Principles of Corporate Finance...Vittoria Cerasi Principles of Corporate Finance 2020-21 16 / 26...

Principles of Corporate Finance

Vittoria Cerasi

2020-21

Vittoria Cerasi Principles of Corporate Finance 2020-21 1 / 26

Banks and direct credit

Model in Holmstrom B. & J. Tirole (QJE, 1997)Three dates (t = 0, 1, 2), alternative return y ≥ 1. Capital markets withinfinite investors.

At t = 0 an entrepreneur needs I but has insufficient liquidity A < I .

At t = 1, once financed, entrepreneur can choose (not observed)between projects H or L. With project L he earns a private benefit B.

At t = 2: project returns Z = {0,X} with X > y .

Pr [Z = X |H ] = pH > Pr [Z = X |L ] = pL

with ∆p ≡ pH − pL.

Assume that ∆pX > B as before.


Three agents: firms (f ), monitoring financial intermediaries (m) anduninformed investors (u).

Firms are heterogeneous: different amount of own funds A ∼ h(A)with A ∈ [0, ∞). Firms have on average capital Kf =

∫ ∞0 Ah(A)dA.

Banks collect capital from investors, have own capital Km

(exogenous), and extend loans to firms. Banks have access tomonitoring: at a private cost c they can reduce the private benefitthat the entrepreneur extracts from project L from B to b < B.Monitoring is efficient c < B − b.

Uninformed investors own capital, Ku, but they don’t monitor(arms-lenght creditors).


Role of direct creditors

Entrepreneur borrows directly from investors the amount Iu = (I − A)and promises to repay Ru when project returns X , 0 otherwise.Investors are willing to finance only H projects, but there is MH.

Entrepreneur behaves if:

(ICf ) pH(X − Ru) ≥ pL(X − Ru) + B

⇔ Ru ≤[X − B

∆p

]This implies a ”maximum pledgeable income” to creditors smallerthan X .

Investors’ rationality requires:

(IRu) pHRu ≥ yIu ⇔ Iu = (I − A) ≤ pHy

[X − B

∆p

]Vittoria Cerasi Principles of Corporate Finance 2020-21 4 / 26

Role of direct creditors

Therefore entrepreneurs will be able to raise direct credit as long as:

A ≥ A(y+) ≡ I − pH

y

[X − B

∆p

](1)


Role of banks

What happens when A < A(y)?

The entrepreneur with A < A(y) could borrow Im from the bank (andIu from investors) by promising to repay Rm to the bank (resp. Ru toinvestors) when project returns X , 0 otherwise.

Provided that the banker monitors, the entrepreneur behaves if:

(ICf ) pH(X − Ru − Rm) ≥ pL(X − Ru − Rm) + b

⇔ Rm ≤ X − Ru − b/∆p

The banker monitors if:

(ICm) pHRm − c ≥ pLRm ⇔ Rm =c

∆p

Combining (ICf ) and (ICm), the ”maximum pledgeable income” isnow enhanced:

Ru ≤[X − (b+ c)

∆p

]Vittoria Cerasi Principles of Corporate Finance 2020-21 6 / 26

Role of banks

Define the rate of return on intermediated funds β = pHR+m

Im= c

∆ppHIm

.

Direct credit is cheaper than bank credit due to the monitoring costlyeffort. The bank lends money to firms instead of disintermediating if:

βIm − c ≥ yIm.

Investors’ rationality requires:

(IRu) pHRu ≥ yIu ≡ y(I − A− Im)

Finally the entrepreneur will be able to raise external finance (a mix ofbank and direct credit) if:

A ≥ A(y+

, β+) ≡ I − Im(β)− pH

y

[X − b+ c

∆p

](2)

It is easy to see that A(y , β) ≤ A(y).


Coexistence of banks and direct credit

Theorem

Firms with A ≥ A(y) issue bonds on financial markets. Firms withA ∈ [A(β, y), A(y)] are funded also by banks, while firms withA < A(y , β) are ”credit rationed”.


Saving squeeze

All this is for given β and y . But these are market interest rates! Frommicroeconomics to macroeconomics: the credit channel.

Market interest rate is y .

Supply of capital (=savings) is S(y+)

Bond issues (demand of credit) are:

Du(y , β) ≡∫ A(y )

A(y ,β)[I − Im(β)− A]h(A)dA+

∫ I

A(y )[I − A]h(A)dA

where Du(y−

, β) (if y ↓ it implies that A(y , β) ↓ and also A(y) ↓)

Suppose a ”savings squeeze” S(y+) ↓: then y ↑ and A(y , β) ↑ . It is

possible to show that also β ↓Vittoria Cerasi Principles of Corporate Finance 2020-21 9 / 26

Credit crunch

Interest rate is given by β.

Supply of loans (= proportional to bank capital) Km.

Bank loans demand is given by:

Dm(y , β) ≡ Im(β)∫ A(y )

A(β,y )h(A)dA

where Dm(y , β−) ( if β↗ then Im(β) ↓ . In addition A(y , β) ↑ ).

Suppose a shock to bank capital Km ↓: then β ↑ and A(y , β) ↑(”credit crunch”). It is possible to show that y ↓


Credit rationing

Notice that total credit is given by the sum:

Dm +Du =∫ I

A(y ,β)[I − A]h(A)dA

When either Du ↓ or Dm ↓ =⇒ A(y , β) ↑, that is more firms arecredit rationed.


Liquidity shock

Finally also firms’ own funds can be eroded. In this case Kf ↓ and theentire distribution h(A) shifts on the left.

The number of credit rationed firms increases and also the percentageof firms relying on external finance. In this case we have both β ↓ andy ↓ .



Exercise 4E owns liquidity A and seeks external funding for an investment that requiresI = 85 at t = 0 and that returns X = {50, 100} at t = 2. E can choose betweentwo projects: a good project H and a bad project L. The success probability isPr {X = 100} = p; project H has a greater success probability pH = 0.8, whileproject L has pL = 0.6. However project L guarantees to E a private benefitB = 10:

1 Compute the NPV of the project H.

2 E raises (I − A) by issuing a bond that repays a face value Ru to investors.Write the incentive constraint for E to choose project H and compute hismaximum pledgeable income (constraint on Ru).

3 Write the investors’ rationality constraint and find the minimum value Ru,assuming that E chooses project H. Find the minimum threshold for A forwhich E manages to raise external financing.


1 The bank monitors at cost c = 2, reducing as a consequence the privatebenefit from B = 10 to b = 5. Assume an E who is credit rationed. E asksfunding exclusively to a bank and promises to repay Rm at t = 2. Which isthe minimum threshold for A to obtain a loan from the bank?

2 Assume now own funds A are uniformly distributed between 0 and 100, thatis A ∼ h(A) = 1

100 on the interval [0, 100], where h(A) is the densityfunction. Compute the percentage of firms that are credit rationed, thosethat are financed by financial markets, those financed by the banks andthose that self-finance the investment.


Banks vs. Arms’ length creditors

”Arms’ length” creditors (Rajan, JF 1992) are creditors who provideexternal finance and keep at distance the firm without monitoringuntil the maturity of the debt contract at T .

Three dates (t = 0, 1, 2) (alternative gross return = 1).

At t = 0 an Entrepreneur has a productive project, but has no money.E needs I > 0 (no internal funds A = 0). Capital markets arecompetitive.

At t = 1/2: E is subject to moral hazard:

might exert a continuous effort e ∈ [0, 1]private cost of effort is e



At t = 1: productive project might be prematurely liquidated. Thereare two possible states {G ,B} that are observed by banks and E.

However liquidation is costly, since L < I .

At t = 2 : the project returns; its revenue is contingent upon therealization of one of the two possible states G (Good) or B (Bad).

The probability of the state G is q(e), while (1− q(e)) is theprobability that state B occurs.

in state G (Good) the project returns X (with probability 1);in state B (Bad) the project returns X with probability p, 0 otherwise.



Assumption 1: Banks are informed creditors, that is they observe thetrue state {G ,B}, while bond-holders are uninformed creditors hencethey do not observe it.

Assumption 2: X > I > L ≥ pX

Assumption 3: q′(e) > 0, q′′(e) < 0. A greater effort increases theprobability of occurrence of state G , although at a decreasing pace.


First Best

E has enough internal funds to finance the project (self-finance).

E decides:

- in state G : given that X > L he will continue theproject and earn q(e)(X − I );- in state B: since pX < L he will liquidate the projectand his income is [1− q(e)](L− I )

⇒ liquidation occurs only in state B.

At t = 1/2 the optimal effort maximizes E’s expected profits, i.e.:

π(e) = q(e)(X − I ) + (1− q(e))(L− I )− e

⇒ q′(e∗) = 1X−L


Direct credit (uninformed credit) - Arms’ length (A)

E issues at t = 0 a financial contract: in exchange for I , promises torepay D ≤ X at t = 2 when the project returns X . Since the creditoris an ”arms’ lenght” creditor (does not observe the state) and willnever liquidate the project.

The decision about liquidation at t = 1 rests with E :

- In state G : E’s payoff is X −D when continuing,while 0 when stopping the project;- in state B: E’s payoff is p(X −D) when continuing,while 0 if he stops it.

⇒ E will always decide for continuation.

At t = 1/2, for given D, the optimal effort of E maximizes:

π(e) = q(e)(X −D) + (1− q(e))p(X −D)− e

⇒ q′(eA) = 1(1−p)(X−D)

.


Direct credit (uninformed credit) - Arms’ length (A)

At t = 0: individual rationality condition for investors requires D tofulfill:

q(eA)DA + (1− q(eA))pDA = I

that is:

DA =I

qA + (1− qA)p

where qA = q(eA). It is possible to show that

q′(eA) =1

(1− p)(X −DA)>

1

X − L

External finance reduces E’s incentive relatively to the First Best, thatis eA < e∗: E pays the full cost of his effort, but the marginal revenueof this effort partially accrues to the external creditor.


Bank finance (B)

E is granted a bank loan with face value D.

The decision to liquidate stands with the bank, after observing statesG or B.

- In stateG : bank’s payoff is D, while L (recovery value)if the project is liquidated. Since D > I and I > L, itfollows that D > L), hence bank does not liquidate theproject;- in state B: the bank’s expected payoff is pD, while Lif liquidated: since L > pX > pD the bank liquidatesthe project.

⇒ The bank liquidates the project in state B.

At t = 1/2: for given D, the optimal effort maximizes profits, that is

π(e) = q(e)(X −D) + (1− q(e))× 0− e

⇒ q′(eB) = 1X−D > 1

X−L


Bank finance (B)

At t = 0 the individual rationality condition the bank requires

q(eB)DB + (1− q(eB))L = I

from which

DB =I − (1− qB)L

qB

where qB = q(eB). Once we substitute the optimal effort,

q′(eB) =1

qB(X − L) + (L− I )>

1

X − L

also in this case eB < e∗ for the same reason as before.


Choice between bank credit (B) and direct credit (A)

Substituting the optimal effort eA and the face value DA into theprofit

π(eA) = qA(X −DA) + (1− qA)p(X −DA)− eA

we derive the equilibrium profit with direct credit:

πA = qAX + (1− qA)pX − I − eA

Substituting instead the optimal effort eB and the face value DB intothe profit

π(eB) = q(eB)(X −DB)− eB

we derive the equilibrium profit with bank credit:

πB = qBX + (1− qB)L− I − eB


Choice between bank credit (B) and direct credit (A)

If the equilibrium efforts were the same in both cases, qA = qB , giventhat L > pX , bank credit would dominate direct credit, sincecontinuation in state B is sub-optimal.

However the two type of creditors have a different impact on E’sincentive:

if qB > qA (the threat of liquidation increases E’s effort in B): bankcredit is superior;if qB < qA (the threat of liquidation demotivates E who reduces hiseffort due to the fear of being expropriated): then direct credit, that isdealing with a more passive creditor, is optimal.

To conclude, banks are tougher creditors compared tobond-holders since they tend to liquidate projects more often:however if this demotivates E, who will exert a lower effort, arms’lenght creditors are preferable.



Exercise 5An E, without own liquidity (A = 0), needs an investment of I = 100 toundertake a risky project at t = 0. The project will deliver at t = 2 a cash flowX = {0, 140}. However there are two possible states which affect the success ofthe project: in state G the project is always successful, that is it delivers 140 withcertainty; while in state B only with probability 0.5 and it fails with probability0.5.If E exerts an effort (project H), state G occurs with probability 3/4, while incase he shirks (project L) state G occurs only with probability 1/4. Effort isprivately costly to E, that is it costs c = 10. Given that the effort is notobservable and the cost is entirely borne by E, there is moral hazard in the sensethat E will try to avoid the effort.At an interim date, t = 1/2, there is the possibility to terminate the project andsell the asset, that is to liquidate the project. In case of liquidation the projectreturns L = 80 with certainty. Finally notice thatX = 140 > I = 100 > L = 80 > p.X = 70.


1 Compute the First Best choice in terms of Liquidation: assume that E hasown funds I to undertake the project. Check his choice in terms ofliquidation and effort.

2 Assume that the project is financed by an ”arms’ length” investor(bond-holder) who requires a face value D in exchange for the initialinvestment I = 100. Assume that 100 < D < 140 and compute the optimalchoice of effort for E given that he is in control of the liquidation choice.Check whether the bond-holder is willing to finance E, anticipating hischoice of effort.

3 Assume now that the bank finances E with a loan with face value100 < D < 140. The bank can observe the realized state, either G or B:therefore the bank decides whether to liquidate the project, depending onthe realized state. Check whether the bank is willing to finance E,anticipating his choice of effort.


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