demand for bonds will be limited to only those individuals with marginal tax rate below or equal to the equilibrium perosnal tax rate.
When the bond market is in equilibrium, there are no further tax advantages from leverage to be obtained by issuing more corporate taxable bonds.
IMAGE
That is, the equilibrium rate of return offered on taxable, corporate bonds is the riskless rate “grossed up” by one minus the corporate tax rate such that the tax-incentive to use debt from the firm’s shareholders point of view is removed.
Weaknes of model
More seriously, Miller’s model only determines the aggregate amount of debt financing in the economy. This is the amount of debt such that the gain from further leverage is zero. As we have seen, the shareholders do not care whether their firm issue bonds or not (since the firm and equity values are unaffected). The bondholders do not care which firms issue bonds either since all corporate bonds are riskless and yield the equilibrium rate of return. Bonds issued by different firms are therefore perfect substitutes. Miller’s model does therefore not predict an optimal debt/equity ratio for an individual firm.
==> So in equilibrium the value of firms, would be independent of its capital structure, depsite the deductibility of interest payments computing corporate income taxes.
(Also discuss who extracts the benefits)
Dividends
Modigliani and Millers dividend irrelevance result: Unfettered access to perfect markets -> any dividend policy can be undone by issuance/repurchase in the markets ‐> investment policy (and operations) is decoupled from dividend policy ‐> no effect of dividend policy on firm value
Relevant cause for deviations from this is things such as; information assymety (M&M) and agency.
Can a firms who wividend policy is irrelevant still be valued using discounted dividend models? Dividend valuation may still be reasonable if dividends are strongly tied to relevant fundamentals such as earnings (net cash flow). Under irrelevance, such a link may be far fetched, but not completely inconceivable.
Capital Structure
Main financial instruments, and APR rule
There are three main categories of liabilities: 1) Debt, 2) Hybrids, and 3) Equity
1) Debt instruments are contractual payments of interests and principal. If the firm do not pay its contractual payments, bankruptcy occurs and control of the firm reverts to the creditors.
2) Hybrid securities are a blend of debt and equity. Convertible bonds and callable bonds are examples of hybrid securities.
3) Equity shareholders have the residual claim on the firm’s cashflow.
The different components of the firm’s capital structure is organized after the Absolute Priority Rule (APR), where the seniority on the firms cashflow increased the higher in the balance sheet the instrument is. Thus, debt instruments have seniority over both hybrids and equity, and ling-term debt have seniority over short-term debt. AS the seniority decrease the risk increased. Equity have therefore more risk than debt.
M&A
- *Merger** - any transaction that forms one economic unit (legal unit, organization) from two or more previous units. Three types:
1. Hortzontal - Merger of two companies in the same market
2. Vertical - Merger of two companies where one is the customer of the other (owning more of the value chain)
3. Conglomerate - Merger of two companies that have less or non relation
–> Can be either hostile or friendly.
Tender offer (Acquire) - the acquiring firm makes an offer directly to the shareholders in the target firm. The shareholders in the target firm submit or tender their shares in exchange for cash or securities.
Joint venture - joint activities limited in scope and time.
Theories of M&A activities
-
Efficicency explanations, differential efficiency due to:
- Inefficient managmnet
- Synergy (We can define synergies as the change in net present value from merging the firms)
- Economies of scale
- Coordination (vertical mergers only) -
Information theories
- Kick in the pants (monitoring - alleviating moral hazard)
- Sitting on a gold minde (assymetric info) -
Agency problems
- Threat of takeover may discipline managers
- Emprie building -
Market power
- Higer market share => less competition
- Tacit collusion -
Tax considerations
- Capital gains instead of income
Aquire unutulized tax shield
Not all these motivations work for pure conlomerate mergers, and are in general harder to find good reasons for. Among those above: Inefficient mgmt, economies of scale, marketing or finacning, tax considerations and information or agency costs. May aslo be due to reduce value of expected bankruptcy cost (small with large makes the small more safe). May also be due to merged firms obtaining a higher debt capacity.
PS! An important consideration in any merger, and especially in a conglomerate merger (typically noe synergies, so may be 0 NPV), is the possible wealth distribution between shareholders and bondholders as a result of the merger. If there is a postive NPV, but merger seems unlikely to happen renegotiation could be a solution (think what type of renegotiation, in which of the merging firms etc, remember renogtiation would happen before the merger). If debt is riskless/nonexistent both before and after merger for all parties this would not be an issue.
When discussing an Mergers (or acquistions) impact on society taking the synergy (value aspect) into consideration is not enough. We need to take a full stakeholder view, employees, competition, quality to customers, emissions etc.
(PS: Poison pill is the opposite of allowing dilution: erosion of value/value transfer. A poison pill allows existing shareholders to dilute a corporate raider’s gains. This discourages takeovers, thereby possibly weakening managerial incentives (because it increase entrenchment) and potentially destorying shareholder value)
Myers and Majluf
Formal model
Two key assumptions
- The decisions to issue and invest are connected, just issuing is not an option.
- Managers acts in the old shareholder interest, and assumes they are passive. (Instead of a) Interest of all shareholders, b) old shareholder interest, but assumes they rationally rebalance their portfolios as the learn from the firm’s action)
Model
Decision at t=0, maxV(old) = V(a+b+E+S;i&i)
The market value will generally not equal actual value, as market only know A and B dsitribution. But market draws inferences about the realization og a and b form firms actions. Logic:
1) For some combinations of a and b it is optimal to issue and invest, for other combinations it is optimal to do nothing.
2) If the firm issues and invests, then we can deduce that a and b must be among the alternatives that make issuing & investing optimal.
3) Conversely, if the firm does nothing, then we can deduce that a and b must be among the alternatives that makes it optimal to do nothing.
Insiders use their knowledge of private information to decide between two alternative courses of action, observing their actions therefore allows us to distinguish between two subsets of possible realization.
But, the properties of subsets we can distinguish may vary.
- Pooling EQ: All subsets are empty except one which equals the entire set of possibilities. [IandI,IandI] or [DN,DN], optimal decision same for all realization and therefore says nothing.
- Partially informative EQ: At least on subset has more than one element, but atleast two non-empty subsets. Therefore gives us some information, but not all.
- Seperating EQ: Each subset is a singelton. [IandI,DN] or [DN,IandI], one optimal decisions for all realization so fully informative.
One possible solution to underinvestment problems btw may be slack or risk-free debt.
Formal model
IMAGE (also think graph)
P’ = V’ - E
The decision whether it is optimal to issue and invest (which a and b lies in MI ) depends on PI which in turn depends on MI. Hence, PI and MI must be determined simultaneously and must be consistent for there to be an equilibrium (which is not necessarily unique)
Conclusions
- The firm prefers to finance new projects with internal funds (slack) and secondarily with debt if internal funds are not available (Pecking order: internal financing → debt → equity).
- The firm will issue new shares only if it does not have available internal funds and it cannot issue debt.
- The firm may forego positive NPV projects if the manager has better information than the financial market and the firm has insufficient internal funds to finance the project.
- The firm will seek to build up internal funds (retain earnings) to avoid having to forego positive NPV projects or having to issue undervalued securities to finance new projects.
- If the firm can issue debt, it will never issue shares. Since debt value is less sensisitve to the true value of frim (due to risk)
The agency cost of debt
Debt financing creates an incentive for asset substitution because the debt makes equity a call option on the firm. Due to the call option characteristics of equity, taking a negative NPV project with high risk may increase the value of the equity more than taking a relatively safe, positive NPV project. This asset substitution effect is an agency cost of debt financing.
Agency costs associated with debt
(1) Value (residual) loss due to the asset substitution (of lower NPV projects for higher NPV projects)
(2) Monitoring and bonding expenses related to writing bond covenants and enforcing them (that may be necessary to reduce the asset substitution problem).
(3) Bankruptcy and reorganization costs
Note: Due to perfect and competetive capital markets, where investors are rational and expect behaivour. These cost will often fall upon the agent, and it is in his/her interest to minimize these costs thourgh covenants etc.
A good answer to the question must contain an explanation of the source of the asset substitution problem that is present here ‐> namely that A+B is a mutual hedge so that there is an (asset substitution type) incentive problem to remove the hedge to increase volatility of assets and thereby equity value.(Think call an put option graphs)
Jensen (1986) pointed out that debt may also have a beneficial effect on the agency costs in the manager - shareholders relationship: Debt commits the firm to pay out “free” cash (liquid assets) and therefore limits the funds available to the manager for expenditure on perquisites.
Two possible solutions if firm cannot obtain debt financing:
- Debt covenants
- Mix of internal and external debt
Modigliani & Miller’s
Assumptions
- Capital markets are frictionless (no transaction costs or other imperfections).
- Individuals can borrow and lend at the risk-free rate
- There are no bankruptcy costs
- The only form of tax is corporate tax
- Symmetric information (no incentives for signaling)
- Managers always maximize shareholders’ wealth (no agency costs)
- No strategic impact on input and output markets
Jensen & Meckling
Summary
Jensen & Meckling (1976) are looking at theory of property rights, agency and finance, and develop a theory of ownership structure. In the paper agency costs regarding issue of equity and debt is central in the paper.
J&M start by considering the situation where the manager own 100% of equity. In this situation, the manager will consume perks, until the marginal utility of consuming perks equal the marginal utility of additional wealth. If the manager decide to sell a fraction of the firm agency cost will arise because the manager no longer has to the full cost of his perks consumption, which leads the manager to consume more perks. This is obviously not ideal for an outside investor, but it can be limited by monitoring activities and budget constraint. But due to the equity markets anticipation of managers behavior, the manager himself will be the one that will bear the cost of his additional perks consumption in full, because his change in behavior would be reflected in the price of the firm. Another agency cost with issuing equity is bonding cost; such as having the financial account audited by a public account, or limits on the managers decision making power. The manager will be willing to use the same amount on bonding costs that minimzes the combiner cost of monitroing and bondig. The total agency cost with selling equity is the sum of monitoring cost, bonding cost and the residual loss due to increased perks consumption. The manager will bear the entire cost through the reduction in price of firms equity.
The paper also considers agency cost involved with issuing debt. They start with an example; a firm that has no debt has the opportunity to take one of two mutually exclusive investment, both of which yields a random payoff. The investment have the same distribution, but different variance. If the manager can decide first to issue debt, and then choose a project, he will not be indifferent, as he would otherwise be. He would be incentivized to take the high variance project, due to limited downside, while still having access to the full upside. However, this will be included in bondholders rational expectations, they will know managers incentives do choose high variance project and price accordingly. This leads to a residual loss, just as with issuing equity. As with non-managing equity holders, bondholder can limit managers behavior. This can be done by using provisions, but to completely protect bondholder those provisions would have to be extremely detailed, almost making bondholders the management. All the monitoring costs (and possible residual loss) and is taking into account when the debt mispriced. Making the manager the one who bear the cost, or makes him unable to attain debt financing.
J&M also considers another agency costs associated with debt; bankruptcy cost. Bankruptcy is not cost-less, and is the concern of debtholders. This is also taking into account when debt is priced.
So far all arguments are in favor of the manager to keep 100% of his assets inside the firm, because then he avoids taking the on the agency costs. However, there is and argument against this, and that is diversification. Because if the manager has 100% of his wealth in the firm he cannot diversify his portfolio, making him bear a welfare loss associated with bearing more risk than is necessary. Given optimal outside financing the diversification is equal to the agency cost. There may also be other factors outside the model that leas to the manager having to refinance.
Tax shield substitutes
A tax shield may be considered a (derivative) asset (on the firm). The cash flows to the tax shield are tax reductions obtained by being able to deduct cash flows to the underlying asset as costs in the firm’s income statement. There is a limit to the total value of tax shields a firm may have. This limit is equal to the value of the government’s entitlement to tax payments (in the absence of TS).
Put another way, when the firm has enough deductions to reduce its taxable income to zero, then no further gain can be attained from tax shields. We may expect that the more tax shields the firm has available through, for instance, depreciation expenses and investment tax credits, the lesser is the tax shield the firm can obtain from debt and therefore, the lesser is the firm’s use of debt financing.
Violation of APR rule
Short- vs longterm debt reasoning, and empirically
One could that short-term debt contracts are in effect more seniorthan longterm debt contracts even if nominally less senior.
Two reasons
1) It is possible that the subordinated debt is paid in full, while the senior debt is not, simply because the subordinated debt matures first.
2) Short-term debt has more power to force bankruptcy in the short-term. (Need to reason why this is, and why shot-term prefers renegotiation over bankruptcy)
(For 2) This gain in seniority may be achieved through renegotiation with the firm or with the senior creditors.
Empirically, bankruptcies (in the US) almost never follow the stated absolute priority rule (APR) which specifies that (in bankruptcy) senior claims are paid in full before junior claims receive any payments. Typically, subordinated debt (and even equity) receives more than it is supposed to according to APR, and senior claims get less.
Cost of capital
Definition, reason for differing and seperability
A project’s cost of capital is the minimum risk-adjusted rate of return the project must earn in order to be acceptable to shareholders. The shareholders’ investment policy is then to adopt all (independent) projects with a rate of return no less than the cost of capital for the project.
CoC may vary between projects for several reasons. Most importantly different systematic risk. Also; different debt capacities, different taxation and so on that also may lead to different costs of capital.
Typical CoC measure: The weighted average cost of capital (WACC) is the weighted average of the cost of equity, ks, and the cost of debt, (1-tc)kb, where the weights depend on the value of debt, B, and the value of equity, S
Seperability of financing descisions
Case 1: The WACC is independent of leverage
The WACC does not vary with leverage in Modigliani & Miller’s model (riskless debt) and in Hsia’s model (risky debt) with no taxes.
In this case, the financing decisions and the investment decisions are completely separable. All independent projects that earn a rate of return higher than the project’s WACC should be accepted
Case 2: The WACC depends on leverage
A) The firm has decided on an “optimal” capital structure and all projects can appropriately be financed with the “optimal” debt/equity ratio. In this case, the WACC calculated using the optimal debt/equity ratio can be used.
B) Different projects have different optimal capital structures and adoption of projects may change the optimal capital structure of the firm. In this case, the investment and financing decisions are not separable. The decision on whether or not to adopt a project must be performed in conjunction with the decision on how the project should be financed.
In A we use old WACC, in b we use new WACC. Important part is to discuss which one to use! Important factors in the decisions would be the size of impact on firms short term capital structure, and if lare, a discussion or wether or not this is likely to be a long- or shor-term shift in the companies capital structure. We use to compare with what we expect to be the long-term WACC!
CoC with risky debt
Risky debt does not imply that M&MI is violated, nor does it imply that VL = VU + tcB is violated in the presence of taxes. On the contrary, there results still obtain given the right circumstances/assumptions.
4 Assumptions:
- Modigliani & Miller’s assumptions + no taxes, so that capital structure is irrelevant
- Black & Scholes’ assumptions so that their call and put formulas hold’
- CAPM holds (ICAPM)
- The firm issues pure-discount bonds
Suppose the firm’s debt matures at time T and has face value D. The debt does not make interim interest payments since it is zero-coupon and we also assume that the firm pays no dividends. Let V denote the value of the firm at T.
If V >= D, then the firm is solvent and the creditors receive D. If V < D, then bankruptcy occurs and the creditors receive V. So at maturity creditors recieve: min(D,V) = D - max(0,D-V) –> risky corporate debt is equivalent to a portfolio of riskless debt plus a written put!!
If V >= D, the shareholders receive what’s left over after the debt is paid off, V - D. If V < D, then the shareholders receive nothing. So shareholders recieve: max(0,V-D) —> Shareholder payoff equal to a call option on the firm with exercise price D.
Binomal option pricing
Arbitrage pricing –> Do not need probabilites, and cannot induce probabilities from it.
We can interpret Pu as today’s price for a dollar delivered at time 1 if the state then is U. Correspondingly, Pd is today’s price for a dollar delivered at time 1 if the state then is D.
rf = 1/(pu+pd)
PS! When risky debt there is a difference between interest rate and expected interest rate. We can only see interest rate, and not expected interest rate (=cost of debt) due to us not having probabilities.
Several periods
Asset B need no longer be completely riskless; it is sufficient that it is locally riskless. This means that the return next period is known, but one does not know the return over periods further into the future. This situation corresponds to rolling over one-period zero-coupon bonds.
We can now price one-period “up” and “down” securities as before, where now these prices in general will depend on the current state. To prevent arbitrage, we need d<r></r>
<p>We can combine DU and UD only if both underlying assets have recombining trees, and we only want to price path independent derivatives. </p>
</r>
Benefit from leverage
A. Miller & Modigliani’s Model
Shareholders extract the benefit from leverage, if they sellf the bonds at fair value, equal to the size of the tax shield (assuming no other frictions)
P - PV(NBC) = B - B*(1-tc) = B*tc = the gain from leverage
B. Miller (1977)
A bondholder will buy a positive fraction x of bond issue if the present value of the cash flows from holding these bonds, exceed the cost of buying them. In equilibrium, an investor buys the taxable bonds if tipB , is less than tc.
The gain to shareholders is equal to the proceeds from the bond issue less the present value of future net cash flows paid to bondholders. So they are unable to extract any gain from leverage, but they do not loose either.
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However, there is a gain from leverage for private investors. The gain from leverage is obtained by all investors that optimally buy corporate bonds in equilibrium. An investor’s gain is proportional to the difference between tipB and tc. Shareholders will want to issue bonds if they have marginal tax rate on income from bonds lower than the corporate tax rate such that they can make a profit by buying bonds.
Pro forma
Balance, income statement, accounting relationship and choices
The left side of the pro forma balance sheet is the present value of future net cashflows from the pro forma income statement. Thus, what one chooses to include under costs* in the pro forma income statement affects the net cashflow, and therefore also the present value of the net cashflow on the balance sheet.
An accounting relationshi__p is an identity, assets must equal liabilites. An accounting identity is an equality that must be true regardless of the value of its variables, or a statement that by definition (or construction) must be true.
Choices: Need to choose what to include on the liabilites side of the balance sheet, as this will cdecide what is included in cost* on the income statement. One choice we need to make is for example if we want to inclide any stakeholders, i.e. taxes or employees (add employyes as liability, do not deduct salar payments in income statement.
If we want a pure shareholder perspective we could remove taxes and debt from the liability side, we should include leases as a type of debt in this intance.
Myers and Majluf
Summary
The logical chain that should be carefully explained should at least contain: info asymmetry ‐> mispricing ‐> distortion of incentives ‐> preference over type of capital (defined by its information sensitivity) ‐> pecking order and over‐/underinvestment.
M&M look at how asymmetric information affects a firms decision to go through with positive NPV projects. The manager has more information about the real value of the firms assets, and the real NPV of the proposed project than the market. Therefore we have asymmetric information. The papers consider three ways of financing; slack, equity issue and debt issue.
The papers start by considering equity issue to finance projects. It is assumed that the management act in the best interest of old shareholder, and that the old shareholders are passive. Myers and Majluf continue to show that firms will not got through with all positive NPV projects, as one at first might assume is the case. Because there is a tradeoff between the slack and assets that go to new shareholders, and the NPV obtained by old shareholders (E/(P+E))*(S+a)<=(P/(P+E))*(E+b). Therefore the firm might not choose to go ahead with positive NPV project because the firm is undervalued by the market. On the other hand firms will have incentive is issue and invest if the equity of the firm is overpriced, which the markets know. Therefore we often see in the real world that stock price on average will fall after the announcement of an equity issue.
While the firm may not go ahead with positive NPV projects that have to be financed with equity, it will always go ahead with positive NPV projects that can be financed with slack. When projects are financed by slack the firm does not have to interact with the market, and whether or not the firms equity is underpriced is of no consequence. Therefore, holdind slack has value for the firm! Risk free debt has the same effect as slack, and the firm will therefore never pass on a positive NPV project that can be financed with risk-free debt.
However with risky debt there may be scenarios where firms will pass on positive NPV projects. This depends on the pricing of the debt. Fewer projects however will be passed on by the firm when their financed by risky debt instead of equity. Risky debt depend less on the actual underlying value of the firm than equity, making debt less risky, and the mispricing also therefore smaller. Therefore we can conclude that when a firm is willing to issue equity and invest, it is also willing to issue debt and invest. On the other hand there are situations in which firms will want to issue debt and invest, but are not willing to issue equity and invest. It follows that the firm will never issue equity when it can issue debt, and the firm will never issue risky debt when it can use slack of risk-free debt. The result of this is the pecking theory: To finance a project, the firm prefers slack/risk-free debt, then risky debt, and equity as a last resort.
So to conclude, adverse selection due to information asymmetry skews the investment decision away from maximization of true value (away from efficiency). In general, both over- and underinvestment may arise in the model.
A multitude of potential solutions exist, from trying to remove the asymmetry directly to coping with it by making use of less information sensitive sources of financing (the famous pecking order), etc. A good answer should provide discussion of pros and cons of various remedies such as disclosure (direct asymmetry reduction), cash balances (contrast with Jensen’s free cash flow), etc. A relevant point to bring in is that firms are in very different circumstances, so solutions should be tailored to the firm. E..g. internal financing is a less plausible solution for a young growth firm than a mature firm, etc.
We should also take two other istuations into account, altough M&M lays most emphasis on the effect of assymetric information if managers act in the interest of old passive shareholder. There are two other situations M&M considers. (1) The management acts in the interest of all shareholders, and ignores the conflict of interest between new and old shareholders, and (2) the management acts in the old shareholders interest, but assumes the old shareholders rationally rebalance their portfolios as the learn of the firms action. In both these scenarios only NPV matters for managers decisions, as financing no longer matters.
