Finance TheoryAn Introduction to the Theory of Corporate Finance

Instructor: Chyi-Mei Chen(TEL) 3366-1086(Email) cchen@ntu.edu.tw

1. Let us start with two fundamental questions in corporate finance.

• First, what is a firm (in economic sense), and what factors deter-mine a firm’s size, boundaries, and scope?

• Second, what should a manager’s objectives be if he is benevolentand loyal to the investors?

2. Consider the first question. The neoclassic theory of the firm, whichcan be found in a standard textbook in Microeconomic Theory, takes apurely technical view. A firm produces its output using several inputs,and some of the inputs (e.g., managerial talent) cannot vary easily withthe scale of the firm. Thus the average cost curve first decreases andthen increases with the output level. This gives rise to an efficientsize (or output level) q∗ of a “firm” (or more precisely, of a “businessunit”).

The neoclassic theory of the firm is useful, for example, in analyz-ing firms’ competition in the product and input markets and theiraggregate behavior, but the theory itself is silent about the internalorganization of a firm, and moreover, it is silent about when two sim-ilar business units each producing q∗ units of output should remainas two separate firms, and when they should instead be included in alarge firm as two divisions or plants.

The principal-agent theory of the firm developed subsequently recog-nizes the agency problems that may happen between two businessunits. For example, a retailer must buy some product from a risk-averse manufacturer, and the product quality, q, which is verifiable,depends on the manufacturer’s effort and some random factors beyondthe two firms’ control. The manufacturer’s effort choice is the manu-facturer’s private information but the retailer can obtain a noisy signals about it. The retailer can offer a menu of wholesale prices P (q; s)to the manufacturer. This is the classic moral-hazard model; see for

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example Fudenberg and Tirole (1990, Econometrica) and Hermalinand Katz (1991, Econometrica). The contract P (q; s) typically failsto implement the first-best outcome (which is attained if risk-sharingand production are both efficient), and the contracting efficiency de-pends on the precision of the signal s, which measures the informationasymmetry between the retailer and the manufacturer. It is usually“argued” that s will become more precise about the manufacturer’s ef-fort choice if the retailer and the manufacturer can merge and becometwo divisions of the same firm. There is something missing here evi-dently, for otherwise the afore-mentioned agency problem would implythat all firms should merge and there should be only one huge firm inthe world.

Note that the first-best outcome is usually not attained in the aboveagency model simply because some relevant variables like the manu-facturer’s effort choice may not be observable to all contracting parties.However, it is assumed that writing a comprehensive contract (a con-tract that specifies very detailed actions that the contacting partiesshould take in every future contractible contingency) is not costly inthe agency model.1

In contrast, the transaction costs-based theory of the firm advanced bythe 1993 Nobel winners Oliver Williamson and Douglas North pointsout and emphasizes the inadequacy of contracting. At first, peopleare boundedly rational, and may not be able to plan for each of thenumerous future contingencies. Second, even if they can plan for eachfuture contingency, two contracting parties may have difficulty findinga common language to communicate about what each of them shoulddo in a particular future contingency. Third, even if they can find acommon language to communicate, they may have difficulty writingdown their agreements for each future contingency in such a way thatthe court of law will fully understand those agreements. Consequently,contracts should be highly incomplete.

Now, to introduce the transaction costs-based theory of the firm, recallthe two business units that we referred to as the retailer and the manu-facturer. These two business units may want to sign a contract to carry

1In fact, following a theorem in Holmstrom (1982, Bell Journal of Economics), thesecond-best agency contract is typically highly comprehensive.

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out some kind of strategic cooperation. To this end, each business unitmay need to make some relationship-specific investments ex-ante, andboth business units must employ their physical assets and managerialtalents in a first-best way in each ex-post contingency. A relationship-specific investment is, by definition, different from a general-purposeinvestment. A general-purpose investment by the manufacturer, forexample, may still generate decent payoffs to the manufacturer even ifthe retailer breaks up with the manufacturer. A relationship-specificinvestment by the manufacturer, on the other hand, can generate de-cent payoffs to manufacturer only when the two firms’ cooperationcontinues.

In many real-world cases, the relationship-specific investments are cru-cial in ensuring high profitability of the cooperation between the con-tracting parties.2 However, contract incompleteness may result in thecontracting parties biasing toward more general-purpose investments.Why? This happens because the values of these ex-ante investmentsare locked into the contracting relationship, and they are unverifiable,and the incomplete contract may be silent about how, ex-post, thecontracting parties should share the surplus generated by one con-tracting party’s ex-ante relationship-specific investment. Ex-post, thecontracting parties may need to bargain about the division of thatsurplus, and worried about his ex-ante investment being expropriatedby other contracting parties (a hold-up problem), a contracting partythus has an incentive to make his ex-ante investment less relationship-specific. This reduces the gain produced by the cooperation of thecontracting parties. Williamson thus argues that the contracting par-ties should merge into one firm when the ex-ante relationship-specificinvestments are important and yet vulnerable to the ex-post oppor-tunism, because the ex-post hold-up problem facing two business unitswithin a firm is less severe than the same problem facing two separatefirms.

Oliver Hart’s property rights-based theory of the firm is motivated byWilliamson’s theory, and he points out that it is unsatisfactory to as-sume that two business units within a firm will automatically have a

2Think about the on-going cooperation in advertising and search between Microsoftand Yahoo!; see their contract athttp://www.sec.gov/Archives/edgar/data/1011006/000119312509163909/d8k.htm.

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less severe hold-up problem (or have a less severe problem of informa-tion asymmetry, as “assumed” in the agency theory). In his work withGrossman (1986, Journal of Political Economy), they ask, respectively,when the above manufacturer should take over the retailer, when theretailer should take over the manufacturer, and when the two shouldremain separate firms.

Grossman and Hart’s main argument is as follows. Each businessunit is run by a talented manager, and may possess some physical as-sets. Strategic cooperation between two business units requires a jointforce of these assets and managerial talents, but how these resourcesshould be employed depends on and varies with the ex-post future con-tingency, and the ex-ante incomplete contract may have to be silentabout it. In this case, the incomplete contract can specify ownershipof a physical asset, or equivalently, it can specify the manager that isin charge of deciding how to use that physical asset. If the retailer’smanager is delegated with the right to decide how to use the retailer’sand the manaufacturer’s physical assets, then we say that the retailerhas “owned” the manufacturer, or the retailer has taken over the man-ufacturer. Similarly, if the manufacturer’s manager has the right todecide how to use the two firms’ physical assets, then we say that themanufacturer has taken over the retailer. In the remaining case, eachfirm’s manager can decide how to use its own physical assets, and wesay that no takeover has taken place.

Grossman and Hart point out that, although under the initial incom-plete contract, the owner of a physical asset may not want to imple-ment the first-best production plan in an ex-post contingency, as longas there is no ex-post information asymmetry between the two firms,the two firms will jointly implement the efficient strategy after rene-gotiation; recall that the same point has been made in Aghion andBolton (1992). (This is simply an application of Coase’s theorem!)Thus ex-post production efficiency is always attained. The problemis whether the two firms have the right incentives to carry out thefirst-best ex-ante relationship-specific investments. The answer is typ-ically negative. Grossman and Hart compare the two takeover optionsand the no-takeover option, and show that whether (and which typeof) a takeover will take place depends on which of the 3 choices canminimize the ex-ante investment inefficiency.

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Recall that, as in Williamson’s theory, the ex-ante inefficiency arisesbecause a party making the relationship-specific investment gets wor-ried about the other party expropriating the surplus generated by hisinvestment. Ex-post, a business unit that “owns” more physical assetscan ensure itself a higher status-quo payoff even if the other businessunit’s manager chooses to not cooperate, and hence the former busi-ness unit has a better incentive to carry out the ex-ante relationship-specific investment. Thus, for example, after the manufacturer takesover the retailer, the retailer would have little incentive to carry outthe relationship-specific investment, but the manufacturer may have amuch better incentive to do so. The opposite tends to happen if theretailer takes over the manufacturer. In the remaining case where thetwo business units remain separate firms, they both have moderate in-centives to carry out their ex-ante investments. Therefore, dependingon which party’s ex-ante investment is more valuable, the two businessunits may decide to undertake a merger, or to remain separated.

Thus Hart’s property rights-based theory gives a formal definition ofownership, or property right, and this theory is useful for us to un-derstand why some firms choose to stay separate and others choose tomerge. This theory also explains why some conglomerates may engagein spin-offs and/or other kinds of divestiture.

Grossman and Hart’s analysis is conducted for a simple economic envi-ronment where there is no asymmetric information between the busi-ness units. Their followers have recently considered more complicatedsituations where business units have asymmetric information and arefaced with multi-lateral moral hazard problems. This literature thendiscusses the optimal design of heirarchical structure of a firm, theoptimal span of control for a manager, and organization of the inter-nal capital market. Internal organization of a firm is closely relatedto and interacts with the industrial organization in which the firm isoperating.

3. Now, consider the second fundamental question in corporate finance,“Who are the investors that the managers should be loyal to, if thefirm’s shares are actively traded in the secondary market?” A definiteanswer is provided by Irving Fisher’s separation principle, which statesthat in making any financing and investment decisions a benevolentmanager should seek to maximize the value of the firm, if financial

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markets are complete and perfect, and product markets are perfectlycompetitive. Thus a benevolent manager does not need to know whoare possessing the firm’s shares at the time he makes a financing orinvestment decision, if the stated conditions hold.

In case the above stated conditions do not hold, then value-maximizationmay not be unanimously accepted by all investors. In the latter case,the benevolent manager must adapt his financing and investment de-cisions to the investors’ preferences. What might happen when theabove conditions fail?

• First, suppose that markets are incomplete so that some con-sumption good is currently not supplied by any firm. In thiscase, it can happen that a shareholder may prefer a productionplan that involves producing that missing consumption good tothe value-maximizing production plan that will not produce thatmissing consumption good. This is referred to as the consumptioneffect.

• Next, if the firm is strategic rather than price-taking (so thatproduct markets are not perfectly competitive), then a value-maximizing plan that will produce a lot of good X may cause theprices of its close substitutes to drop, thereby hurting a share-holder who carries a lot of these goods. This is referred to as theprice effect; see Gabseiwicz and Vial (1972, Journal of EconomicTheory).

• Finally, by changing its production plan in incomplete financialmarkets, the firm (however small) can typically alter the linearspan of traded financial claims, which changes a shareholder’sinvestment opportunity set. A production plan may benefit ashareholder via this effect than a value-maximizing productionplan. This is referred to as the security effect; see Hart (1979,Review of Economic Studies).

In view of the above discussions, taking value-maximization as a firm’sgoal is improper in most cases. Nonetheless the most part of corporatefinance literature has chosen to bypass the aforementioned effects byfocusing on a perfect financial eocnomy with risk-neutral people andone single consumption good. The former assumption implies that

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financial markets are perfect and complete, and the latter assumptionbypasses the consumption effect.

4. The modern theory of corporate financing starts with Modigliani andMiller’s (1958) Proposition 1, which shows that when perfect financialmarkets are in equilibrium, firms holding the same assets but makingdifferent financing decisions must have the same market value. Indeed,if this were not the case, then an arbitrage opportunity would exist,proving that the markets must be in disequilibrium.3

Given perfect financial markets, can a firm with fixed investmentprojects change its equilibrium value by making different financingdecisions? The answer is negative if markets are complete; that is, ifevery conceivable financial asset is already marketed and traded.4 5

On the other hand, if markets are incomplete, then the answer is gen-erally positive. This explains why a firm may benefit from engaging infinancial innovation by issuing new corporate securities. The followingexample, adapted from a working paper of mine, shows that if onefirm makes an innovative financing decision to alter its own marketvalue, its financing decision also changes the value of other firms hold-ing the same assets as it does. This example also shows that a firmmay reduce its value by engaging in financial innovation, and whetherfinancial innovation benefits a firm depends on investors’ preferencesamong other things.

Example 1 Consider a two-period frictionless economy with a singleperishable consumption good and three price-taking agents. Agent 0owns firm 1, which generates 1 unit of consumption at date 1. Agent

3If firms A and B are holding the same assets at date 0 but firm A has a higher marketvalue than firm B does, then an investor can buy, say, 1% of the securities issued byfirm B and sell short 1% of the securities issued by firm A, and this trading strategyyields a date-0 cash inflow for the investor without any future cash inflows or outflows.Clearly, the existence of such arbitrage opportunities is inconsistent with securities marketsequilibrium.

4A special case is where all investors are risk neutral without time preferences. This is astandard assumption adopted in the corporate finance literature. In such an environmentthe value of a firm is the expected value of the sum of its future cash flows, regardless ofhow the firm is financed. Thus we can conclude that in this case, with fixed investmentdecisions, financing decisions do not affect the firm value.

5For a firm that can make investment decisions after making its financing arrangements,financing decisions generally affect its value, and this is so even if the financial marketsare perfect; see for example Maksimovic (1988, Rand Journal of Economics).

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0 wants to consume at date 0 only, and hence he wants to sell the firmat date 0. For this reason, agent 0 would like to maximize the value offirm 1 (denoted by S) at date 0.

Agents j ∈ {1, 2} seek to maximize

u(c0j) + E[u(c1j)],

where u(·) = log(·), and c0j and c1j are respectively agent j’s con-sumption at dates 0 and 1. There are two equally likely states at date1. In state i, agent i is endowed with X > 0 units of consumption, butagent j is endowed with nothing, where i, j = 1, 2. We shall denotethe state-k realization of c1j by ckj, where k = 1, 2. Both agents 1 and2 are also endowed with one unit of consumption at date 0.(i) First suppose that agent 0 must issue one share of common stockto sell firm 1. Show that the equilibrium firm value is 2X+2

3X+2 , and both

agents 1 and 2 hold 12 shares of the common stock.

(ii) Next, suppose instead that at date 0 , agent 0 decides to sell firm 1by issuing two Arrow-Debreu securities to the market (each with unitsupply), and we denote their prices by p1 and p2 respectively.6 Letaij be the number of shares of the i-th Arrow-Debreu security held byagent j. Show that in equilibrium

a11 = a22 =1−X

2, a12 = a21 =

1 +X

2, p1 = p2 =

1

2 +X

so that the firm value in this case is

2

2 +X,

which is less than2X + 2

3X + 2.

Conclude that a firm’s changing its capital structure may change itsvalue in equilibrium, and that a firm’s value may be higher when mar-kets are incomplete than complete. Interpret.(iii) Now, assume that there exist another 3 investors in the econ-omy, referred to as agents 3, 4, and 5 respectively. Agent 3 wishes

6An Arrow-Debreu security for state i pays its holder 1 dollar if the date-1 state is i,but it pays nothing if the date-1 state is not i.

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to consume only at date 0, and his endowment consists of firm 2,which generates 1 unit of consumption at date 1. Agent 4 has thesame preferences and endowments as agent 1 does. Agent 5 has thesame preferences and endowments as agent 2 does. Assume that firm1 has decided to issue the two Arrow-Debreu securities at date 0, butfirm 2 must remain all-equity financed. Find the equilibrium values forrespectively firms 1 and 2.

Solution. Consider part (i). When the firm issues only equity, withprice S, the maximization problems for agents 1 and 2 have the samefirst-order condition, which is

Su′(1− Sa) = Su′(c0) = E[u′(c1)],

where a is the two agents’ (common) equilibrium stockholding. Notethat we have used the fact that by symmetry, a = 0.5 in equilibrium,and c01 = c02 ≡ c0. Now, it follows from

E[u′(c1)] = 0.5[u′(X + a) + u′(a)] = 0.5[u′(X +1

2) + u′(

1

2)],

that

S · 1

1− S2

=1

2[

1

X + 12

+112

] ⇒ S =2X + 2

3X + 2.

Now, consider part (ii). If markets are complete with pi being thedate-0 price of the i-th Arrow-Debreu security, then by symmetry wemust have p1 = p2 ≡ p in equilibrium. Agent j’s budget constraint isthus

c0j = 1 + pX − p(c1j + c2j).

By symmetry, with complete markets the two agents must also sharethe date-1 aggregate consumption equally in equilibrium, and hencewe have

c11 = c21 = c12 = c22 =1 +X

2.

To carry out these consumption plans, agents 1 and 2 must have thefollowing asset holdings in equilibrium:

1−X

2= c11 −X = a11 = a22 = c22 −X,

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1 +X

2= c21 − 0 = a21 = a12 = c12 − 0.

Moreover, the two agents’ common first-order condition becomes

pku′(c0j) = 0.5u′(ckj), k = 1, 2,

or equivalently, upon recognizing that S = p1 + p2 = 2p and that7

c0j = 1− S

2= 1− p,

we can write the above first-order condition as

Su′(1− S

2) = Su′(c0) = E[u′(c1)],

which looks just like the first-order condition obtained in part (i).

The only difference here is that, in the equilibrium with completemarkets, c1 will be non-random (because agents 1 and 2 are risk averse,and full insurance makes them happy), and in fact

c1 = 0.5(X + 1).

Thus we can re-write agent j’s first-order condition as

S

1− S2

=2p

1− p=

112(X + 1)

⇒ p =1

X + 2,

implying that

S =2

X + 2.

Note that

2

X + 2− 2X + 2

3X + 2=

6X + 4− 2X2 − 6X − 4

(X + 2)(3X + 2)< 0.

Hence the firm value is lower in part (ii) than in part (i).

More generally, if u′(·) is strictly convex (which is true when u(·) isthe logarithmic utility function), then by Jensen’s inequality we have

u′(0.5(X + 1)) < 0.5[u′(X + a) + u′(a)],

7The date-0 market for the consumption good must clear, and hence we must havec01 + c02 + S = 2, where S is agent 0’s date-0 consumption, and recall that the date-0 aggregate consumption is 2. By symmetry, we must also have c01 = c02 ≡ c0 inequilibrium.

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implying thatSu′(c0) = Su′(1− 0.5S)

is higher when the firm issues only equity than when it issues thetwo Arrow-Debreu securities. Note that the function Su′(1 − 0.5S)is strictly increasing in S. We conclude that the equilibrium value offirm 1, S, must be higher when the firm issues only equity than whenit issues the two Arrow-Debreu securities. Apparently, the oppositeholds true when u′(·) is strictly concave.

Now, consider part (iii). Let Sk be the equilibrium value of firm k atdate 0. We claim that in equilibrium

S1 = S2 =2

2 +X

and the prices of the two Arrow-Debreu securities are as described inpart (ii). The equilibrium consumption and portfolio decisions madeby agents 1 and 2 are also as described in part (ii). Note that agents4 and 5 must make the same equilibrium consumption and portfoliodecisions as respectively agents 1 and 2 do. Indeed, taking p1, p2, S1

and S2 as given, agent 4’s equilibrium trading strategy is to buy afraction 1−X

2 of ownership of firm 2, and to buy X units of the secondArrow-Debreu security; while agent 5’s equilibrium trading strategy isto buy a fraction 1+X

2 of ownership of firm 2, and to sell X units ofthe second Arrow-Debreu security. Thus at the prices p1, p2, S1 andS2, markets clear once again.

We have learned two things from this example. First, a firm’s financingdecision can change its value (parts (i) and (ii)), and its financingdecision creates an externality on the value of another firm holdingthe same assets as it does (part (iii)). Second, a firm need not have anincentive of engaging in financial innovation, even if the latter incursno costs.8 The upshot here is that with perfect but incomplete marketsboth investment decisions and financing decisions may affect the valueof a firm.

5. From now on, we shall mostly confine our attention to the case whereall investors are risk-neutral without time preferences. Recall thatin this environment, if investment decisions are pre-determined and

8See Allen and Gale (1994) for more theories on financial innovation.

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financial markets are perfect, then financing decisions can no longeraffect the value of a firm.

If financial markets are imperfect, then financing decisions may af-fect the value of a firm even if investment decisions have been made.Indeed, in the presence of taxes and costs of financial distress and/orbankruptcy, the static trade-off theory (Myers 1984) asserts that therein general exists an optimal mix of debt and equity for each firm. Miller(1977) points out that with investors having heterogeneous personaltax brackets and firms having heterogeneous corporate tax brackets,there generally exists an optimal mix of debt and equity for the entirefinancial economy, but firms belonging to the same risk class need notend up making the same financing decisions in equilibrium. In otherwords, in the competitive equilibrium of financial markets with taxes,firms that possess the same assets may end up with different capitalstructures; thus there is no single optimal capital structure for a firm.The following is an example.

Example 2 In a simple world composed of 3 groups of investors, thefollowing table summarizes the personal tax rates for these investors.

Group Tax RateA 60%B 40%C 0%

Investors can choose to hold (i) perpetual municipal bonds, (ii) per-petual corporate bonds, and/or (iii) common stocks. Municipals andcommon stocks attract no personal tax. Interest payments from cor-porate bonds attract personal tax but is deductible for corporate tax.The corporate tax is flat at 50%. Interest payments on municipals to-tal $20 million in each period. Cash flows (before interest and taxes)from corporations total $300 million in each period, and corporationsdo not retain earnings. You are told that the equilibrium holdings ofeach group of investors are worth the same, which also represent theequilibrium wealth of that group of investors. All investors require anafter-tax rate of return of 10% on every security.

Show that in equilibrium the aggregate value of equity is $37007 million,

the aggregate value of corporate debt is $102007 million with coupon rate

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16.67%, and the total value of municipal bond is $200 million withcoupon rate 10%.9

Solution. Suppose that group i investors receive pretax cash flow xifrom corporations in each period. Since the current wealths of the 3groups of investors must be the same, we have

xA · (1− 50%) = x− 20,

xB · (1− 40%) = x,

xC · (1− 0%) = x,

where x is the after-tax cash flow to every investor in each period.Note that we have made the observation that all municipals must beheld by group A investors in equilibrium (why?). Since

xA + xB + xC = 300,

we have

x =510

7million.

Now the rest is easy.

6. Following Modigliani and Miller’s Propositions, the existing theoryof corporate finance has mostly assumed imperfect financial marketsand/or post-financing investment decisions. Corporate agency modelswere first developed in Jensen and Meckling (1976) and Myers (1977).The former emphasizes (i) the agency cost that arise from separation

9Try to answer the following questions.(a) Suppose that companies are initially financed by equity only. Firm X now decidesto allocate 1 million dollars of its pretax cash flow to interest payments on debt. Whichgroup or groups of investors will buy this debt? At what interest rate? What will be theeffect on the value of firm X?(b) Suppose that other firms have followed firm X and interest payments now total 150million dollars. At this point, firm Y decides to allocate 1 million dollars to interestpayments on debt. Which group or groups will buy this debt? At what interest rate?What will be the effect on the value of firm Y?(c) Total interest payments has somehow risen to 250 million dollars. Now firm Z decidesto substitute common stock for debt, thereby reducing interest payments by 1 milliondollars. Which group or groups of investors will sell their debt to Z? At what rate ofinterest can firm Z repurchase the debt? What will be the effect on the value of firm Z?

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of management from full ownership and (ii) the asset substituion prob-lem pertaining to the use of risky debt. The latter paper emphasizesthe debt overhang problem pertaining to the use of long-term debt.Then, financial signaling models were developed in the 1970s and 1980sto explain the signaling role of financing decisions. The literature ofoptimal financial contracts has been growing since 1980s. The studyof the interactions between financing decisions and product marketcompetition was burgeoning in the 1980s and 1990s. We shall reviewin this note the literature of financial signaling and the various stan-dard financing instruments, and talk about two models of incompletefinancial contracts. The rest will be discussed in another lecture note.

To start, we shall briefly go over two financial signaling models in the1970s. They are Ross’s (1977) debt signaling model and Leland andPyle’s (1977) ownership signaling model.

7. Let us consider Ross’s (1977) debt signaling model. Everyone to ap-pear in this model will be risk-neutral without time preferences. Mr.A owns and manages a firm at date −1. With probability k, he maybe hit by a liquidity shock at date 0, and in that case he needs to sellthe firm to outsiders at price V0. With probability 1 − k, he can runthe firm till date 1 without having to sell the firm to anyone by thattime. The firm generates a one-time cash earnings X at date 1. Itis common knowledge at date −1 that X is uniformly distributed on[0, t], conditional on the firm’s true quality t, which is a continuousrandom variable with support [c, d], where d > c ≥ 0.

The game proceeds as follows. At date −1, Mr. A privately observesthe realization t of t. Then Mr. A must reorganize the firm’s capitalstructure by issuing debt with face value F and using the proceeds torepurchase shares. The choice of F has the following consequence atdate 1: Mr. A will incur a reputation loss L (in monetary terms) atdate 1 if he is still running the firm at date 1 and if F > X. At date 0,upon observing Mr. A’s choice F , the public investors then compute

V0 = E[X|F ].

Then Mr. A must sell the firm for V0 if he is hit by the liquidity shock;or else, the game moves on to date 1, and in the latter case, Mr. A’sdate-1 payoff is X if F ≤ X and X − L if F > X.

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We shall look for a separating equilibrium, in which Mr. A’s choiceof face value is F ∗(t) if his type is t ∈ [c, d], and in which the publicinvestors’ posterior beliefs are such that the firm’s true type is a(F )with probability one upon seeing face value F , and hence they pricethe firm at

V0 =a(F )

2.

If such an equilibrium exists, then at date −1, F ∗(t) must solve thefollowing maximization problem for Mr. A:

maxF

ka(F )

2+ (1− k)[

t

2− LF

t].

Let us conjecture that F ∗(t) satisfies the following first-order condition

ka′(F ∗(t))

2= (1− k)

L

t,

and we shall confirm this conjecture later on.

Now, recall that in a Nash equilibrium beliefs are all correct; that is,we must have t = a(F ∗(t)), ∀t. Thus we get

k

2dF ∗(t)dt

=ka′(F ∗(t))

2= (1− k)

L

t,

or equivalently,kt

2(1− k)L=

dF ∗(t)

dt,

implying that for some constant b, we have

F ∗(t) =k

4(1− k)

t2

L+ b.

Now we can impose the boundary condition F ∗(c) = 0 (i.e., the lowesttype does not signal in a separating equilibrium) and get

F ∗(t) =k

4(1− k)L[t2 − c2].

Observe that

a(F ) =

√4(1− k)LF

k+ c2

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is a concave function in equilibrium, and hence our conjecture thatF ∗(t) must satisfy the first-order condition is indeed correct.

Note that in the above separating equilibrium (i) there is an optimalcapital structure for each risk class t; and (ii) the firms within thesame risk class have the same value V0. Although this is a separatingequilibrium, note the inefficiency resulting from excessive use of debt.The idea is that it is less costly for a high quality firm to take moredebt, and hence a high quality firm can undergo such a costly signalingprocess to distinguish itself from its low quality counterpart.

8. Now we review Leland and Pyle’s (1977) ownership signaling model.Mr. A owns a firm at date 0 and he wants to sell a fraction (1 − k)of ownership in order to diversify. Suppose that the Sharpe-LintnerCAPM holds, and that Mr. A will allocate the proceeds of sellingequity to the market portfolio and the riskless asset. The firm mustinvest one dollar at date 0, which generates cash earnings

X = µ+ e

at date 1, where µ ∈ [µ, µ], and e ∼ N(0, σ2). Assume that µ is Mr.A’s private information, but outsiders take k to infer µ via µ = g(k),where g(·) is some monotone function. We shall look for a separatingequilibrium where the outsiders’ belief g(·) is fulfilled. Recall thatgiven g(·), according to the CAPM, the value of the firm is

V (k) =g(k)− λ

1 + rf,

where

λ =cov(X, rm)

var(rm)[E(rm)− rf ].

Mr. A only consumes at date 1, and he maximizes his expected utilityfrom date-1 consumption E[u(c)], where

u(c) = −e−c.

Thus, given g(·), Mr. A’s problem is

maxk,a,b

E[−e−c]

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subject toc = k(µ+ e) + a(1 + rm) + b(1 + rf )

a+ b+ 1 = w + (1− k)V (k).

Note that w is Mr. A’s date-0 initial wealth, a the amount to invest inthe market portfolio at date 0, b the amount to invest in the risklessasset at date 0, and the date-0 capital outlay is 1 dollar. For simplicity,let w = 1, so that

E[c] = kµ+ a(1 + µm) + [(1− k)V (k)− a](1 + rf )

= kµ+ a(µm − rf ) + (1− k)[g(k)− λ],

where

λ =(µm − rf )cov(e, rm)

var(rm),

andvar(c) = k2σ2 + a2var(rm) + 2akcov(e, rm).

Now, Mr. A seeks to

maxa,k

E[c]− 1

2var(c).

The first-order condition with respect to a gives

a =µm − rf − kcov(e, rm)

var(rm),

and the first-order condition with respect to k gives

µ− g(k) + λ+ (1− k)g′(k)− acov(e, rm)− kσ2 = 0.

It follows that

µ− g(k) + (1− k)g′(k)− kγ = 0,

where

γ =σ2var(rm)− cov(e, rm)2

var(rm)≥ 0,

Assume that γ > 0. Now, recall that in equilibrium beliefs are correct;that is,

g(k(µ)) = µ, ∀µ ∈ [µ, µ].

17

This implies that g(·) must solve the following ordinary differentiableequation

(1− k)g′(k)− kγ = 0,

and its solution takes the form of

g(k) = −γ[log(1− k) + k] + d,

where d is some constant. Next, recall that the lowest type does notsignal in a separating equilibrium; that is,

µ = g(0) = d.

It follows thatg(k) = −γ[log(1− k) + k] + µ.

Thus we have a separating equilibrium in which g(·) is strictly in-creasing. In equilibrium, the market believes that it is more costlyfor the entrepreneur to not diversify when µ is smaller. The size ofinsider-owned equity is thus taken as a signal for the quality of thefirm.

9. Now, we continue with the signaling model of Myers and Majluf (1984).Recall the by now familiar pecking-order theory developed in Myers(1984) and Myers ande Majluf (1984), which asserts that a firm shouldfinance its new investments using its financial slack (cash, marketablesecurities, and the riskless debt capacity), and it should choose riskydebt over outside equity if it runs out of financial slack and mustseek external financing. This theory is based on the conjecture that,compared to the equity value, the value of debt is less sensitive tothe true quality of the firm’s assets, so that issuing new equity willencounter a more severe lemons problem than issuing debt. The mainprediction of the pecking order theory is that regardless of its truequality, a firm seeking external financing should always choose debtfinancing over equity financing, or in the jargon of game theory, there isa pooling equilibrium where the firm seeking external financing alwayschooses to issue debt rather than equity.

Now let us briefly introduce Myers and Majluf’s model. There is anall-equity financed firm run by a manager loyal to existing sharehold-ers. The number of outstanding shares is normalized to one. Publicinvestors are risk neutral with no time preferences. At date 0, it is

18

common knowledge that the firm’s assets in place will generate A atdate 2, and the firm will have a new investment project that needscash I at date 1 and generates B at date 2. At date 1, the managerprivately observe the outcomes of A and B , denoted a and b respec-tively. At this time, the firm has financial slack S ≥ 0. If S ≥ I,then it is a dominant strategy that the manager uses the slack to fi-nance I. Suppose then that S < I, and the firm must issue new equityE = I−S. (Note that riskless debt is by definition included in S; riskydebt will be discussed later). At date 2, the realized a and b becomepublic information.

The game actually starts at date 1. The manager first announces theequity issuance and the market responds by naming a share price P forthe stock. Given P , the existing shareholders’ ownership becomes P

P+E

and the new shareholders’ ownership is EP+E if the manager decides to

go along with the deal. The manager can either accept the transactionprice P and raise E or simply give up the new project. Being loyal(only) to the exising equityholders, the manager will accept P andissue the equity if and only if

P

P + E(E + S + a+ b) ≥ S + a ⇔ P

P + E(E + b) ≥ E

P + E(S + a).

The interpretation is that the manager weighs the gain from the presentvalue of the project (the left-hand side) against the loss from sharingthe assets in place with the new shareholders (the right-hand side).The manager will go along with the deal if and only if the gain out-weighs the loss. Thus when the realization of a is high and the real-ization of b is low, the manager tends to give up on the new project.An underinvestment problem thus arises. Since Myers and Majluf as-sume that ex-post (after financing) the manager can at least put theproceeds E in a money market account, here b ≥ 0, and hence therecan be no over-investment problems in this model.

Based on the above analysis, Myers and Majluf argue informally thatrisky debt should always be preferred by the manager to new equity.The idea is that, at date 2, the true value of the firm will be realized.Recall that the date-1 price of equity is the expectd value of its date-2payoff (conditional on the public investors’ beliefs), which is a convexfunction of the firm’s date-2 value. On the other hand, the date-2payoff of debt is a concave function of the firm’s date-2 value. Myers

19

and Majluf then argue that a change in the firm’s asset value leadsto a bigger change in the firm’s equity value (from date 1 to date 2)than in the debt’s value, and since it is the adverse selection problemthat affects the new investors’ valuation for the issued equity or debt,Myers and Majluf concludes that the firm should optimally issue debtrather than equity.

The problem with this informal argument is that, when the managerchooses different financing instruments, the market will form differentposterior beliefs about the firm’s quality; the choice between risky debtand new equity per se is used by the market to infer the firm value.If the market’s beliefs could be held independent of the firm’s choicebetween debt and equity, then Myers and Majluf’s argument wouldseem very appealing, but the whole point of their 1984 paper is todiscuss the signaling role of financing decisions! As we shall see below,their informal argument has been proven to be generally incorrect.

Now, let us examine a numerical example for Myers and Majluf (1984).

Example 3 Firm A has a single owner-manager Mr. A, who needsto raise $100 in order to take a positive NPV project. There are twopossible states, called G and B. In state G, the assets in place of firmA worth $150 and the new project’s NPV equals $20. In state B,the assets in place worth only $50 and the NPV is accordingly $10.The state is Mr. A’s private information. The public investors thinkthat the state is G with prob. a, and they are Bertrand competitive.The game proceeds as follows. The firm chooses to or not to issue newequity. If new equity is issued, the public investors ask for a proportionof ownership with value equal to $100. Find all the pure strategy PBE’sof this signaling game.

Solution We first look for separating equilibria. Suppose there werea separating PBE where only type G issues new equity. Then in ex-change of the $100 raised, the outsiders ask for a share α = 100

150+20+100of the ownership. The type B firm will deviate: By issuing, the insidergets

(1− 100

150 + 20 + 100)(50 + 10 + 100) = 100.74,

which is greater than 50, the value of type B firm if passing on thenew project. Hence, there is no such separating equilibrium. Now,

20

suppose there were a separating PBE where only type B issues newequity. Then, the public investors would ask for a share of ownershipequal to 100

10+50+100 . Type B insider would indeed want to issue: Byissuing, he gets

(1− 100

10 + 50 + 100)(100 + 50 + 10) = 60,

greater than 50. On the other hand, type G insider would not issue ifand only if

(1− 100

10 + 50 + 100)(100 + 150 + 20) = 101.25 < 150,

which indeed is true. Thus this separating equilibrium does exist.

Next, we look for pooling equilibria. Suppose that in equilibrium nei-ther type issues new equity. But then type B wants to deviate: Byissuing, type B cannot do worse than being identified, but even inthat case, issuing is preferred to not issuing. Therefore there is nosuch pooling equilibrium. Suppose now that in equilibrium both typesissue. The fair share of ownership that outsiders would ask for (as-suming risk neutrality of outsiders), α, solves

α[a(150 + 20 + 100) + (1− a)(50 + 10 + 100)] = 100,

and hence

α =100

160 + 110a.

Type G insider must be willing to issue in equilibrium:

(1− 100

160 + 110a)(100 + 150 + 20) > 150;

and so must type B insider:

(1− 100

160 + 110a)(100 + 50 + 10) > 50.

(Note that the outsiders’ beliefs following the off-equilibrium signal“not issuing” is irrelevant here.) Thus the pooling equilibrium existsif a > 13

22 . In this game, both pure strategy PBE’s that we obtainedare robust against Cho and Kreps’ intuitive criterion.

21

This example has several implications. First, when there is informationasymmetry in financial markets, financing does interfere with invest-ment decisions. If the firm is financed by its financial slack (internalequity or riskless debt), then it will accept the new project for sure.External financing involves the problem of adverse selection, and henceit may result in the high-quality firm giving up a valuable investmentproject. Second, as in Ross (1977) and Leland and Pyle (1977), evenif a separating equilibrium exists, it is dissipative. Third, in equilib-rium there is a tension between informational efficiency and productiveefficiency. More precisely, the pooling equilibrium is productively effi-cient because the new project is always financed in equilibrium, but thestock market fails to transmit useful information to public investors ina pooling equilibrium. The separating equilibrium, on the other hand,is informationally efficient, but it involves under-investments on thepart of the high-quality firm. As shown in Brennan and Kraus (1987),this tension need not exist if we enlarge the firm’s strategy space.In other words, if the firm is allowed to adopt more general financ-ing strategies, then Bhattacharya’s (1980) conditions may be satisfied,which ensure the existence of a separating equilibrium where all ef-ficient investment projects are adopted. In this case, in equilibriumboth informational efficiency and productive efficiency are attained.

10. In Myers and Majluf’s model, (i) the insider of the firm has only twopossible types; (ii) the insider has only two feasible signals, to or notto issue new equity (riskless debt of a fixed capacity is part of theslack and is always used up, and risky debt is not rigorously examinedin the paper); (iii) the investment decision is pre-determined and itinvolves a fixed amount of initial outplay; (iv) the insider aims atmaximizing the existing shareholders’ welfare rather than the value ofthe firm; and (v) the firm seeking external financing is currently allequity financed, so that there is no debt outstanding. It turns out thateach of these assumptions is relevant to Myers and Majluf’s peckingorder conclusion.

Regarding (i), Noe (1988) shows that when the firm has more than 2types and can issue either equity or debt , and when the insider, inspite of his superior information about the firm’s true quality, is stillfaced with earnings uncertainty, the firm’s equilibrium financing be-havior may violate the pecking order. Regarding (ii), Heinkel (1982)shows that if the firm can issue risky debt, and if the credit risk of

22

the debt increases with the firm value, then a separating equilibriumthat incurs no investment inefficiency may exist. Regarding (ii) and(v), Brennan and Kraus (1987) show that by issuing equity and retir-ing some existing debt, the firm may be able to fully reveal its truequality without sacrificing investment efficiency. In fact, Brennan andKraus (1987) allow general “financing” strategies, and show that ina non-dissipative separating equilibrium in the financing game, eachfinancing bundle is priced as if the firm is of the type who, if takingthis financing strategy, gives the lowest value for the financing bun-dle. This condition, appearing in other papers in different forms aswell, translates into meaningful characterizations for efficient financ-ing instruments, when the firm’s types are assumed to be ranked byfirst-order or second-order stochastic dominance.

Regarding (iii) alone, Krasker (1986) shows that by allowing the firmto endogenously choose the investment level, the management loyalto existing shareholders and restricted to using only equity financingmay still be able to perfectly reveal the firm’s true quality in equi-librium, although such a separating equilibrium may be dissipative.Regarding both (ii) and (iii), Constantinides and Grundy (1989) showthat by allowing for more general financial instruments than debt andequity (and more general financing activities like share repurchase),a nondissipative fully revealing financing equilibrium may exist. Es-sentially, a more complex instrument and a more complicated financ-ing strategy serves as a multi-dimensional signal, and it promotes thelikelihood of an efficient fully revealing equilibrium. Regarding (iv),Dybvig and Zender (1991) show that with optimally designed man-agerial contracts, the management can be ensured to invest efficiently,and since this can then be inferred correctly by the public investors inequilibrium, there will be no investment inefficiency caused by equityofferings. Persons (1994) show that, the contract derived by Dybvigand Zender (1991) may not be ex-post optimal for the existing share-holders and the manager. If the compensation contract cannot beobserved by the market, and can be renegotiated between the man-ager and the existing shareholders, then no contracts robust againstrenegotiation can ensure investment efficiency. Thus Persons’ paperlays a formal foundation for Myers and Majluf’s rather informal andincomplete theory.

To sum up, several lines of research have beem motivated by Myers

23

and Majluf’s work, and we shall selectively review these papers inthe remaining sections. See Harris and Raviv (1991; 1992) for moresurveys of the earlier theories.

11. Noe (1988) studies a modified version of Myers and Majluf’s problem,where

(a) the firm is initially all-equity financed;

(b) the new project costs I;

(c) everyone is risk-neutral without time preferences;

(d) the insider running the firm (assuming that there is one insider,who will be referred to as the firm interchangeably from now on)has a type t ∈ T ≡ {t1, t2, · · · , tw}, where t = (t1, t2), wheret1 ≥ 0 and t2 ∈ ℜ are respectively the future cash flows to begenerated by the firm’s assets in place and the new project;10

(e) for all t ∈ T , the prior probability p(t) > 0, and each type t hasa distinct t1 + t2;

(f) the firm has 3 feasible signals: e (equity financing), d (debt fi-nancing), and c (giving up the new investment project); and

(g) upon seeing the firm’s signal, the competitive public investors caneither reject the firm’s financing request (n) or ask for a fractionα of ownership if the sigal is e or ask for a face value k of debt ifthe signal is d.

Noe first looks at the case where the firm given its superior informationis faced with no earnings uncertainty; i.e., t1 and t2 are non-randomfrom the insider’s perspective. In this case, Noe’s Lemma 1 showsthat if there exists some type t whose equilibrium signal is d, then forall t′ ∈ T , t′ weakly prefers sending signal d than sending signal e inequilibrium. The idea is as follows. Note that if t′1 + t′2 < k, then t′

will never send d, where k is the equilibrium face value of debt uponseeing the signal d. Thus sending d means that the debt will neverdefault, and this implies that k = I in equilibrium. Now, supposethat some type t′′ strictly prefers sending e to sending d. By sendingd, t′′ would only need to pay the new investors k = I, and hence t′′’sequity issue must be worth less than I. Since the average value of the

10Thus the firm may have a negative-NPV project. Can you offer a reason why a firmmay need to carry out a negative-NPV project after raising the fund I?

24

equity issues reaching the market must equal I, there must exist someother type t′′′ whose equity is worth more than I, but this type shouldhave deviated and sent signal d, because the latter would only cost I.Hence we have obtained a contradiction.

Noe’s Lemma 1 does not rule out the pooling-at-equity equilibriumwhere all types of the firm issue equity, and issuing debt (a zero-probability event!) will be regarded as the worse possible type (thetype with the mimimal t1 + t2). Noe argues that such an equilibriumdoes not satisfy a modified Cho-Kreps criterion, and hence should beignored. Indeed, the only equilibrium where nobody adopts a weaklydominated strategy and where players’ equilibrium behavior satisfythe modified Cho-Kreps critierion is the pooling-at-debt equilibrium,which is Noe’s Proposition 1.

Noe then considers the case where the insider is also faced with earn-ings uncertainty, and he shows that the firm’s equilibrium financingbehavior will in general violate Myers and Majluf’s pecking order con-jecture. The following example is taken from Noe’s paper. Supposethat w = 3, so that the insider has 3 possible types. Suppose thatI = 1, and

t1 = (3

10,12

10), p(t1) =

1

1000,

t2 = (15

10,12

10), p(t2) =

991

1000,

t3 = (200

10,12

10), p(t3) =

8

1000.

The total future cash flow for type tj is equally likely to be tj1+ tj2+1510

or tj1 + tj2 − 1510 .

There is a robust equilibrium for this game in which t1 and t3 issuedebt and t2 alone issues equity. In equilibrium, k = 18

17 and α = 1027 .

Note that t3 is a lot better than t2, which explains why t3 does notwant to issue equity and be treated as t2 in equilibrium. t1 wouldbenefit from mimicking t2 also, but its payoff is higher when it mimicst3. If t2 issues debt, then the debt would be risk-free, meaning that t2

has to pay k for sure. Note closely that the same is not true for t1; thelatter would default its debt with probability 1

2 . It is now clear whythe insider’s facing earnings uncertainty matters here.

25

Despite that the signaling equilibrium in this case may violate Myersand Majluf’s pecking-order conjecture, Noe’s Proposition 2 establishesthat when d and e are both equilibrium signals, the average quality offirms sending d is higher than that of firms sending e. This result isconsistent with the empirical evidence about the announcement effectof debt financing.

The intuition underlying Noe’s Proposition 2 is as follows. If t sends drather than e in equilibrium, then its debt issue must be cheaper thanthe equity issue that it has chosen to not issue. For all these types,therefore, the average value of the equity issues that these types havechosen to not issue is therefore greater than I. But, I is exactly theaverage value of the equity issues reaching the market. Finally, recallthat the firm is originally all-equity financed, and hence the value ofequity (whether the equity issue was avoided or not) is proportionalto the value of the firm. Hence in equilibrium the average value of thefirms issuing debt is higher than the average value of the firms issuingequity.

12. Dybvig and Zender (1991) argue that Myers and Majluf’s analysishas been based on a special assumption about the objectives of thefirm manager; that is, the latter is motivated to maximize the existingshareholders’ welfare, not the firm value. Indeed, in Myers and Majluf(1984), it is the existing shareholders that must bear the losses result-ing from inefficient investment decisions, whereas the manager makesinefficient investment decisions in the first place because he is loyalto the existing shareholders! If the existing shareholders have perfectforesight, then they should have designed a managerial contract thatinduces the manager to always make efficient investment decisions.

Assuming that ex-ante an entrepreneur can fully commit to an optimalmanagerial contract that induces the firm manager to subsequentlymaximize the firm value, Dybvig and Zender (1991) show that invest-ment efficiency can be attained no matter whether the firm issues debtor new equity to finance its new projects, as opposed to the pecking-order conjecture advocated by Myers and Majluf. Dybvig and Zenderfocus on the “no-residual-uncertainty” case of Noe (1988); that is, con-ditional on the manager’s information, the value of assets in place andthe net present value of the new project involve no uncertainty.

Their model is as follows. An entrepreneur spends Ia to set up the

26

firm and hires a manager with a compensation s(·) at date 0, sells thefirm (via IPO) at the end of date 0, and at date 1, the future cashflow to be generated by Ia, which is a, together with b, the futurecash flow to be generated by a new project, is privately observed bythe manager, before the latter makes the financing and investmentdecisions. They allow the share prices, the investment decision, andthe total net future cash earnings accrued to the firm over the threedates to be contractible variables. They show that the following linearmanagerial contract (or compensation scheme)

s(a+ d(b− I), d, P1, P2) = α+ β[a+ (b− I)d]

implements investment efficiency, leaving the financing an irrelevantdecision. (In the above, β > 0, Pt is the share price at date t, andd ∈ {0, 1} indicates whether the project is undertaken or abandoned.)According to this compensation scheme, the manager’s payoff dependsonly on the date-2 true value of the firm, and with properly chosenconstants α ∈ ℜ and β > 0, the manager finds it in his own interestto adopt the project if and only if b ≥ I, and his ex-ante individualrationality condition is satisfied under this optimal investment pol-icy. Hence investment efficiency is attained by the optimally designedmanagerial contract, and in this case, the firm’s financing decision iscompletely irrelevant.

The above compensation scheme is able to guard investment efficiencybecause it has two important features. First, s does not rely on P1 orP2; that is, the decision about debt or new equity financing will notalter the manager’s pay; only the investment decision d will. Second, sis apparently a claim that is senior to common stock. Because of thesefeatures, the manager is not one of the existing shareholders, and infact, at date 1 the manager does not seek to maximize the welfare ofthe existing shareholders.

Of course Dybvig and Zender must reconcile their theory with theempirical fact that a new equity issue is generally interpreted as badnews by the market. They argue that if a and b are negatively corre-lated, then this phenomenon can mean nothing but that the firm lackshigh-quality projects following a new equity issue. Imagine that thefirm cannot predict how soon the product market will be saturated. Ifconsumers enter slowly, then a is small but b is large; or else, a is large,

27

but b is small. If a+ b is also negatively correlated with b, then when-ever the firm seeks external financing to implement the new project,the market must revise the firm value downward. Finally, Dybvig andZender show that the following compensation scheme can induce themanager to make financing and investment decisions that fulfill bothinvestment efficiency and the financial market informational efficiency:

s(a+ bd,B) = α+β(a+ bd)−k ·1[{a+bd<0,B>0}∪

{a+bd≥0,B =I}](a+ bd),

where k > 0 is a constant, and B is the proceeds from issuing debt.With this compensation scheme, the manager would like to ensure thatthe last term is zero. Thus debt financing is used when and only whena+ bd ≥ 0. This explains why empirically debt financing is consideredbetter news than equity financing: in fact the firm is struggling tomaintain a stable debt-to-equity ratio.11

13. Thus unlike Myers and Majluf (1984), Dybvig and Zender (1991) con-tend that the empirically documented announcement effects pertainingto external financing can be accompanied by efficient investment de-cisions, as long as the existing shareholders know how to optimallydesign a managerial compensation scheme and can fully commit tosuch a scheme.

Persons (1994) emphasizes that it is unrealistic to assume that thefirm can commit to Dybvig and Zender’s optimal managerial contract,especially when the firm can secretly offer a new contract to replacethe existing contract without being detected by the market. Indeed,if the firm does not have full commitment power, then any existingcontract is subject to the risk of being renegotiated. Persons showsthat Dybvig and Zender’s optimal contract is not renegotiation-proof.

In Persons’s (1994) model, at date 0, after the market observes theinitial contract that the entrepreneur offers to the manager, the en-trepreneur can offer a new contract to the manager before the lattermakes financing and investment decisions. Persons shows that, as longas the market does not observe the second contract, investment effi-ciency is never attained in equilibrium. This happens because givenany full-commitment contract that implements investment efficiency,there always exists another secret Pareto-improving contract for the

11For related empirical evidence, see for example Masulis (1980; 1983), Masulis andKorwar (1986), Mikkelson and Partch (1986), and Smith (1986).

28

entrepreneur and the manager, which will either induce the managerto issue new equity to finance a project with negative NPV, or whichwill induce the manager to not issue equity and to forego a projectwith positive NPV. Thus Persons provides a formal foundation forMyers and Majluf’s (1984) incomplete theory that issuing new equitytends to reduce investment efficiency.12

14. Now let us review Brennan and Kraus (1987),13 which considers afirm that wishes to raise I > 0 from risk-neutral competitive investorsin order to carry out a positive-NPV project at date 0, where cashinflows x are generated at date 1. Unlike Noe (1988)14 and Myersand Majluf (1984),15 Brennan and Kraus consider general financingstrategies, where a general financing strategy is denoted by z, whichis a vector of parameters describing the aggregate net claim issuedunder the financing strategy. The set of feasible financing strategies isdenoted by Z. Let T be the set of possible types of the issuing firm.Let f(x, t) be the density function of x given the firm’s type beingt ∈ T . Let y(x, z) be the cash flow promised by financing z in theearnings state x.

Let V (z, t) be the true value of the financing z given that the firmis of type t ∈ T . Let P (z) be the date-0 equilibrium price of thefinancing z. The type-t firm manager seeks to maximize P (z)−V (z, t),subject to P (z) = I, by choosing z ∈ Z. Let z∗(t) be the type-t firmmanager’s equilibrium financing choice. Let τ(z) be the set of t ∈ Tfor whom z is one equilibrium financing choice. An efficient value-

12In the jargon of game theory, Persons (1994) presents a signal-jamming model wherethe market does not observe the real managerial contract and the firm’s investment ef-ficiency. If the market (naively) believes that the firm’s investment decisions are alwaysefficient, then this belief gives the entrepreneur and the manager an opportunity to colludeand reduce investment efficiency at the expense of the naive new shareholders. Thus theonly possible equilibria are those in which the market believes that the firm is making in-efficient investment decisions, and such beliefs are confirmed to be correct in equilibrium.We shall have more to say about the financial signal-jamming models in another note.

13Brennan, M., and J. A. Kraus, 1987, Efficient Financing under Asymmetric Informa-tion, Journal of Finance, 42, 1225-1243.

14Noe, T., 1988, Capital structure and signaling game equilibria, Review of FinancialStudies, 1, 331-355.

15Myers, S., and N. Majluf, 1984, Corporate financing and investment decisions whenfirms have information that investors do not have, Journal of Financial Economics, 13,187-221.

29

revealing equilibrium is one where for all z ∈ Z such that τ(z) = ∅,

I = P (z) = V (z, t), ∀t ∈ τ(z).

Thus in an efficient value-revealing equilibrium, every type of the firmgets to finance its positive-NPV project at a cost of I. This fulfillsproductive efficiency and maximizes the firm’s payoff.

Note that there may be multiple types choosing the same z in a value-revealing equilibrium, as long as the value of z issued by each of thosetypes contained in τ(z) equals I. The value-revealing equilibrium isalso fully revealing, if for all z ∈ Z, τ(z) is either empty or a singletonset.

The paper’s first result is a necessary condition for the above-definedefficient value-revealing equilibrium, which says that given any z ∈ Z,if τ(z) is non-empty in the value-revealing equilibrium, then it mustbe that

P (z) = mint∈T

V (z, t).

That is, every z ∈ Z with a non-empty τ(z) is believed to have beenissued by the type whose z is the least valuable among the z issuedby all types t ∈ T . The proof is rather straightforward: if insteadP (z) > mint∈T V (z, t), there then would exist some t ∈ τ(z) withV (z, t) = P (z) = I and some t′ ∈ T such that V (z, t′) < P (z) = I.There must be some z′ ∈ Z such that t′ ∈ τ(z′) and V (z′, t′) = P (z′) =I. This type t′ can deviate from its equilibrium financing package z′

and issue z instead, which would raise its payoff by P (z)− V (z, t′), acontradiction.

The paper then shows that (Theorem 3) when the firm’s type isordered by first-degree stochastic dominance,16 for a value-revealingequilibrium to exist, y(·, z) must not be monotone. To see this, notethat if, given z, y(·, z) is monotone, then given z,

V (z, t) =

∫xy(x, z)f(x, t)dx,

is a monotone function of t, so that it can never reach a minimum at aninterior t ∈ T . This means that an interiro type cannot find a financing

16That is, ∀t1, t2 ∈ T , t1 = t2, either f(x, t1) first-order stochastically dominates f(x, t2)or f(x, t2) first-order stochastically dominates f(x, t1)

30

package to distinguish itself from other types, which is a contradictionto the assumption that an efficient value-revealing equilibrium exists.

By the same token, (Theorem 4) if instead the type is ranked bysecond-degree stochastic dominance,17 then for a value-revealing equi-librium to exist, y(·, z) must be neither convex nor concave. Thusstraight debt (concave) and equity (convex) are ruled out. On theother hand, convertible bond is likely to work. Two examples nowfollow.

Example BK-1: At date 0, the firm has 40 shares of common stockoutstanding, and it has debt with face value equal to 100 that will bedue at date 1. The firm needs to raise I = 10 for a new investmentproject. The firm has two possible types, called A and B. There are twoequally likely date-1 states of nature, called s1 and s2. The followingtable summarizes the relevant cash-flow information.

Date-1 cash flows/states s1 s2Assets in place 100 140

Type-A new project 0 60

Type-B new project -20 55

Again, we assume that everyone is risk-neutral without time prefer-ences. Without new investments, the date-0 firm value is

1

2(100 + 140) = 120,

and the debt is risk-free with a date-0 value of 100.

With full-information about the firm’s type, the securities markets willprice the type-A firm’s equity at 40, its debt at 100, and the type-Bfirm’s equity at 37.5, and the latter’s debt at 90. The new claimant’sworth is 10, equal to I.

Now, return to the case with information asymmetry. Consider zA = {to retire all the outstanding debt at the tender price 100 and issue 110new shares}; and zB = { to issue 10.67 new shares}. We claim that

17That is, ∀t1, t2 ∈ T , t1 = t2, either f(x, t1) second-order stochastically dominatesf(x, t2) or f(x, t2) second-order stochastically dominates f(x, t1)

31

there is a value-revealing equilibrium in which zA ∈ Z ≡ {zA, zB} istype A’s equilibrium financing and zB ∈ Z is type B’s equilibriumfinancing.

Let us verify this by computing V (zA, t) and V (zB, t). Note that

V (zA, A) = −100 +110

40 + 110× [

1

2(100 + 0) +

1

2(140 + 60)] = 10,

V (zA, B) = −80 + 100

2+

110

40 + 110×[

1

2(100−20)+

1

2(140+55)] = 10.83;

and

V (zB, A) =10.67

40 + 10.67× (40 + 10) = 10.53,

V (zB, B) =10.67

40 + 10.67× (37.5 + 10) = 10.

In equilibrium, we have

P (zA) = V (zA, A) = V (zB, B) = P (zB) = 10,

and let us check that given these prices chosen by the securities mar-kets, neither type A nor type B wants to deviate.18 If the type-A firmissues zA, it gets

40

40 + 110× 150 = 40;

and if it deviates by issuing zB, then it gets

40

40 + 10.67× (40 + 10) < 40.

Similarly, if the type-B firm issues zA, it gets

40

40 + 110× 137.5 = 36.67;

and if it sticks to zB, then it gets

40

40 + 10.67× (37.5 + 10) = 37.5 > 36.67.

18If Z is broadened to include other financing choices, we can find supporting beliefsthat ensure that the firm cannot benefit from offering other financings as well.

32

A comparison between V (zA, A) and V (zA, B) reveals the fact thattype B can benefit from mimicking type A’s issuance of 110 new shares,but in order to convince public investors that the issuing firm is typeA, type B must also pay 100 to retire its debt, which is worth only90! The point here is that type A is engaged in multi-dimensionalsignalling, which makes it more difficult for type B to mimic type A’sfinancing strategy.19

This example also explains why financing debt repurchases using pro-ceeds from issuing new equity may appear as good news, as docu-mented by Masulis and Korwar (JFE, 1986).

Example BK-2: Suppose that the type t firm’s cash inflow gener-ated by the new investment is uniformly distributed over [m−t,m+t],where the mean m is common knowledge. The firm has senior debtoutstanding, with face value B0. Z consists of the set of subordi-nated convertible bonds (CB, from now on); each CB is representedby (α, F ), where F is the face value of the junior CB, and α is thefraction of equity the CB is allowed to convert into. Assume thatt ≥ B0 −m + F

α and t ≥ m − B0 for all t ∈ T . Thus for each t ∈ T ,the CB has a locally convex region that involves positive payoffs, andacross all t ∈ T , the senior debt remains risky. By definition, the truevalue of financing (α, F ) is then

V (α, F, t) =

∫ B0+F

B0

(x−B0)1

2tdx

+

∫ B0+Fα

B0+FF · 1

2tdx

+

∫ m+t

B0+Fα

α(x−B0)1

2tdx

=F 2(1−α)

α + α(m+ t−B0)2

4t,

so that from∂V (α(t), F (t), t)

∂t= 0

19A similar point has been made in Biais and Hillion (1994), where it is shown thatmimicking a liquidity trader becomes more costly to an informed speculator after theformer is allowed to trade 3 rather than 2 assets.

33

andV (α(t), F (t), t) = I,

we obtain

α(t) =2I

m+ t−B0, F (t) =

√α(t)

1− α(t)[4It− α(t)(m+ t−B0)2.

This in turn implies that the firm’s type that the markets can recoverfrom the observed CB is

t(α, F ) =

√(m−B0)2 +

F 2(1− α)

α2,

which is decreasing in α and increasing in F .

Since equity has payoff convex in the firm’s earnings, this result pre-dicts that (if T is really ordered by second-degree stochastic domi-nance) the announcement-period stock returns are respectively nega-tively and positively related to the conversion ratio and the firm’s debtratio. Although there is no evidence showing that the firm’s possibleprospects are actually ordered by second-order stochastic dominance,these predictions are consistent with empirical evidence.

Brennan and Kraus (1987) thus shows that an efficient financing equi-librium is likely to arise if, unlike in Myers and Majluf (1984), the firmis allowed to choose from a rich set of financing strategies. Allowingfor more complex financing packages means that the firm is allowedto send a multi-demensional signal, and as the related literature (En-gers 1987; Milgrom and Roberts 1986; Wilson 1985) shows, separatingequilibria are more likely to arise when the informed player can signalwith many signals.

15. So far, we have assumed that a firm must obtain external funds byissuing debt or equity. We have not explained why a firm cannotissue exotic securities instead. In the sequel, we shall first reviewseveral theories regarding the pros and cons of other fimiliar corporatesecurities, such as convertible bonds, warrants, and preferred stock,and then we shall give a short introduction to the theory of optimallydesigned financial contracts.

34

16. In addition to straight debt and common stock, there are other preva-lent financing instruments such as convertible debt, preferred stock,and leasing. Due to the limited space, we shall only mention brieflyseveral theories related to the use of these instruments.

• (Convertible Debt.)

(a) Like warrant, convertible debt is an option-like security. Thisnature of convertible debt implies that it can be used to curbthe entrepreneur’s incentive problems if relevant informationis observable but un-verifiable. The following is an example.

Consider an economy which extends for three dates (t =0, 12 , 1). At t = 0, an entrepreneur endowed with illiquidasset K and no cash attempts to raise funds from competi-tive investors by issuing a bond. The entrepreneur and theinvestors are all risk neutral without time preferences. Theentrepreneur can choose either project X or project Y. Bothprojects incur an outlay c > 0 at t = 0. Project X generatesa sure cash flow x > 0 at t = 1, with x > c. Project Ygenerates a random cash inflow y at t = 1, which is equallylikely to be y and 0. Assume that

2c > y > 0, (1)

andx− c < y − x. (2)

Thus project X has a positive NPV and project Y has anegative NPV. The illiquid asset can be liquidated to gen-erate cash at t = 0. To generate one dollar of cash, the en-trepreneur has to liquidate 1

1−λ dollars of the illiquid asset,where 0 ≤ λ < 1. Assume also that

K(1− λ) > c. (3)

First suppose that the entrepreneur decides to raise b ∈ (0, c]by issuing a (probably risky) pure discount bond maturingat t = 2 with face value f and finance the rest c − b byliquidating the illiquid asset. Given the bond (b, f), at t = 0,the entrepreneur gets max(0, x− f) by taking project X and12 max(0, y − f) by taking project Y. As f > y makes no

35

sense for the entrepreneur, consider either (i) f ≤ x or (ii)f ∈ (x, y]. It can be readily verified that if f ≤ 2x − y,then the entrepreneur prefers project X to project Y afterraising b = f . If instead (i) is true and f > 2x − y, thenthe entrepreneur prefers Y to X after raising b = f

2 . Finallyif (ii) is true, then taking Y is the entrepreneur’s dominantstrategy and hence b = f

2 . It is clear that with the bondfairly priced the entrepreneur will not choose f > 2x− y, forotherwise the entrepreneur’s expected payoff is

y − f

2−

c− f2

1− λ< 0. (4)

Thus the entrepreneur chooses f ≤ 2x− y, and to minimizethe cost of liquidation, the optimal straight bond for theentrepreneur is (b∗, f∗) = (2x− y, 2x− y).

What is the price of the straight bond if f = c? The pre-ceding analysis says that the entrepreneur will take projectY after issuing the bond. The bond price is then

b =c

2. (5)

We shall domonstrate that a convertible bond with the sameface value (i.e. f = c) is worth twice as much as its straightbond counterpart even if it is commonly agreed that conver-sion will never occur in equilibrium. To this end, assumethat at t = 1

2 the bond can be converted into shares whichrepresent a proportion γ of the ownership, with

c

y< γ <

c

x. (6)

The triple (b, f, γ) fully describes a convertible bond.

Assume that the bondholder (assume there is only one bond-holder; this is inessential) can observe the project chosen bythe entrepreneur at date 1

2 . If project X is chosen, then con-verting the bond yields

γx < c, (7)

36

for the bondholder, where the right-hand side is the bond-holder’s payoff if the bond is left unconverted. Thus conver-sion does not take place at t = 1

2 if the entrepreneur choosesproject X at t = 0. On the other hand, if project Y is chosenthen converting the bond yields for the bondholder

γy

2>

c

2, (8)

where the right-hand side is again the bondholder’s payoffif the bond is left unconverted. We conclude that the bondwill be converted at t = 1

2 if and only if the entrepreneurchooses project Y at t = 0. Backward induction implies thatthe entrepreneur will take project X at t = 0. It follows thatthe convertible bond is worth twice as much as its straightbond counterpart. In fact, the optimal convertible bond isnot unique in this case, and they all dominate the optimalstraight bond (b∗, f∗) derived earlier because the latter in-volves a high cost of liquidating the illiquid asset.

The lesson to be learned here is that, as a legally bindingcontract, the option attached to a bond can serve as a meansof commitment which allows the entrepreneur to convincethe bondholder that she will not get opportunistic after fi-nancing is granted. With the agency problem removed, thebond is valued higher. This example also shows that pricingthe option-like corporate securities using the classical optionpricing methods may lead to pricing errors. In particular,the latter approach implies that an option is worth zero ifit will never be exercised, which totally ignores the commit-ment value of the option-like securities. (This example istaken from a very old working paper of mine.)

(b) That option-like securities can be issued to the entrepreneuror to investors so as to alleviate incentive problems has longbeen recognized in the finance literature. For earlier contri-butions, see for example Emanuel (1983)20 and Green (1984).21

20Emanuel, 1983, Warrant valuation and exercise strategy, Journal of Financial Eco-nomics, 12, 211-235.

21Green, 1984, Investment incentives, debt, and warrants, Journal of Financial Eco-nomics, 13, 115-136.

37

Seward (1990) shows that, because the payoff generated bya convertible debt as a function of the issuing firm’s earn-ings is concave in low-earnings states and convex in high-earnings states, it can be used to simultaneously alleviate anentrepreneur’s multiple incentive problems.

In Seward (1990),22 the borrowing firm can allocate the fundsthat the entrepreneur raises at date 1 between a high-risk anda low-risk projects. The two projects generate cash flows atdate 2, where a portion of the date-2 cash flows are costly toverify. Thus there co-exist the asset substitution and costlystate verification problems in Seward’s model. The authorshows that the optimal design of the corporate security is toallow state verification to take place in the low-earnings states(which mimics the payoff of a standard debt), and to allowthe security holder to convert that security into equity in thehigh-earnings states. The former resolves the state verifica-tion problem in the cheapest way, and the latter optimallymitigates the asset substitution problem. Thus a convertibledebt is optimal.

(c) We have mentioned above that convertible debt is useful insignaling a firm’s quality to new investors; see Constantinidesand Grundy (1989) and Brennan and Kraus (1987). Thishappens because the payoff generated by a convertible debtas a function of the issuing firm’s earnings is concave in low-earnings states and convex in high-earnings states, a propertythat is required for the security to help result in an efficientvalue-revealing equilibrium.

There is actually another reason why convertible debt can beused to signal a firm’s true quality: a convertible debt cantypically be called before debt maturity, after informationasymmetry that existed at the time the firm raised funds hasdisappeared.

Consider the following signaling model a la Myers and Ma-jluf (1984) examined in Stein (1992).23 The penniless en-

22Seward, 1990, Corporate Financial Policy and the Theory of Financial Intermediation,Journal of Finance.

23Stein, 1992, Convertible Bonds as Backdoor Equity Financing, Journal of Financial

38

trepreneur has three possible types, referred to as respec-tively G, M, and B. The entrepreneur’s type is his privateinformation at date 0, when he needs to raise I = 1

3 dol-lars from competitive investors. The investors and the en-trepreneur are risk-neutral without time preferences.

Regardless of his type, the entrepreneur’s project will returneither 0 or 1 dollar at date 2. Type j will generate 1 dollarwith probability πj . Assume that

πG = 1, πM =8

9, πB =

4

9.

Thus all types can produce non-negative NPVs.

Suppose that at date 0, the entrepreneur can either issue pureequity (which specifies a fraction α of ownership giving to thenew investor in exchange for the I dollars), or straight debt(which specifies a face value F of debt to be mature at date2), or convertible debt (which specifies a price K at whichthe entrepreneur can buy back the convertible debt at date1 if he likes to, a face value F of debt, and also a conversionratio β). Thus this is a signaling game with three possibletypes and three signals.

At date 1, two things happen. First, the entrepreneur’s typebecomes public information. Second, more precise informa-tion about type B arrives, which shows that either type Bwill generate nothing at date 2 or type B has improved itselfand has become type M; these two events are equally likely.Finally, at date 2, if default on debt takes place, then as inRoss (1977) the entrepreneur must incur a loss c = 4

9 .

It can now be easily verified that the following constitute aseparating equilibrium at date 0:

– type G invests after issuing a riskless debt with face valueequal to 1

3 ;

– type M invests after issuing a convertible debt with F > 0and 0 < K < 1

3 , which can be converted into a fraction38 of equity at date 1 (and date 2); and

Economics.

39

– type B invests after issuing a fraction 34 of equity.

In this model, c is large, and hence the entrepreneur wouldlike to avoid issuing risky debt. Type M issues convertibledebt at date 0, which will be turned into equity at date 1 uponbeing called. Type B cannot mimic type M’s move, becauseif it did with probability 1

2 conversion will not take placeat date 1, and given that c is large, the loss will outweighthe gain from mimicking type M and selling the overpricedconvertible debt.

To sum up, the opportunity to force conversion by calling theconvertible debt after information asymmetry disappears butbefore the debt matures allows type M to distinguish itselffrom type B. Stein shows that without convertible debt, thiscannot be achieved via pure equity or straight debt financing.

(d) Finally, convertible securities are prevalent in venture capitalfinance. For example, in the sample of Kaplan and Stromberg(2000, p. 13)24 convertible securities were used in 189 out of200 financing rounds.

Schmidt (2003)25 provides a rationale for the prevalent useof convertible debt and convertible preferred stock in venturecapital (VC) finance. His argument runs roughly as follows.The ultimate success of a high-potential, entrepreneurial firmdepends not only on the quality of the project and the effortprovided by the entrepreneur, but also on the commitmentof the venture capitalist.26 Since the entrepreneur and theventure capitalist must exert efforts in a sequential fashion,the optimal VC financing contract must resolve a sequential

24Kaplan and Stromberg, 2000, Financial contracting theory meets the real world: Anempirical analysis of venture capital contracts, CEPR Discussion Paper No. 2421.

25Schmidt, 2003, Convertible Securities and Venture Capital Finance, Journal ofFinance.

26Venture capitalists provide not only the necessary financial means to develop theproject, but that they are also actively involved in the management of the firm. Venturecapitalists are well connected in the specific industry, they help to recruit key personnel,they negotiate with suppliers and customers, they advise the entrepreneur on strategicdecisions, they play a major role in structuring mergers, acquisitions, and initial publicofferings, and sometimes they are even involved in the day-to-day operations of the firm.If things turn sour, venture capitalists often replace the founder of the company by aprofessional CEO and/or sell off or liquidate the firm.

40

double moral hazard problem.

Schmidt shows that in this case a wisely designed convertibledebt can be issued to the venture capitalist to induce bothparties to invest efficiently without making both of them fullresidual claimant on the margin. Schmidt’s incentive mech-anism exploits the fact that the venture capitalist will in-vest only if he exercises his conversion rights, and that hewill convert only if the entrepreneur worked sufficiently hard,which, in turn, induces the entrepreneur to put in the efficientamount of effort. The optimally designed convertible secu-rity strictly outperforms any standard debt-equity contractin this case. Moreover, Schmidt shows that convertible secu-rities implement efficient investments only if the contributionof the venture capitalist to the project is sufficiently impor-tant. Thus, Schmidt’s theory can explain both why convert-ible securities are so popular in venture capital finance, andwhy convertible securities are uncommon in the case wheresmall firms are financed by banks or other passive investors.

• (Preferred Stock.) Preferred stock, sometimes referred to mez-zanine financing, resembles debt in that it promises to pay regulardividends, but unlike interests on debt, preferred dividends arenot tax-deductible to the issuing firms, and omission or deferralof preferred dividends, which is at the manager’s discretion, doesnot constitute default.

The existing literature has recognized the value of preferred stockas mostly related to regulation and taxation. For example, firmsin the closely regulated public utilities industries may find it ad-vantageous to issue preferred stock instead of debt, because pre-ferred stock is considered equity by the regulators, although itprovides a pattern of payments similar to that of debt. See Pons-Sanz et al. (2004)27 for the optimal financing mix that includespreferred stock in a Miller (1977)-type of equilibrium with corpo-rate taxes.

Emmanuel (1983)28 was the first article that emphasizes the divi-

27Pons-Sanz, et al., 2004, When are Preferred Shares Preferred? Theory and EmpiricalEvidence, Working Paper No. 03-19, International Center for Finance, Yale University.

28Emmanuel, 1983, A Theoretical Model for Valuing Preferred Stock, Journal of

41

dend flexibility associated preferred stock—the dividends promisedby preferred stock can be omitted or extended by the firm with-out penalty, as opposed to omission of interest payment on debt.Titman (1984),29 suggests that preferred stock can be used toeliminate stockholders’ incentive to liquidate too much, and inthat sense preferred stock can be an optimal security.

Heinkel and Zechner (1990)30 present an informational equilib-rium with preferred stock. They show that preferred stock canenhance a firm’s debt capacity, because it creates additional in-centives to invest. In their model, senior long-term debt createsincentives for under-investment (via the debt-overhang problememphasized in Myers 1977) whereas equity creates incentives forover-investment (as in Myers and Majluf 1984). In a world with-out taxes these two effects may cancel out under the optimal mixof long-term senior debt and short-term junior debt, attainingthe first-best investment efficiency. In the presence of corporatetaxes, however, the firm may wish to issue further debt in or-der to capture the tax shields created by debt financing, at theexpense of investment efficiency. In this case, if the firm is al-lowed to issue preferred stock, then investment efficiency can bere-stored, because the entrepreneur has an incentive to defer pre-ferred dividends when a good investment opportunity appears.Heinkel and Zechner also show that firms with moderate growthopportunities are most likely to issue preferred stock.

• (Leasing.) Finance people used to believe that leasing is asubstitute for debt financing, because lease payments are fixedobligations like other loans. It has been argued that if one as-sumes that firms have an optimal debt-equity ratio, then, to theextent that leasing represents ”off-balance sheet” financing, leas-ing reduces debt capacity. For example, Ross, Westerfield, andJaffe ((1990), p. 632)31 state: ”If a firm leases, it will not use asmuch debt as it would otherwise. The benefits of debt capacity

Finance.29Titman, 1984, The Effect of Capital Structure Choice on a Firm’s Liquidation Deci-

sion, Journal of Financial Economics.30Heinkel and Zechner, 1990, The Role of Debt and Preferred Stock as a Solution to

Adverse Investment Incentives, Journal of Financial and Quantitative Analysis.31Ross, S., R. Westerfield, and J. Jaffe, 1990, Corporate Finance, Second Ed. Boston,

MA: Irwin.

42

will be lost, particularly the lower taxes associated with interestexpense.”

Lewis and Schallheim (1992)32 show that the relation betweendebt and leases can be complementary. That is, a lessee firmoptimally uses a greater proportion of debt with leasing than itwould if it restricted itself to debt. Lewis and Schallheim alsoshow that, even if the marginal tax rate is the same for the lessorand the lessee, the lessee flrm still derives a benefit from leasing.

Unlike the earlier literature that treats debt and leases as sub-stitutes, Lewis and Schallheim point out that the substitution isbetween debt and nondebt tax shields. Thus when a flrm makesan optimal capital structure choice it must trade off the tax ben-efits of debt flnancing against the costs associated with its poten-tial redundancy relative to other tax shields (e.g., depreciationexpenses). Leasing offers an opportunity to transfer or ”sell”nondebt tax shields to another firm. If the lessee flrm can locatea buyer (the lessor) who has a higher probability of using thesetax deductions, this buyer will pay more for them than they areworth to the lessee. Thus the lessor ”buys” these tax shields byreducing the lease payment (which is consistent with the IRS’stax treatment of financial leases), which in turn motivates flrmsto lease.

The sale of nondebt tax deductions is the key observation forLewis and Schallheim’s argument that debt and leases can becomplements. As nondebt tax deductions are sold, their poten-tial redundancy with debt deductions is reduced and the marginalvalue of debt becomes positive. The lessee responds to this incen-tive by issuing additional debt. Thus, there is a positive relationbetween the use of debt financing and leases.

17. The theory of financial contracts is the foundation for the moderntheory of financial institutions and corporate finance. Indeed, differ-ent institutions (like commercial banks and insurance companies) aredefined by the different contractual relationships among contractingparties. Some financial contracts (e.g. a managerial compensation

32Lewis and Schallheim, 1992, Are Debt and Leases Substitutes?, Journal of Financialand Quantitative Analysis.

43

contract or a bank loan contract) are private contracts, which cannotbe freely transferred to a third party. There are also financial con-tracts that can be transferred among people, and these are mostlytraded securities.

A complete financial contract can specify for each contracting party hisor her obligations and rights in every possible future contingency. Thereal-world contracts are inevitably incomplete, because it is sometimesvery hard to verbally describe in the contract a future contingency sothat the latter will not be confused with another future contingency,and also because it is sometimes very hard to describe in the contract acontracting party’s future obligations (such as a managerial decision tobe made in a specific future event). A future event whose occurrence ornon-occurrence will become known to all contracting parties is referredto as an observable event. A future event whose occurrence or non-occurrence will become known to the court of law (which is supposedlythe legal entity that will help enforce the contract signed today) isreferred to as a verifiable event. Only observable and verifiable eventscan be written into a contract and effectively enforced. A contractis incomplete exactly because there are many important events whichare either unobservable or non-verifiable.

For example, in the classic moral hazard model where the owner of afirm hires a professional manager to run the firm, the manager’s effortchoice is his private information, and is hence observable only to themanager, not to the owner of the firm. In this case, the manager’s effortchoice is not an observable variable that can be put in the managerialcompensation contract. Now, even if we suppose that the manager’seffort choice is observable to the owner, it may not be verifiable tothe court of law. For example, imagine that the firm is producing andselling electronic devices, and the owner and the manager both havephd in electronic engineering. Imagine that the managerial contracthas required that the manager exert a specific effort to improve theproduct quality, but the manager has actually violated this require-ment. Because of their common background in E.E. the owner and themanager both know that the manager has violated the requirement,but when the owner and the manager debate in the court of law, thejudges and atterneys will not be able to tell which party is telling alie—the judges and atterneys only have law degrees, and they may

44

know very little about electronic engineering.

A financial contract possessed by an investor (which may be an indi-vidual or an institution) must specify the investor’s future cash-flowright. A cash-flow right provision states the cash flows accrued to thatinvestor in each future earnings contingency, and what the investorcan do if the firm fails to deliver the promised cash flows. For ex-ample, in a one-entrepreneur-one-investor setting, if the financial con-tract is a standard debt contract, then the cash-flow right will allowthe debtholder to get a fixed repayment (the face value of debt) in theevent that the firm does not default, and to otherwise get everythingin the firm in the event that default takes place.

When people can sign complete contracts, the financial contract pos-sessed by an investor only needs to specify the cash-flow right—managerialdecisions and actions to be taken in the future can be written into thecomplete contract and carried out accordingly. When the financial con-tracts are incomplete, merely specifying the cash-flow right for eachinvestor cannot ensure investment efficiency. In this case, the finan-cial contract must also specify for each investor his or her control right,which can be used to alleviate or remove managerial incentive problemsand promote investment efficiency.33 Since monitoring and interven-tion are costly to individual investors, only wisely designed cash-flowrights can induce investors to perform costly intervention. By opti-mally designing the investors’ control rights and cash-flow rights, dif-ferent classes of investors can be induced to monitor the manager andintervene to improve firm performance in different situations. Aghionand Bolton (1992) is a pioneering article discussing how control shouldbe allocated among an investor and an entrepreneur to guard invest-ment and Pareto efficiency. The literature has shown that when facedwith other managerial incentive problems, the firm should optimallyissue debt and inside equity, and probably some outside equity also; seeZender (1991), Optimal Financial Instruments, Journal of Finance, 46,1645-1663; and Dewatripont and Tirole (1994), A Theory of Debt and

33There are several forms that a control right can take. For example, shareholders mayhave a voting right which they can use to collectively alter a major decision made by theexisting manager or even to replace that manager, a senior creditor may be given the rightto replace the manager when the firm defaults on its debt, and major investors (holdingblocks of shares) can constantly ask for updated information which allows them to monitorthe manager and intervene in his decisions.

45

Equity: Diversity of Securities and Manager-Shareholder Congruence,Quarterly Journal of Economics, 109, 1027-1054.

Evidence has shown that control rights are indeed important and valu-able. Some firms in the US, Israel and Italy have respectively issuedtwo classes of equity, one with and the other without a voting right(which is a special form of control right), and the class of equity witha voting right was typically sold at a significant premium, reflectingthe private benefits that can be brought about by the specified controlright.34 The private benefits may include an informed investor’s trad-ing profits, which an investor in control may obtain at the expense ofother investors (as in Maug 1998, where other investors are subject toliquidity shocks and may need to sell their stakes when the investor incontrol is engaging in insider trading), but they may also include gainsthat an investor in control obtains without hurting other investors.35

Thus control right allocation is an important issue in corporate governance.36

According to Holmstrom and Kaplan (2001), merger activity was themajor means of corporate governance for the US firms in the 1980s,and shareholder activism took over the role of merger activity in the1990s.

18. Consider the following much simplified version of the Aghion-Boltonmodel. At date 0, entrepreneur E is penniless and needs to raise K > 0from a competitive investor I. I is very rich, but E will remain wealth-constrained till date 2. Both of them, and others to appear in thebackground of this model, are risk-neutral without time preferences.

34See respectively Lease, McConnell, and Mikkelson, (1983), The Market Value of Con-trol in Publicly-Traded Corporations, Journal of Financial Economnics, 1, 439-471; Levy(1983), Economic Valuation of Voting Power of Common Stock, Journal of Finance, 38,79-93; and Zingales (1994), The Value of the Voting Right: A Study of the Milan StockExchange Experience, Review of Financial Studies, 7, 125-148.

35For an example see footnote 5 of Zingales (1995), Insider Ownership and the Decisionto Go Public, Review of Economic Studies, 62, 425-448. For a good discussion of the sourceof private benefits, see Barclay and Holderness (1989), Private Benefits From Control ofPublic Corporations, Journal of Financial Economics, 25, 371-395.

36Corporate governance is the study of legal and economic mechanisms under whichcorporations and managements can be governed; see Holmstrom and Kaplan (2001), Cor-porate Governance and Merger Activity in the United States: Making Sense of the 1980sand 1990s, Journal of Economic Perspectives, 15, 121-144. See also the survey by Shleiferand Vishny (1997), A Survey of Corporate Governance, Journal of Finance, 52, 737-783.

46

At date 2, an action a ∈ A must be chosen, which generates onedollar with probability y(a) and a non-transferable private benefit l(a)accrued to E alone. Again, a is too costly to describe, and hence notcontractible. Assume that whenever renegotiation takes place, E canmake a take-it-or-leave-it offer to I.

We shall for the time being consider only the set of contracts thatassign all the monetary gain to I. Thus at date 2, if E is in control,then E would choose some aE ∈ A that maximizes l(·); and if I is incontrol, then I would choose some aI that maximizes y(·). Note thatto simplify we have assumed there are no date-2 uncertain states.

Assume that y(aI) > K > y(aE),37 and hence an investor-in-control

contract is feasible, but it fails to attain ex-post efficiency. (E, however,can ask I to pay an up-front fee of y(aI) − K at date 0 if E decidesto go along with this investor-in-control contract.) An entrepreneur-in-control contract is, however, infeasible, because it cannot make theinvestor’s date-0 IR condition satisfied.

Now, assume that at date 1, the realization of a public signal x isverifiable, and at date 0, it is commonly known that x is uniformlydistributed over [0, 1]. Moreover, for all Borel set B contained in [0, 1],the Arrow-Debreu security written on B (which pays 1 dollar at date1 if and only if the realization of x is an element of B) is traded atdate 0.

In this case, define π∗ as the solution to the following equation of π:

πy(aE) + (1− π)y(aI) = K.

Show that there exists a long-term coupon bond that E can issue to Iat date 0, which improves on the investor-in-control contract describedabove.

Solution.

Let B = [0, π∗], and consider the following long-term coupon bond thatE sells to I at the price K + π∗ at date 0. At date 0, after investingK in the project, E purchases 1 unit of the Arrow-Debreu securitywritten on event B and carries it till date 1. (The date-0 price of

37This justifies the above assumption that we can restrict attention to the contractsthat allocate all cash flow rights to the investor.

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that Arrow-Debreu security is exactly π∗.) At date 1, the bond shouldmake a coupon payment of 1 dollar to the bondholder I, and E willremain in control at date 2 if there is no default for the date-1 couponpayment. If default occurs at date 1, then control is transferred to I.In either case, the long-term bond should pay 1 dollar to I at date 2(which is the maturity date of the bond).

As can be easily seen, at date 1, default occurs if and only if event Bdoes not happen, and hence the investor may be in control at date 2with only probability 1−π∗. With probability π∗, the entrepreneur willbe in control instead, and when that happens, the ex-post investmentefficiency is attained.38 Under the above long-term coupon bond, theinvestor’s date-0 IR condition is binding, since

π∗[1 + y(aE)] + (1− π∗)y(aI) = K + π∗.

Since the ex-post investment inefficiency is reduced and since the long-term coupon bond leaves no surplus to the investor at date 0, thecurrent long-term coupon bond improves on the investor-in-controlcontract.

19. The Aghion-Bolton 1992 model assumes that cash flows are verifiable,but in other incomplete-contracts models, cash flows are assumed tobe non-verifiable. In the latter case, investors would rather abandon apositive-NPV project ex-ante if they expect the firm to always under-report its realized cash earnings ex-post. To persuade the inverstorsto commit funds ex-ante, either the firm must commit ex-ante to incura cost of auditing which produces verifiable evidence ex-post regard-ing the true amount of cash earnings (which is the CSV model to bereviewed after the midterm exam), or the firm must have some valu-able physical assets ex-post, whose existence is verifiable, and the firmmust give the investors the right to ex-post liquidate partially or all itsphysical assets when the firm fails to make the promised repayments.The latter is the so-called cash diversion model developed by Hart and

38That is, the first-best effort a∗ =argmaxa∈A y(a)+l(a) will be implemented, instead ofaE . This happens because I is not wealth-constrained, and Coase’s theorem implies thatrenegotiation will take place to ensure ex-post efficiency. Note that I’s payoff is still y(aE)since E has all bargaining power during renegotiation. Note also that Coase’s theoremdoes not apply when I is in control: E is penniless, and hence renegotiation cannot takeplace.

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Moore (1989, Default and Renegotiation: A Dynamic Model of Debt,MIT working paper no. 520), which will be reviewed briefly in thissection.

Consider a model where at date 0 an entrepreneur (E) endowed withinitial wealth w ≥ 0 needs to raise from competitive investors at leastK − w > 0 in order to implement an investment project which willgenerate cash flows at dates 1 and 2 but needs an immediate outlayof K at date 0. Exactly one investor will be selected to finance theproject, and we shall refer to him the investor, or C. Both the investorand the entpreneur are risk-neutral without time preferences.

If B ≥ K − w is raised at date 0, then K must be invested (whetherthe entrepreneur actually makes the investment at date 0 is verifiable),but the remaining cash balance B +w−K becomes unverifiable afterdate 0. In particular, it is not possible to put B+w−K in a trust fundat date 0; otherwise, this amount would become a verifiable incomeat date 1, which the investor would then be able to obtain withoutdifficulty.

After K is spent at date 0, the firm has some assets in place, whichgenerate cash earnings y1 at date 1, and if these assets in place arekept intact till date 2, then they will generate cash earnings y2 at date2. If these assets are fully liquidated at date 1, then asset sale willgenerate a proceeds of L. These assets can be partially liquidated atdate 1 as well, and liquidation of a fraction (1 − f) of the assets willgenerate verifiable income (1−f)L at date 1. The date-2 salvage valueof these assets is zero.

The key assumption in Hart and Moore model is that cash earnings y1and y2 are unverifiable, and at date t the entrepreneur can simply stealyt away. On the other hand, the presence of the physical assets is ver-ifiable, and liquidation of the physical assets also generates verifiableincome.

In this case, the investor cannot get repayments at date 2: any cashearnings at date 2 will be taken away by the entrepreneur, regardlessof the promises the entrepreneur made to the investor before date 2.The investor may however get repaid for his date-0 investments atdate 1, if he is given a right to sell the physical assets to generate cash

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at date 1. Thus in this environment a feasible financial contract is ashort-term debt (with maturity equal to date 1, not date 2), whichgives the creditor (the investor) a liquidation right when default takesplace. A short-term debt is then represented by a pair (B, P ), whereP is the face value of the debt, and B is the date-0 price of the debt,and if the entrepreneur fails to fully repay P at date 1, the debtholderis allowed to sell as much the physical assets as needed in order tominimize his loss.

Hart and Moore assume initially that y1 and y2 are non-random, andalthough y1 and y2 cannot be verified in the court of law, yt can beobserved by the investor and the entrepreneur at date t. It is alsoassumed that

y2 > L, y1 + y2 > K ≥ L.

The first inequality says that date-1 liquidation of physical assets isinefficient. The second inequality says that the investment project hasa positive NPV, but liquidation would result in a sure loss.

Now, let us derive the subgame-perfect equilibrium of the above Hart-Moore model. First consider the date-1 subgame, where both partieshave seen y1 and the entrepreneur must decide whether to fully repayP . Hart and Moore assume that the entrepreneur can liquidate thephysical assets without the investor’s permission in order to repay P .In this case, if L ≥ P , then the debtholder will be fully repaid: if Edoes not fully repay P , C can sell the physical assets to get P himself.On the other hand, if P > L, then E will default at date 1 and thenbeat C down to L in the subsequent renegotiation. (Hart and Mooreassume that E has all the bargaining power when renegotiation takesplace.)

This implies that what the debtholder can actually receive at date 1is

P ≡ min(P , L),

and we can represent the short-term debt equivalently by (B,P ).

Hart and Moore then ask, “In what form is P received?” Since y2 > L,E would like to pay as much as possible of P in the form of cash incomey1 and as little as possible in the form of asset sales. E’s date-1 cash

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holding, which is unverifiable, is

B + w −K + y1.

If this amount is greater than P , then there will be no asset sales.Otherwise, there will be asset sales. The remaining fraction of assets,f , which will be carried into date 2, must then satisfy

f = min(1, 1− 1

L(P −B +K − w − y1)).

Now, we can move backwards to consider the date-0 equilibrium priceB of the debt. The investor buying the debt must exactly break even,and hence we have

P = B ⇒ f = min(1, 1− 1

L(K − w − y1)).

Recall that the actual repayment P received at date 1 by C cannotexceed L. On the other hand, in order for the firm to make the date-0outlay K, we need

B ≥ K − w.

It follows that financing is infeasible at date 0 if either

K − w > L,

or E’s IR constraint cannot be satisfied with the equilibrium f :

K > y1+fy2+(1−f)L = y1+L+min(1, 1− 1

L(K−w−y1))(y2−L).

When either of these two situations occurs, the firm must pass on thepositive-NPV project, and we refer to this event as a kind of ex anteinefficiency.

Even if financing is feasible and obtained at date 0, f may be strictlyless than 1 in equilibrium, which occurs if

K > w + y1.

Since asset liquidation at date 1 is inefficient, we refer to this event asa kind of ex post inefficiency. We say that the firm attains the first-best efficiency if neither the ex-ante nor the ex-post inefficiency takesplace.

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Finally, note that when financing is obtained at date 0, there existsa continuum of optimal debt contracts. If B = K − w, then the firmcan borrow anything up to L. Thus the liquidation value of physicalassets is an important factor that determines the firm’s debt capacity.We shall encounter a similar result in the Repullo and Suarez (1998).

We shall have more to say about the literature of optimal financialcontracts in the next lecture note.

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