corporate finance: agency models of capital structurespiegel/teaching/corpfin/ppt... · 2016. 5....

Corporate Finance:Agency models of capital structure

Yossi SpiegelRecanati School of Business

Jensen and Meckling, JFE 1976

The agency cost of outside equity

Corporate Finance 3

The investment model

The timing:

V’(I)>0>V”(I) and V(0) = 0

V’(0) = and V’() = 0 (interior sol’n)

The entrepreneur’s payoff: U(I) = V(I) + (R-I)

Period 1 Period 2

The firm is establishedby an entrepreneur whohas R dollars and needsto invest I

The investment yieldsV(I), R-I is consumed as perks

V(I)

I

Corporate Finance 4

Internal financing F.O.C for the entrepreneur’s problem:

.1*)('01')(' IVIVIU

V’(I)

I

1

I*

Corporate Finance 5

Internal financing The entrepreneur’s payoff at the

optimum:

But what if I* > R? In that case the entrepreneur must have external financing

RIIVIU ***)(

Corporate Finance 6

Debt financing The entrepreneur issues debt with face value D to raise

I*- R upfront The entrepreneur’s payoff:

U(I,D) is maximized at I* (the firm invests optimally) Debt is safe: ex post the firm has V(I*) > I* > I*-R

D* = I*-R The entrepreneur’s payoff:

Perks

anteex flowCash

postex Payoff

*),( IRIRDIVDIU

RIIV

IRIRDIVDIU

**)(

*****)*,(

Corporate Finance 7

Equity financing with commitment The entrepreneur issues equity with equity

participation 1- (the entrepreneur keeps ) and commits to invest I*

To raise I*-R:

The entrepreneur’s payoff:

.*)(

*1***)()1(*

IVRIRIIV

E

RIIV

IREIVIU

**)(

*****)*,(Perkspayoffpost Ex

Corporate Finance 8

Equity financing without commitment The entrepreneur issues equity with

equity participation 1-, but cannot commit to invest I*

After receiving E, but before choosing I, the entrepreneur’s payoff:

Perkspayoffpost Ex

),( IREIVIU

Corporate Finance 9

Equity financing without commitment F.O.C for the entrepreneur’s problem:

We get underinvestment (more outside equity) I* (more

underinvestment)

V’(I)

I

1

I** I*

V’(I)

.1*)*('01'),(' IVIVIU

Corporate Finance 10

The agency cost of outside equity The entrepreneur’s payoff:

The entrepreneur’s payoff with commitment:

By revealed preferences (and since I** < I*):

The entrepreneur bears the cost of underinvestment (outside investors break even)

RIIVRIIVIV

RIEIVIU

***)*(***)*(1*)*(

******)*,*(

RIIVIU **)()*,(

RIIVRIIV ***)*(**)(

Corporate Finance 11

The optimal choice of How does affect U(I**,)?

The entrepreneur will raise up to the point where

E**=0 at = 0 (since then I**=0) and at = 1 E** is inverse U-shaped

0**1*)*(')*,*(

)()(

/1

IIVIU

**

**1**E

IVRI

Corporate Finance 12

The entrepreneur’s budget constraint:

The relevant sol’n is with the maximal

The optimal choice of

**

E**

R

I**

Corporate Finance 13

The effort model

The timing:

V’(e)>0>V”(e) and V(0) = 0

V’(0) = and V’() = 0 (interior sol’n)

The entrepreneur’s payoff: U(e) = V(e) - e

Period 1 Period 2

The firm is establishedby an entrepreneur whohas R dollars and needsto invest I and exerteffort, e

The effort yieldsV(e), the cost of effortis e (no perks)

V(e)

e

Corporate Finance 14

Internal financing F.O.C for the entrepreneur’s problem:

1*)('01')(' eVeVeU

V’(e)

e

1

e*

Corporate Finance 15

Internal financing The entrepreneur’s payoff at the

optimum:

But what if I > R?

Debt financing: debt is safe so D*=I-R

***)( eeVeU

Corporate Finance 16

Equity financing without commitment The entrepreneur issues equity with

equity participation 1-

After receiving E, but before choosing e, the entrepreneur’s payoff is:

eeVeU ),(

Corporate Finance 17

F.O.C for the entrepreneur’s problem:

We get underinvestment

Equity financing without commitment

V’(e)

e

1

e** e*

V’(e)

1*)*('01'),(' eVeVeU

Corporate Finance 18

The agency cost of outside equity The entrepreneur’s payoff:

The entrepreneur’s payoff with commitment:

By revealed preferences (and since e** < e*):

The entrepreneur bears the cost of underinvestment (outside investors break even)

****)*,*( eeVeU

***)*(**)( eeVeeV

**)*,( eeVeU

Corporate Finance 19

The optimal choice of How does affect U(e**,)?

The entrepreneur will raise up to the point where

E**=0 at = 0 (since then e**=0) and at = 1 E** is inverse U-shaped

0**1*)*('*)*()*,*(

0

eeVeVeU

**

**1E

eVRI

Corporate Finance 20

The entrepreneur’s budget constraint:

The relevant sol’n is with the maximal

The optimal choice of

**

E**

R

I

Jensen and Meckling, JFE 1976

The asset substitution problem

Corporate Finance 22

A simple example Consider a box with two sealed envelopes: one with $100

and the with $0

You can either pick one envelop from the box or receive $70 for sure – what would you do?

Now suppose you owe someone $50 out of your gains

If you take $70, your payoff is $70 - $50 = $20

If you pick one of the sealed envelops then you either have $100 - $50 = $50, or you pick the empty envelop and your payoff is 0 because you cannot pay the $50 your expected payoff is ($0+$50)/2 = $25

The lottery is better even though its NPV is only $50

Corporate Finance 23

The model Two projects: Safe project with return Z Risky project with return X ~ [0, )

The firm has debt with face value D

The management is perfect agent for equityholders – the agency problem is between equityholders and debtholders

Corporate Finance 24

Payoffs under the two projects Equityholders’ payoff with the risky project:

Equityholders’ payoff with the safe project:

The firm surely chooses the risky project if Z ≤ D assume that Z > D. Hence

0,DZMaxYS

D

R XdFDXY )(

DZYS

Corporate Finance 25

Comparing the two projects The safe project is better iff:

Properties of XC(D):

D

CRS XdFDXDDXZYY )()(

D

C

DFDFXdFD

DX )()(11)(1)(

XXXdFX C ˆ)()0(0

Corporate Finance 26

Choice of projects with leverage XC(D) > for all D > 0

A leveraged firm prefers the risky project even when it is inefficient

safe project is efficient

X )(DX C

X

safe project is chosen when D>0

risky project is efficient

risky project is chosen when D>0

Myers, JFE 1977

The debt overhang problem

Corporate Finance 28

The model

The timing:

In period 1 it is common knowledge that X~[0, ) Absent debt, the firm invests iff X ≥ I. The value

of the firm:

Period 1 Period 2

The firm is establishedby an entrepreneur who issues debt with face value D

Period 1.5

I

XdFIXV )()0(

The entrepreneur learnsthe return, X, from a project that costs I anddecides whether to invest

X is realized anddebt is paid

Corporate Finance 29

Illustrating – All-equity firm

XX1

Xf (X)

If(x)

I

E(0)

Corporate Finance 30

Short-term debt (due at period 1.5) Suppose debt has to be paid before it is

time to invest

If X – I ≥ D, the firm will invest

If X – I < D, the firm will not invest and will go bankrupt. The debtholders will invest provided that X ≥ I

The firm invests iff X ≥ I investment is efficient

Corporate Finance 31

The value of the firm with short-term debt The value of debt:

The value of equity:

The total value of the firm:

ID

ID

I

XDdFXdFIXDB )()()(

ID

XdFIDXDE )()(

I

ID

ID

I

XdFIX

XdFIXXdFIXDV

)(

)()()(

Corporate Finance 32

Illustrating the debt overhang problem

XX1

Xf (X)

If(x)

D+I

B(D)

E(D)

(D+I)f(x)

I

Corporate Finance 33

Long-term debt Suppose debt has to be paid after it is

time to invest

If X – I ≥ D, the firm will invest

If X – I < D, the firm will not invest and will go bankrupt. The debtholders get a firm with no investment opportunities

Corporate Finance 34

The value of the firm with long-term debt The value of debt:

The value of equity:

The total value of the firm:

The value is lower than under short-term debt. This is the debt overhang problem

ID

XDdFDB )()(

ID

XdFIDXDE )()(

ID

XdFIXDV )()(

Corporate Finance 35

Illustrating the debt overhang problem

XX1

Xf (X)

If(x)

D+I

B(D)

E(D)

(D+I)f(x)

I

Loss

Berkovitch and Kim, JF 1990

Overinvestment and underinvestment

Corporate Finance 37

The model

The timing:

g’(I)>0>g”(I) and g(0) = 0

g’(0) = and g’() = 0 (interior sol’n)

z~[0, )

Period 0 Period 2

The firm is establishedby an entrepreneur who issues debt with face value D

The cash flow X isrealized and the firminvests I

Period 1

Investment yields zg(I), D is due

g(I)

I

Corporate Finance 38

Excess funds: X > I Cash flow at the end of period 2:

The firm is solvent iff

The expected value of equity:

IXIzg )(

)()( 1 Ig

XIDzzDIXIzg

1

)()()(1z

zdFIDXIzgDE

Corporate Finance 39

Illustrating – excess funds

z1

(X-I)f(z)

z1

E1(D)

(zg(I)+X-I)f(z)

Df(z)

Corporate Finance 40

Investment with excess funds F.O.C for investment:

Rewriting:

0)(1)()('

)(1)(')(

1

1

1

1

zFzzdFIg

zdFIzgIDE

z

z

1

1

|1

)(1

)(

1)('

1

zzzE

zF

zzdFIg

z

Corporate Finance 41

Deficit: X < I The firm covers the deficit by issuing

extra equity Cash flow at the end of period 2: zg(I) The firm is solvent iff

The expected value of equity:

)()( 2 Ig

DzzDIzg

2

deficit cover the tofunds Extra

2 )()()(z

XIzdFDIzgDE

Corporate Finance 42

Illustrating – deficit

z1

(X-I)f(z)

z2

E2(D)

zg(I)f(z)

Df(z)

Corporate Finance 43

Investment with deficit F.O.C for investment:

Rewriting:

01)()('

1)()(')(

2

2

2

z

z

zzdFIg

zdFIzgIDE

2

)(

1)('

z

zzdFIg

Corporate Finance 44

The value of the firm with excess funds

IXIgz

zdFIXIzg

zDdFzdFIXIzg

zdFIDXIzgDV

z

z

z

)(ˆ

)()(

)()()(

)()()(

0

Debt

0

Equity

1

1

1

1

Corporate Finance 45

The value of the firm with deficit

The value of the firm is exactly as in the case of excess funds

IXIgz

XIzdFIzg

zDdFzdFIzgXIzdFDIzgDVz

z

z

)(ˆ

)()(

)()()()()()(

0

Debt

0

Equity

2

2

2

2

Corporate Finance 46

Efficient investment F.O.C for investment:

Excess funds:

Deficit:

zIgIgz

IDV

ˆ1)('01)('ˆ)(

zzzdF

Ig

z

ˆ1

)(

1)('

2

zzzzE

zF

zzdFIg

z

ˆ1

|1

)(1

)(

1)('1

1

1

Corporate Finance 47

Comparison

Ig’(I)

z1

1|1

zzzE

2

)(

1

z

zzdF

I2 I1I*

Excess funds overinvestment Deficit underinvestment