blind man buff ocs interges kd var 20v2

7/27/2019 Blind Man Buff Ocs Interges Kd Var 20v2

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Blind man's buff:

ON THE SEARCH OF THE OPTIMAL CAPITAL STRUCTURE

IGNACIO VLEZ PAREJA,

FELIPE MEJA

JAMES KOLARI

AUGUST 30, 2012

AbstractAbstractAbstractAbstract::::

In these slides we discuss the practical and conceptual difficulty of finding anOptimal Capital Structure. We propose a normative approach we call ImplicitBankruptcy Costs Theory. We proceed to find the optimal capital structureand value when leverage is both constant and variable from one period tothe next and the discount rate for tax shields is the cost of levered equity, Ke.Numerical procedures and a recursive closed-form non-circular expressionsfor the finite-period and perpetuity cases are presented, which facilitateimplementation including Monte Carlo simulations.

Number of Pages in PDF File: 32

Keywords: Optimal capital structure, valuation, non-circularity, finite cashflows, perpetuities tax shield, cost of equity

JEL Classification: M21, M40, M46, M41, G12, G31, J33

29/09/2013 EOC Vlez Pareja, Meja y Kolari 2


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Blindman'sbuff(Goya, 1789)

Women playing the Blindman'sbuff1803



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These slides are based upon the followingpapers

Kolari, James W. and Ignacio Vlez-Pareja. 2010. Corporation Income Taxesand the Cost of Capital: A Revision. Available at SSRN:http://ssrn.com/abstract=1715044 )

Vlez-Pareja, Ignacio, Meja Felipe and James Kolari. 2012. Optimal CapitalStructure for Finite Cash Flows

(Work in process)http://ssrn.com/abstract=1799605

Salas Prez, Rafael, Gutirrez Ruiz, Juan and Ignacio Velez-Pareja. 2011.

Value of Debt Tax Shields in Colombia: An Empirical Study.http://papers.ssrn.com/abstract=1919305


What is this paper about? We explore the possibility of identifying a level of debt that results in

an optimal value of the firm.

We propose a method for finding a normative optimal capitalstructure for finite flows in two versions: (1) an Excel spreadsheet

method for optimal structure, and (2) an analytical formulation. Ourapproach works when it is assumed that debt interest tax savings arediscounted at the cost of equity, Ke.



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Problem not solved in financeProblem not solved in financeProblem not solved in financeProblem not solved in finance

Optimal capital structure (OCS) has been a very elusive issue formany years and experts believe that is one of the unsolvedproblems of corporate finance.

Everybody speaks of the OCS, but no one has seen it.


Theories of OCS

Tradeoff theory

Pecking order theory or hierarchy of available resource utilization

Cash flow theory of Myers (1993)

Implicit bankruptcy costs theory (consistent with our proposal)



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Tradeoff theory

Tradeoff theory assumes that the firm defines an OCS and tries toreach it in the future. It recognizes that there are benefits called taxsavings on interest tax deductions on debt payments versus costs offinancial distress (including potential bankruptcy costs). Bothincrease with indebtedness and eventually cancel each other out atthe OCS.

This is the most popular theory, which can be found in corporatefinance textbooks.


Then I borrow up to 100%

Discounting the tax savings (TS) at Ku or Kd yields the result that (ifnot adjusted for bankruptcy costs) the optimal capital structure is100% debt. However, this result is not reasonable, because as a firmborrows debt funds, there exists some contingent and/or hiddencosts associated with the fact that the firm may not be able to pay thedebt in the future and become insolvent. This means that there is an

expected value or cost of bankruptcy or financial difficulties thatreduce the value of the firm. The existence of these costs prevent, ingeneral, firms to borrow up to 100%.

This idea is known as the trade-off theory.



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Financial distress costs

When a firm starts to borrow, it increases the risk perceived by thirdparties, for example, the debt holders. A bank could charge more fornew loans. This higher cost is reflected in lower cash flow which inturn increases cash requirements and could increase indebtedness.


Trade-Off Costs

Debt information spreads easily and providers can lose confidenceand stop providing credit (at zero cost) and require payment inadvance on outstanding debt. This reduces liquidity and increasesthe need for funding, which means a higher cost. Creditors can alsoreduce the amount of credit facilities such that the firm loseseconomies of scale and gross margin is reduced.Customers, who also learn of the situation, possibly will not buy

the same amount because they prefer a secure supplier.



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Human Resources Costs

When the firm gets into financial difficulties, it is possible that qualityemployees resign from the company. Each new employee must betrained and the loss of intellectual capital is difficult to measure andreplace.


A Vicious Circle

The firm can get into a vicious debt cycle that forces it to explorecostlier financial sources. Financing costs above usury rates may notaccepted by law to be deducted. That is, the tax savings or shields, TS,are lost. On reaching the extreme situation of near bankruptcy, advisersare required in different areas of the firm such as lawyers in particular.

These added costs of financial difficulties can be considerable.



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EOC and firm value


D/E = Debt/Equity Optimal leverage

Firm Value Vlevered = Vunlevered + PV(TS)

Firm Value

Present value of TS

Distress CostsMaximum value of levered firm Vlvd

Vunlevered

OptimalOptimalOptimalOptimal WACCWACCWACCWACC


WACC

Mnimum WACC

D/E Optimal Capttal Structur

u (unlevered firm)

Kd(1-T) = cost of debt after taxes

WACC= KeE% + Kd(1-T)D%

Ke = cost of equity


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OCS and Other Theories

The pecking order theory that proposes a hierarchy ofuse of available resources as well as cash flow theorydo not identify an OCS.


In Search of the OCS

Many researchers in finance have been trying to discover how andwhy firms borrow and how they get (if at all) to the OCS.

The trade-off theory is most popular approach to finding an OCS.



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Some Empirical Evidence

The different theories have to be compared with what we see in reality.Below there is some evidence from Colombia, the U.S., and LatinAmerica.


Colombia: 25 traded firms 2001-2010

y = 0.3559x-0.16

R = 0.0401

0

1

2

3

4

5

6

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Totalva

lue/Bookvalue

D%

Total value/Book value

(D+E)/Vass

Potencial ((D+E)/Vass)



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Regression LnTVt TSt and Dt

Dependent variable Tax shields Debt

Relation Does not affect Does not affect

Variable dependiente: horros en Impuestost Deudat

Ln (VTt)3,62E-07

(5,01E-07)-

Ln (VTt) -2,86E-07

(1,80E-07)

Relacin No afecta No afecta

Regression LnTVt TSt-1 and Dt-1


Relation Positive Does not affect

Variable dependiente: Ahorros en Impuestost-1 Deudat-1

Ln (VTt)7,21e-06

(5,59e-07)***

Ln (VTt) - 1,61e-07(1,71e-07)

Relacin Positiva No afecta


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Regression TVt TSt and Dt


Relation Negative Does not affect

Variable dependiente: Ahorros en Impuestost Deudat

-26,12253

(3,329189)***

1,266308

-1,401219

Relacin Negativa No afecta

VTt -

VTt -

Regresin VTt TSt-1 y Dt-1


Relation Does not affect Does not affect

Variable dependiente: Ahorros en Impuestost-1 Deudat-1

VTt4.500237

(4,745917)-

VTt - 1,271748(1,448643)

Relacin No afecta No afecta


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PV(TS at Kd)/TotAsst vs D%


0

0.2

0.4

0.6

0.8

1

1.2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

VTS_

Kd/TotAsst

D%_t-1

VTS_Kd/TotAsst

PV(TS at Ke)/TotAsst vs D%t-1


0

0.05

0.1

0.15

0.2

0.25

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

VTS_K

e/TotAsst

D%_t-1

VTS_Ke/TotAsst


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Regression statistics

VTS(Ke) vs D%t-1

R2 0,46416

R2 adjusted 0,455902

Observations 188

Coeff. t p-value

D%t-12 -0,29762 -7,17238 1,69E-11D%t-1 0,312791 10,92598 8,75E-22


With Kd and Ku there is no OCS

Clearly, as Kd and Ku are not dependent from D%, for the basicmodel of M & M, the greater D% the higher VTS is, a linearrelationship. Kd can be modeled as a function of D%. But theincrease in Kd is NOT the only cost of bankruptcy. Other costs arecaptured by Ke, as will be seen.

There is a contradiction between the behavior of VTS calculatedwith Ke and the behavior of TV (D + # stocks * Price). The data

suggest that VTS = PV (TS at Ke) (which is what generates theoptimum) behave nearly as an inverted U. But the market does notrecognize it. Not so with VTS = PV (TS at Ku or Kd). The behavior isdecreasing when D% grows.



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USA Quarterly 1951 - 2010

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

.20 .25 .30 .35 .40 .45 .50 .55

DEBTTOTOTVALU

TOTVALTOTASSET


USA by industry 1998-2010

0

1

2

3

4

5

6

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

T

otalvalue/TotAsst

D%

Total value /TotAsst industries USA



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USA by industry lagged data 1998-2010

0.00

1.00

2.00

3.00

4.00

5.00

6.00

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

Totalvalue/TotAsst

D%

Total value /TotAsst industries USA1998-2010

vt_at_1

vt_at_2

vt_at_3

vt_at_4

vt_at_5

vt_at_6

vt_at


USA and Latam 2010 (M. Merlo)

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

10.00

0.0% 10.0% 20.0% 30.0% 40.0% 50.0% 60.0% 70.0% 80.0% 90.0% 100.0%

Total value /TotAsst



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TheTheTheThe Blind Man's BuffBlind Man's BuffBlind Man's BuffBlind Man's Buff We want to find a D% that maximizes the value of the firm, but managers do not know

how or where it is located.

If there is debt, the firm might earn tax benefits. It is known that the tax savings or taxshields are there, but shareholders do not directly see them because the dividendpayments they receive do not clearly show these tax benefits.

At the same time, with debt comes some financial costs. The hard part is that it is not clearwhat those future potential bankruptcy costs. Everyone knows how they arise forexample, commercial, financial, and legal costs but they do not know how to measurethem. And nobody says how.

Although debt has some tax benefits, shareholders investment is risky due to being thelast in the chain to receive their investment and profits.

At the same time, many people misunderstand what was said by Modigliani and Miller in

1958 that the capital structure does not affect the value of the firm. This is true only ifthere are no taxes.

In short, you have to guess the OCS. No one knows how to find it, or how to calculate it itis a game of blind man's buff!

Facsimile of illustration of a class of in a book ofChinese elementary school in 1912.



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In Search of the EOCS

There are works that try to find the optimal debt, others seekthe speed with which the firm approaches the OCS, etc.

It is a frantic search for the simple reason that no one knowswhere or how to calculate the OCS. Everyone talks about theEOC but no one has seen it.


Implicit Bankruptcy Costs Theory (1)

While the trade-off theory leaves things "alone" in order to reach anoptimal, the proposed discounting of TS at the levered cost of equity, Ke, isnormative and prescriptive.

After discounting the TS with Ke, an optimum is obtained, and you can tellmanagement that there is an optimum and can make decisions to reachthat optimal level of leverage.

It is not left to the "invisible hand" to handle the costs of financial distressand bankruptcy.

The trade-off theory does not tell management what to do, but says thatthere are some theoretical costs that may appear and then get anoptimum.



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Implicit bankruptcy costs TheoryImplicit bankruptcy costs TheoryImplicit bankruptcy costs TheoryImplicit bankruptcy costs Theory(2)(2)(2)(2)

Our proposal that tax savings or shields, TS, are discounted at thecost of equity, due to the fact that TS belongs to the shareholder(CFE = FCF + TS - CFD), there is a firm valuation effect associated withdebt that does not occur with discount rates Kd and Ku are used(i.e., commonly proposed in corporate finance literature).

The Ke formula when it is supposed that Ke is the discount rate forTS is:

By having the debt involved in the formula for Ke, it captures the effect

of debt, and an optimum is obtained, as seen in the chart below.


( )

( )TS

1i1i

1-iiiii

1-i

Un

1i

1-iiiii

VE

DKdKuKuKe

DV

DKdKuKuKe

+=

+=

OCS when Ke is the discount rate of TS


9.9

10

10.1

10.2

10.3

10.4

10.5

10.6

10.7

10.8

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

VL

D/V

Firm Value, VL vs D% perpetuity


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The case of finite cash flows and constant D%

The procedure maximizes firm value with constantD%. The optimizer model isMax VLsubject to0 D 1% (single cell)VL is the firm value and D% is the constant leverage.This procedure generates a circularity and you have toiteratively calculate value to reach a solution.


ExampleExampleExampleExample

Year 1 2 3 4

T 35% 35% 35% 35%

Kd 11.00% 11.00% 11.00% 11.00%

Ku 15.00% 15.00% 15.00% 15,00%

D% 50.00%

FCF 17.00 20.00 22.00 25.00



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APV, provisionalAPV, provisionalAPV, provisionalAPV, provisional tabletabletabletable

Year 0 1 2 3 4

FCF 17..00 20.00 22.00 25.00

PV(FCF at Ku) 58.66 50.46 38.03 21.74

Debt. D 30.50 26.04 19.48 11.05 -

Interest 3.36 2.86 2.14 1.22

TS 1.17 1.00 0.75 0.43

Ke = Ku + (Ku-Kd)Dt-1/(VUt-1 - Dt-1) 19.33% 19.27% 19.20% 19.13%

VTS=PV(TS at Ke) 2.34 1.62 0.93 0.36

Total value VL 61.01 52.08 38.96 22.10

E=VL-D 30.50 26.04 19.48 11.05 -

29/09/2013 EOC Vlez Pareja. Meja y Kolari 41

D% = 30,5/61,01 = 26,04/52,08 = 50%

APV, finalAPV, finalAPV, finalAPV, final tabletabletabletable

Year 0 1 2 3 4

FCF 17.00 20.00 22.00 25.00

PV(FCF a Ku) 58.66 50.46 38.03 21.74

Debt, D 46.43 39.60 29.58 16.74 -

Interest 5.11 4.36 3.25 1.84

TS 1.79 1.52 1.14 0.64

Ke = Ku + (Ku-Kd)Dt-1/(VUt-1 - Dt-1) 30.18% 29.58% 29.00% 28.39%

VTS=PV(TS a Ke) 3.03 2.16 1.27 0.50

Total value, VL 61.70 52.62 39.31 22.24E=VL-D 15.26 13.02 9.72 5.50 -


D% = 46.43/61.70 = 39.60/52.62 = 75.2587%


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PV of CFE. FinalPV of CFE. FinalPV of CFE. FinalPV of CFE. Final TableTableTableTable

Year 0 1 2 3 4

FCF 17.00 20.00 22.00 25.00VU = PV(FCF a Ku) 58.66 50.46 38.03 21.74

Equity PV(CFE at Ke) 15.26 13.02 9.72 5.50 -

Value of Debt 46.43 39.60 29.58 16.74 -

Principal 6.83 10.02 12.84 16.74

Interest 5.11 4.36 3.25 1.84

TS 1.79 1.52 1.14 0.64

CFD 11.94 14.38 16.10 18.58

CFE= FCF CFD + TS 6.85 7.15 7.04 7.06

Ke =Ku+(Ku-Kd)Dt-1/(VUt-1 - Dt-1) 30.18% 29.58% 29.00% 28.39%

Total value, VL 61.70 52.62 39.31 22.24


D%=46.43/61.70 = 75.2587%

Optimal D%

D% VL E-VTS VU E-VTS

0% 58.7 - 58.7 58.7

10% 59.2 0.5 58.7 52.7

20% 59.6 1.0 58.7 46.7

30% 60.1 1.4 58.7 40.6

40% 60.6 1.9 58.7 34.4

50% 61.0 2.3 58.7 28.260% 61.4 2.7 58.7 21.8

75.2587% 61.7 3.0 58.7 12.2

80% 61.6 3.0 58.7 9.4

90% 60.9 2.2 58.7 3.9

99.98% 58.7 0.0 58.7 0.029/09/2013 EOC Vlez Pareja, Meja y Kolari 44


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OCS,OCS,OCS,OCS, constantconstantconstantconstant KdKdKdKd


.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

0% 20% 40% 60% 80% 100% 120%

V

VTS

Vun

AllAllAllAll methodsmethodsmethodsmethods yieldyieldyieldyield thethethethe samesamesamesame resultresultresultresult

There is consistency among methods: FCF, APV, CCF, CFE

Equilibrium equations among cash flows and values are fulfilled.

The proposed Ke reveals the OCS:

Note that Ke does not imply a constant D% nor a constant WACC (WACC).

( )

( )TS

1i1i

1-iiiii

1-iUn1i

1-iiiii

VE

DKdKuKuKe

DV

DKdKuKuKe

+=

+=


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TheTheTheThe case ofcase ofcase ofcase of finitefinitefinitefinite cashcashcashcash----flow and variable D%flow and variable D%flow and variable D%flow and variable D%

The procedure maximizes firm value with constantD%. The optimizer model isMax VLsubject to0 D 1% (several cells D% for each period)VL is the firm value and D% is the constant leverage.This procedure generates a circularity and iterativelycalculate the solution.


With variable D%

Year 0 1 2 3 4

D% 72.983% 75.600% 78.566% 82.324%

FCF 17.00 20.00 22.00 25.00

Debt D 45.04 39.79 30.90 18.32

Principal payment 5.25 8.90 12.57 18.32

Interest 4.95 4.38 3.40 2.02

Tax shields. TS 1.73 1.53 1.19 0.71

CFD 10.20 13.28 15.97 20.34CFE = FCF - CFD + TS 8.53 8.26 7.22 5.37

PV(FCF at Ku) 58.66 50.46 38.03 21.74

Ke = Ku + (Ku-Kd)D/(VU- D) 28.22% 29.92% 32.31% 36.45%

VTS 3.05 2.17 1.29 0.52



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Analytical Solution for variable OCSfor variable OCSfor variable OCSfor variable OCS

We find Debt that generates OCS


Solucin numrica

Year 0 1 2 3 4

Ku 15.00% 15.00% 15.00% 15.00%

Kd 11.00% 11.00% 11.00% 11.00%

Ke 28.22% 29.92% 32.31% 36.45%

T 35.00% 35.00% 35.00% 35.00%

FCF 17.0000 20.0000 22.0000 25.0000

VU 58.6647 50.4644 38.0340 21.7391 0.0000

CFE 8.5342 8.2569 7.2180 5.3679

E 16.6724 12.8434 8.4286 3.9341 0.0000

TS 1.7340 1.5320 1.1895 0.7054

VTS 3.0463 2.1720 1.2897 0.5170 0.0000

DOpt 45.0385 39.7930 30.8951 18.3221

VL = P+ D 61.7109 52.6364 39.3237 22.2561 0.0000

D% = DOpt/VL 72.9831% 75.5998% 78.5660% 82.3237%29/09/2013 EOC Vlez Pareja, Meja y Kolari 50


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OCSOCSOCSOCS withwithwithwith variablevariablevariablevariable KdKdKdKd = F(D%)= F(D%)= F(D%)= F(D%)

Although the formulation of Ke when the TS are discounted at the samerate Ke appears Kdt implying that Kd can vary, in Kd it is not includedimplicitly the variation we are interested in: that is, the effect of the valueof leverage on Kd.

Examining lending rates for Colombia between 1998 and 2010 and "riskfree" rates (TES bonds), a risk premium for debt RPD can be estimated asthe difference between the two. With that RPD a relationship between RPDand leverage D% was established. Analyses were performed for non-financial sectors using a total of 771 observations (sector/year). We usedthe accounting D% and the database of the Superintendence of Companiesof Colombia. The use of book value of leverage is justified because it is themost evident measure of leverage perceived by the market.


Type of loan Coeff. D% Constant

Ordinary 0.010947417 0.066444642

t 1.494076504 43.94521461

p-value 0.135565818 6.3017E-212

Preferential 0.021257514 0.018028755

t 2.118903459 8.708730903

p-value 0.034418611 1.86309E-17

Treasury 0.026173809 0.008466045t 2.068165896 3.241824153

p-value 0.038958241 0.001238853RPDpref= 0.018028755 + 0.021257514D% o RPDTesor = 0.008466045 + 0.026173809 D%

Kd = Rf + RPD

RPD = risk premium for debt according to each type of loans; Kd = cost of debt; Rf = risk freerate.


Algunos resultados


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Example

Year 1 2 3 4

T 35% 35% 35% 35%

Rf 7.00% 7.00% 7.00% 7.00%

Ku 15.00% 15.00% 15.00% 15.00%

FCF 17.00 20.00 22.00 25.00


Definition ofDefinition ofDefinition ofDefinition of KdKdKdKd

We assume that Kd is estimated based on the risk premium for debt,PRDKd = Rf + RPDRPDpref= 0,018028755 + 0,021257514 D%This estimate is obtained using Solver optimal.



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OptimalOptimalOptimalOptimal D%D%D%D% withwithwithwith variablevariablevariablevariable KdKdKdKd

D% V VTS Vun Kd

0% 58.66 - 58.66 8.80%

10% 59.06 0.40 58.66 9.02%

20% 59.47 0.81 58.66 9.23%

30% 59.89 1.22 58.66 9.44%

40% 60.31 1.64 58.66 9.65%

50% 60.72 2.05 58.66 9.87%

60% 61.09 2.43 58.66 10.08%

76.5834% 61.45 2.78 58.66 10.43%

80.0% 61.42 2.75 58.66 10.50%

85.0% 61.24 2.57 58.66 10.61%

90.0% 60.79 2.12 58.66 10.72%

95.0% 59.93 1.27 58.66 10.82%

99.9% 58.69 0.03 58.66 10.93%


OCSOCSOCSOCS withwithwithwith variablevariablevariablevariable KdKdKdKd f(D%)f(D%)f(D%)f(D%)


-

10.00

20.00

30.00

40.00

50.00

60.00

70.00

0% 20% 40% 60% 80% 100% 120%

value

D%

D% optimal (OCS)

V

VAI

Vun


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DoDoDoDo interestinterestinterestinterest paymentspaymentspaymentspayments affectaffectaffectaffect OCS?OCS?OCS?OCS?

Perhaps not. What debholders have to pay intaxes should not affect TS earned by the firm,which tbelong to shareholders.

It is similar in logic to assuming that tax savingsdue to labor payments affect TS obtained by thefirm due to the taxes employees pay.


Do personalDo personalDo personalDo personal taxestaxestaxestaxes destroydestroydestroydestroy TS?TS?TS?TS?

In principle, this occurs in countries with double taxation. That is theposition of those that asume that there is no such thing as OCS.

They apply this formula: (1-Tdebt) = (1-Tcorp)(1-Tpers) and they say this makesTS 0.

As we are concerned with the maximization of shareholders wealth, weshould not worry about debtholders wealth. They receive contractualinterest and principal payments. What we have to look for is if Int*Tcorp

Int*Tdebt Div*Tpers = 0 personal taxes destroy TS (T is tax rate). Why this?Because firms do not always distribute 100% of net income. This meansthat TS=0 if Div/Int = (Tcorp- Tdebt) Tpers.

The condition of full distribution could be tested with information oflisted firms.



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WhyWhyWhyWhy personalpersonalpersonalpersonal taxestaxestaxestaxes doesdoesdoesdoes affectaffectaffectaffect TS?TS?TS?TS?

Personal taxes on dividends affect TS because TS belong toshareholders. This occurs where there is doubl taxation.

Taxes paid by debtholders cannot affect TS that belong toshareholders.


How personal taxes affect TS? TSnet = TS Div*Tpers = Tcorp*Int - Div*Tpers (1)

This is, net TS after the effect of personal taxes on receiveddividends by the shareholders.

TS is tax shields, Tcorp is the corporate tax rate, Div is the dividendspaid by the firm to shareholders, and Tpers is the tax rate paid bythe shareholder.



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Relationship between dividends and interest payments

If we define that dividends are some proportion of interest, we haveDiv = b*Int (2)

If we define that the personal tax rate, Tpers, is a portion of thecorporate tax rate Tcorp, we have

Tpers =a*Tcorp (3)

Then TS could be defined as

TS = Int*(Tcorp - b*Tpers) (4)

TS = Int*Tcorp *(1 - b*a) (5)

TS = Int* Tcorp - Div* Tpers TS will be 0 if Div/Int = Tcorp/ Tpers

This can be tested with actual data and is valid if we asumeshareholders are individuals.


What is the relationship when there is corporate shareholders? When equity is shared by personal and institutional (corporate) shareholders, the

previous relationship can be rewritten as

TS Net = TS Dividends*ca*Tcorp Dividends*pa* Tpers

= Tcorp*Interest Dividends*(ca*Tcorp +pa* Tpers)

where pa + ca = 1, with pa = % of equity owned by individuals and ca = % of equity

owned by corporate investors.

What we are interested in is the case when net TS is zero. In that case,

Tcorp*Interest = Dividends*(ca*Tcorp +pa* Tpers)

Tcorp/(ca*Tcorp + pa* Tpers) = Dividends/Interest



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Then we can examine the relationship between dividends andinterest payments compared with the LHS of last equation. With this,we can estimate if it is true that personal taxes (on dividends) whenthere is doubl taxation destroys TS and, hence, there is NO OCS.


Value of Div/Int for TSnet = 0

ca Tcorp/(ca*Tcorp + pa*Tpers)0.0% 3.30

12.5% 2.56

25.0% 2.10

37.5% 1.77

50.0% 1.53

62.5% 1.35

75.0% 1.2187.5% 1.10

100.0% 1.00



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What does the previous table tell us?

Assuming Tcorp=33%, and Tpers = 10%, we obtain the previous table fordifferent percent of institutional (corporate) shareholders. This assumesdouble taxation.

The table says that, if shareholders are 100% corporations, thendividends and interest payments are identical, and TS vanishes. Thismeans that there is no OCS; if the right column value is greater than 1,then net TS would be negative and OCS should be 100% debt. If theproportion in the first column is 50%, when Div/Int is at least 1.53, TS =0. In the case there is 100% individuals, Div/Int must be at least 3.3 for

TS = 0.


DivDivDivDiv////IntIntIntInt inininin somesomesomesome firmsfirmsfirmsfirms tradedtradedtradedtraded inininin ColombiasColombiasColombiasColombias Stock ExchangeStock ExchangeStock ExchangeStock Exchange

b = Div/Int

(times)Frecuency Cummulated%

0.0 26 28.89%

0.5 9 38.89%

1.0 3 42.22%1.5 5 47.78%

2.0 3 51.11%

2.5 5 56.67%

3.0 2 58.89%

43.21 29 91.11%


b = Div/Int (times) Frecuency Cummulated%

83.42 1 92.22%

123.63 1 93.33%

163.84 1 94.44%

204.06 2 96.67%

244.27 0 96.67%

284.48 1 97.78%

405.11 1 98.89%

>405.11 1 100.00%

In a sample of 11 firms traded on the stock Exchange of Colombia between 2001

and 2009, we obtained the following


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We show some evidence that contradicts what has beenstudied in the literature on capital structure. Using the trade-off theory for finding an optimal structure, our graphicevidence implies a preference for low leverage.

An explanation for this behavior is that, given the ignoranceof what the OCS is, managers and owners prefer to be on thesafe side of the curve. That is, they tend to use low leverage.It is as if there were an horror debitisimilar to horror vacuiifound in nature.

We presented a normative model that allows managementto identify in advance their firms optimal capital structure

and focus efforts toward that goal.


Conclusions (1)

There is some indication of the behavior of VTS asoptimizer when calculated with Ke although the marketdoes not recognize it.

The optimal capital structure is found by numericalmethods using Excel Solver and analytical solution usingdata such as Ku, K, T, FCF and TS.

Management must model the cashflow behavior that

not only reflects the expected leverage but includes theeffects of leverage on some variables of the mode. Forexample, it is possible to model the variable cost of thedebt as a function of leverage. It could be done withother variables as this is not the only cost of bankruptcy.


Conclusions (2)


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There remains the problem that occurs when Ku - Kd isvery small. This affects the optimum, Debt and TS whenD and D% are very large. That is, when there are lowlevels of Ku Kd, it might collapse when the leverage ishigh. We have to study this issue.

Last but not least, we have to study what is thecomposition of ownership (individual and corporation) inorder to measure the effect of doubl taxation on theexistence of an OCS.


Conclusions (3)

Summary

TasaKd Ku Ke

WACC

FCF

WACC

CCFKu

(no circularity)

Ke(no circularity)

9/29/2013 Copyright Ignacio Vlez-Pareja 2011 70

( )1i

TS

V

VKd-Ku-Ku

1-i

( ) 1iV

TS1-iV

1iDUn

1iV

1iD

Kd-KuKu

+

( )1-tV

TS1tV

KdKu-

1tV

tTKu

S

1tV

tTKu

S

( )1iV

TS1-iV

1iDUn

1iV

1iDKd-Ku

1iV

iTS-Ku

+

( )

1-tE

VTS

1tV

1tE

1-tD

KdKuKu

+ ( )1tE

1-tDKdKu

Ku

+

( )1-iD

Un

1iV

1-iDKdKuKu

+


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Thank you!


Ahorros en impuestos

Son un subsidio que el gobierno da a la firma por cada gasto deduciblede impuestos de renta. Esto se llama una externalidad. El value de estesubsidio es de TKdDt-1, donde T es la tasa de impuestos, Kd es el costo dela Debt y D es la Debt.

As las cosas, el value de la firma se incrementa por el value presente delos ahorros en impuestos o escudo fiscal (tax shield). Es decir, una firmacon Debt vale ms como un todo que una firma sin Debt.

VCD = VSD + VTS =PVatrimonio + VDebt

Estos valuees tienen asociados respectivamente los siguientes flujos decaja .

FCF + TS = CFE + CFD



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Recordar: El TS depende de la UO

1. Si UO+OI Gastos financieros (GF)entonces

TS = T GF

1. Si 0 UO +OI< GF entonces

TS = T (UO+OI)

1. Si UO+OI < 0 entonces

TS = 0

Esto significa que TS es

T Mximo((Mnimo(UO+OI, GF), 0).

Si se puede amortizar prdidas, los TSno ganados en un perodo sepueden recuperar en el futuro

El CPPC tradicional, CPPC = Kd D%(1T)+ KeP% aplica para el caso 1 si se paganlos impuestos en el mismo perodo enque se causan y los Interest son la nicafuente de TS. Es un caso particular deCPPCFCF_t = Kut TSt/Vt-1


TS en funcin de UO

AI vs UO

-5

0

5

10

15

20

25

-100 -50 0 50 100 150 200 250 300 350

UO

AI


blind man buff ocs interges kd var 20v2

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