Value of Debt Tax Shields in Colombia an Empirical Study

8/10/2019 Value of Debt Tax Shields in Colombia an Empirical Study

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Introduction

Since the seminal work of Modigliani and Miller (hereafter MM) (1958, 1963),

tax shields from debt (TS) have been of significant importance in many articles and

textbooks that deal with the firm capital structure. This issue is at the heart of a

critical question: How does the firm choose its capital structure?

Currently, the TS represent a significant share of companies total value (TV)

and the VTS is supposed to define the optimal capital structure, OCS. Hence,

literature about how to assess the value of TS has grown in the search for the OCS.

However, the number of papers based upon real case studies estimating the

value of debt TS has been modest compared to its counterpart, the theoretical

approaches to discounting the TS. Very few authors have measured it. Among them

the work done by Graham has been persistent (see Graham (2000, 2003), Graham

and Lemmon (1998) and Van Binsbergen, Graham, and Yang (2010)).

The purpose of this paper is to estimate the Value of Tax Shields (VTS) and

the proportion (weight) of this value on the total market value of firm and equity for

23 non-financial firms traded at the Colombian Stock exchange from 2001 to 2010

(Bolsa de Colombia).

Debt tax shields are a subsidy that government gives to firms that incur in

deductible financial expenses. According to the results of this paper, the VTS

ranges from 5.4% to 56.73% of TV depending on the discount rate and the

calculation method. (see Table 1).

Literature Review

Debt tax shields are a topic of interest in the current financial literature

because they challenge the assumption that debt destroys value through the

generation of tax subsidies that represent value for companies.

The debate on TS continues to generate copious literature. Kemsley and

Nissim (2002, p. 2045) claim that "... therefore, the firm valuation and capital


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structure implications of the debt tax shield are unclear, so empirical investigation is

required."

Wrightsman (1978) proposed an algorithm to estimate TS directly related to

the operating earnings. Subsequently, these ideas were taken up independently by

Tham and Velez-Pareja (2004) and Vlez-Pareja (2006, 2010). Those four works

are the basis for calculating TS in this paper.

The main debates and disagreements over the TS occur when defining which

the appropriate discount rate to calculate the VTS is. Fernandez (2006) identified

about 23 different theories on the calculation of present value of TS, which range

from the postulates from MM (1958, 1963) through Myers (1974), Damodaran

(1994), and Harris and Pringle (1985) among others.

There are three main lines of thought about what should be the appropriate

method and discount rate to calculate the VTS for a firm. The first one considers

that TS should be discounted at Kd, the cost of debt, more precisely at the cost of

risk free debt. Among the authors who endorse this approach are MM (1958, 1963),

Myers (1974), Luehrman (1997), Brealey and Myers (2003) and Damodaran (2005).

Another line of thought asserts that the correct discount rate is the cost of unlevered

equity (see Harris and Pringle, (1985); Ruback, (2002), Tham and Vlez-Pareja,

(2001, 2004)). Finally Kolari (2010), Tham, Velez-Pareja and Kolari (2010) and

Kolari and Velez-Pareja (2010), suggest that the appropriate discount rate is the

cost of levered equity, Ke.

On the other hand, Miller (1977), Fama and French (1998) and Myers (2001),

unlike MM (1963), see no advantage in debt financing. For Miller, the value of tax

shields is equal to zero, because personal taxes destroy any tax shield advantage

that might be received by the shareholder. This insight is shared by Benninga and

Sarig (1997).

In relation to the valuation of TS, Kemsley and Nissim (2002) worked cross-

sectional data to estimate the VTS with regressions, and found that it represents

10% of total firm value. He worked out data from Compustat and designed the

following statistical model as a starting point of his analysis:


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(1)Where V L:is the levered value of the firm calculated as the market value of

equity plus the book value of debt plus the value of the preferred shares; D is Debt

calculated as the short-term debt plus long term debt; T is corporate tax rate; and

FOI is Forecasted Operating Income for the next five years, calculated as the

projected operating income growth taking into account the historical average; is

the capitalization rate, which depends on the risk for the firm.

This proposal from Kemsley and Nissim (2002) rests on the equilibrium

equation for cash flows (similar to the same equation for values). They value the left

side of equation (2).

FCF + TS = CFD + CFE (2)

Where FCF is free cash flow, TS are the tax shields. CFD is the cash flow to

debt, and CFE is cash flow to equity. In their model is equivalent to Ku, the

unlevered cost of equity and 3is the multiplier of D (equivalent to T). Equation (1)

assumes a perpetuity to avoid the correlation problem using what they call a

reverse approach.

Graham (2000) worked with accounting information from Compustat to

estimate the average VTS of a large sample of firms and found it to be

approximately 10% of TV and showed that firms can obtain substantial TS from

financial debt.

Graham (2003) simulated the profit function of interest deductions and used

this simulation to estimate the tax shields for each additional dollar of interest

payment. He simulated the expected marginal TS for different tax rates and

concluded that it decreases with increasing debt. He found that the weight of the

VTS is between 7.7% and 9.8%. Graham (2000, 2003) used the average rate of

corporate bonds to estimate Kd, the market discount rate of TS.

Graham and Lemmon (1998) used the simulation of the tax benefits curve to

approximate the marginal tax structure of each company and determine the


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incentives of debt. In their study, they estimated the value of tax benefits by all

traded U.S. firms was $1.4 trillion of their total market value of $12.7 trillion in 1991

and that the VTS represented 11.02% of the value of the firms. This is comparable

with results (for different years) shown in table A9, in the appendix.

Van Binsbergen, Graham and Yang (2010) estimated marginal cost of debt

from changes in the functions of marginal benefit of debt for thousands of

companies from 1980 to 2007. These authors determined that in equilibrium, the tax

benefits of debt on average represent 3.5% of the book value of assets. Van

Binsbergen, Graham and Yang (2010) used the approach of Graham (2000) to

simulate the functions of tax benefits, and also made time series regressions and

cross-sectional data.

Masulis (1980) has sought direct market evidence to explain the impact of

TS, for example, on the price of the shares of a company. He found that, in general,

the trade-off between debt and equity increased the share price. Similarly, Engel,

Erickson and Maydew (1999) found that firms obtained substantial net TS when

exchanging tax-deductible TruPs (Preferred Shares that combine benefits of both

debt and shareholders) for non-deductible common preferred stock.

Data and Sample

This paper works with the database from the Superintendencia Financiera de

Colombia and measures the market value of the firm (TV) as the market value of

equity (MVE) plus the book value of debt (D). VME is the number of shares

outstanding by the closing price of the share at the end of the fiscal year. D was

calculated as the sum of financial long and short term debt, bonds and market

securities. This calculation excludes all debt liabilities that do not generate financial

expense.

Using the book value of debt as a proxy of their market value introduces an

error in the estimates of D and TV. However, according to Kemsley and Nissim

(2002, p. 2054) the gap between book value and market value of debt is small when

the book value is measured as the total financial obligations; in addition, MM (1963)


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argue that it is unlikely that this type of error biases the estimates. In the Colombian

case, most firms do not hold bonds. As the possibility of bias exists, the results

should be interpreted taking into account these caveats.

The analysis includes 23 non-financial companies listed in the Colombian

Stock Exchange. The sample of companies was selected according to two criteria:

the marketability of the stock and the fact that the stock is included in the General

Index of the Bolsa de Colombia (IGBC) during the study period (2001-2010). Tables

A1 to A3 in the Appendix include the firms with their respective VTS.

Methodology

The following paragraphs explain the procedures for estimating the TS and

the VTS and the inputs in order to make that estimation. In particular the variables

studied are the TS themselves, the market risk premium, the unlevered cost of

equity, etc.

Determining the correct amount of Tax Shields

It is necessary to understand how to calculate the TS with the method

proposed by Wrightsman (1978). He defines TS as the difference between the

taxes to be paid by the unlevered and the levered firm, hence,

(3a) (4a) TS = 0(5a)

Vlez-Pareja (2010) demonstrates this very easily

(3b)

(4b) (5b)

Where EBIT is Earnings before Interest and Taxes, I is the interest paid, T is

the corporate tax rate and TS is tax shields.


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Applying equations (3a) to (5a) result in the estimation of TS. In this case

instead of using interest in deriving TS, calculation is done with financial expenses

(FE) that include interest, banking commissions and foreign exchange loss. Instead

of using EBIT, EBIT plus Other or non-operating income, OI is compared with FE.

The calculation was done using the algorithm (6) that synthesizes equations (3a) to

(5a).

Max (T Min (EBIT+OI;FE);0) (6)

Losses Carried Forward are applied extensively whenever EBIT + Other

Income (OI) is lower than FE. The sum that offsets the financial expenses and

allows having or not TS earned is precisely EBIT + OI.

Estimating the Market Cost Debt (Kd)

This paper distinguishes between the contractual cost of debt which is the

basis for determining the interest charges and the market cost of debt, the rate at

which the market discounts CFD and TS.

One proxy to estimate the market cost of debt is to define a weighted

average of cost of debt from the preferential lending rates of banks. Banco de la

Repblica (The Colombian Central Bank) provides historical series of lending rates

from 1998 to 2010 and reports a weekly data of different annual compounded

lending rates for all loans granted during each week.1The lending rates were

weighted by the amounts of loans lent. Figure 1 depicts the weighted cost of debt

Kd, from 2002 to 2010.

1See http://www.banrep.gov.co/series-estadisticas/see_tas_inter5.htm (visited on August 19, 2011.


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Figure 1.Cost of levered and unlevered equity, market cost of debt and risk freerate

(2002-2010)

Source: Authors' calculations based on data from Banco de la Repblica

This graph depicts the behavior of Kd with a downward fluctuating trend over

the past ten years. This trend was interrupted in 2008, but declined again to levels

between 6% and 7% in 2010. The only year that Kd was above 15% was 2001. In

2008 was around 14.82%, due to the high level of inflation of 7.67%.

Estimating Risk Free Rate and Market Return

Rf is the return on risk-free assets, and the assumption is that bonds issued

by the Colombian government (TES B) are a good proxy for a risk free asset with a

low default risk. Estimations for Rf are taken from the database from the Central

Bank2covering years 1998 to 2010.

The database has more than 3000 observations and rates were adjusted by

inflation to the end of each year.

Figure 1 depicts the behavior of the risk-free rate in Colombia over the past

decade, with a downward trend, from 14.36% in 2001 to 8.18% in 2010. The

2Seehttp://www.banrep.gov.co/series-estadisticas/see_finanzas_publi.htm#5(visited August 18, 2011)

00,05

0,1

0,15

0,2

0,25

0,3

0,35

0,4

0,45

0,5

2000 2002 2004 2006 2008 2010 2012

Ke

Ku

Kd

Rf
http://www.banrep.gov.co/series-estadisticas/see_finanzas_publi.htm#5http://www.banrep.gov.co/series-estadisticas/see_finanzas_publi.htm#5http://www.banrep.gov.co/series-estadisticas/see_finanzas_publi.htm#5http://www.banrep.gov.co/series-estadisticas/see_finanzas_publi.htm#5


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behavior of Rf followed the same trend of inflation rate, as expected, which has

declined over the past ten years.

The General Index of the Bolsa de Valores de Colombia (IGBC) is the

indicator to estimate Rm. Data cover from July 20013until December 2010. The

monthly per year return is adjusted with the inflation rate for each year to December

31stand averaged the results using equations (8) and (9).

(8)

Where is one month of year t, is the inflation rate at December andsince Rm in tis defined for each month t, then:

(9)Equation (9) is the annual average stock market return. The average annual

return from 2002 to 2010 was 35.49% and Figure 2 depicts the trend of annual

returns.

3Since July 3, 2001 Bogot, Medelln and Occidente stock exchanges merged to create the Colombian Stock

Exchange (Bolsa de Valores de Colombia). There is no known chain-linking among the series of data for the

three periods (Bogot Stock Exchange, Bogot, Medelln and Cali Stock Exchanges and Colombian StockExchange).


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Where Rf is the risk free rate, Rm the return on market portfolio and the

difference is the market risk premium and u is the unlevered beta.The behavior of

Ku is depicted in figure 1.

Estimation of Cost of Levered Equity, Ke

Estimation of the cost of levered equity is done with the following equation

proposed by Tham, Velez-Pareja and Kolari (2010):

etutut-dtD

t-

Et--

(9)

In this case the circularity problem arises because to calculate the VTS Ke 5 is

needed. Ke is depicted in figure 1.

The Value of Tax Shields from Debt

VTS is calculated as the amount of TS for each year (calculated with (3a) to

(5a)), discounted at three discount rates: Ke, Ku and Kd. One assumption is that the

TS will be constant from 2011 and onwards; hence VTS2010is a non-growing

perpetuity and is combined with finite TS prior to 2011. With the amounts of annual

TS and the last year perpetuity, the basic tenet of finance yields the proper value:

(10)

Where is value, CF is cash flow and DR is the discount rate.VTS2010is calculated as a perpetuity without growth as follows:

D

D (11)

Where DR is the discount rate, Ke, Ku or K as appropriate and VTS2010is the

value of TS and TS is tax shields, 2010 divided by the discount rate as appropriate.

Then applying formula (10) from 2001 to 2009, VTS is estimated as follows.

5This can be easely solved activating the iteration feature of the spreadsheet.


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(12)

Empirical Results: Value of Tax Shields

Estimations of VTS, are listed in the Appendix (see Tables A1, A2 and A3).The years where appears the abbreviation NA are those for which financial

information was not obtained. In most cases, because they were not publicly traded

at that date.

It should be noted that Bavaria S.A. ceased trading on the Stock Exchange in

2007. Generalizing, the calculation of VTS starts with the last year for which there is

complete information. On the contrary, several companies began trading on the

exchange between 2001 and 2010. That is, some companies began trading after2001 and have the value of TS as a perpetuity in 2010, but for some years they

were not trading in the stock market, hence their VTS is not available.

Ratio of VTS to Total Firm Value and Equity

Equation (2) has a counterpart in terms of value as follows

VUn+ VTS = VD+ VE (13)

Where VUnis unlevered value, VTS is value of tax shields, VDis market value

of debt and VEis market value of equity.

This means that an estimation of total value can be calculated as debt plus

market value of equity (number of stocks times price).

With the estimation of VTS and total value the proportion of VTS on value is

given by

t

t

t

EtDt (14)

t

Et (15)

The results of (14) and (15) are shown in table 1.


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Table 1.Share of VTS (%) on TV according to discount rate

With outliers* 9,65 24,75 12,01 33,60 56,73 201,57 6,57 20,65

Without outliers* 7,62 10,39 9,33 13,36 37,02 51,11 5,40 9,28

*Coltejer and Aceras

Source:Authors' calculations

Coltejer and Aceras are firms whose financial performance was uneven

during the study period. For example, Aceras has signed a restructuring agreement

(similar to Chapter 11 in the US Commercial Law) in July 2003 in order to avoid a

possible liquidation because of poor financial results. Coltejer had a debt level of

346.873 million pesos between 2001 and 2007, well above the total assets of

60.041 million pesos in the same period, yielding an average D/P ratio of 8.4 at

2007. This situation is explained, according to Meisel (2008) by the high labor costs,

the peso appreciation and the smuggling of textiles.

Moreover, these two companies have been undervalued in the stock market;

neither has had a share price exceeding 100 pesos, so its equity market value has

been less than the equity book value in most years. For Aceras, on average

throughout the study period, the market value of equity accounted for 63.7% equity

book value. The same average for Coltejer was 55.7%. Due to these factors, some

of the results for these two companies were considered atypical (outliers).

Observations were numerically distant from the rest of the data. Hence, the

estimation of weight for VTS on value with and without these firms is shown in Table

1.

According to Table 1, when VTS was calculated with Ke as the discount rate,

including Coltejer and Aceras, accounted for approximately 9.65% of TV of 23

major companies trading in the Colombian Stock Market between 2001 and 2010,

and 24.75% of market equity value, while excluding Aceras and Coltejer these

values were 7.62% and 10.39% respectively.

When TS was discounted at Ku, the proportion of VTS on TV and equity

increases as expected to 12.01% and 33.60% when Coltejer and Aceras are


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included and 9.33% and 13.36% when they were not included in the average. In the

case where Kd is the discount rate, the proportion of VTS on TV and equity also

grows to 37.02% and 51.11% when excluding the two companies, whereas when

these companies are included, the weight of the VTS is overestimated, accounting

for 56.73 % on TV and 201.57% on equity value.

The results obtained in this study were compared with six previous works that

estimated the VTS of individuals or groups of companies in the United States.

Comparison with literature results are shown in table 2, below and does not include

outliers.

Table 2.Comparison of weights of VTS among several works.

Authors VTS/VT (%) Period

Graham (2000) 9.7 1980-1994

Kemsley and Nissim (2002) 10.0 1963-1993

Graham and Lemmon (1998) 11.0i 1991

Graham (2003) 7.7 a 9.8 1995-1999

Van Binsbergen, Graham, and Yang (2010) 3.5ii 1980-2006

Korteweg (2010) 5.5 1994-2004

Salas, Gutirrez and Vlez-Pareja (Ke) (2011) 7.6 2001-2010

Salas, Gutirrez and Vlez-Pareja (TD) (2011) 5.4 2001-2010

Salas, Gutirrez and Vlez-Pareja (Kd) (2011) 37.0 2001-2010Salas, Gutirrez and Vlez-Pareja (Ku) (2011) 9.3 2001-2010

Excluding outliers.iThey calculate the share of total VTS on total TV for all firms and this result is comparable

with the ones shown in table A9.iiCalculated on the weight of VTS Book Value of Total Assets. Kd, Ku, Ke and

TD in parenthesis indicate method and/or discount rate for TS used. See Table 1.Source:Prepared by the authors.

The results with Kd (market rate) as the discount rate (37.02%) are much

higher than those found by Graham (2000)6, as shown in Table 2. Graham (2000)

reports that VTS was equal to 9.7% of total firm value or 4.3% net of personal

taxes7. The difference between percentages can be explained by the procedure to

estimate the cost of debt, as well as differences between the economies from onecountry to another (United States-Colombia), which involves structural changes in

6Graham (2000) and Graham, Van Binsbergen y Yang (2010) use the corporate bonds yields as an estmate of

market Kd.7This tax rule does not apply in Colombia. Stocks returns are not taxed.


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the market. One relevant difference is the absence of an extensive and relevant

corporate bonds market.

Van Binsbergen, Graham and Yang (2010), using a calculation methodology

similar to that of Graham (2000), report that VTS weight calculated on the book

value of total assets is 3.5%.

Graham (2003) reports that the share of VTS represent from 7.7% to 9.8% of

TV. Likewise Graham and Lemmon (1998) find that the VTS represents 11.02% of

TV analyzing one year. Finally, Korteweg (2010) found that the weight of VTS

represents approximately 5.5% of the firm value.

In the Colombian case the VTS as a fraction of book value of Total Assets,

when discounted at Kd, the average is 17.7%. This result compares with thereported by Van Binsbergen, Graham, and Yang (2010).

MM (1958, 1963) conclude that VTS is equal to TD assuming Kd as the

discount rate of the TS and do not distinguish between market rate and contractual

rate. Applying the proposal by MM (1958, 1963), that VTS is the product of the

corporate tax rate times total debt (TD t-1), the weight of the VTS on the TV was

5.40% and when calculated on equity was 9.32%. These results are reasonably

close to those found in the literature (see Table 1), in particular, the results are veryclose to the results reported by Korteweg (2100). When discounted using Ku,

results are close to Graham (2000, 2003). When discounted with Ke results are

close to Graham (2003) as well. When using Kd (market rate) as the discount rate

of TS, the VTS/TV is equal to 37.02%,while when calculated on equity this values

was 51.11%.

As can be seen, the results of using Kd as the discount rate of TS are quite

different depending on the methodology used. By using the proposed methodology,the assumptions are that the TS are obtained from all financial charges and the Kd

is not the contractual rate at which each firm borrows debt, but it is the average

lending rate from banks. On the other hand, MM (1958, 1963) assume TS are

generated solely by the interest paid, which in turn represent the cost of debt


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(contractual rate) and it is the same rate used for discounting tax shields on

perpetuity.

Market Leverage

Leverage for Colombian firms during the study period is relatively low. On

average, the 23 companies analyzed borrowed 19.22% of TV (see table 4).

According to Figure 3, in general, during the period under analysis, most

companies had a leverage of less than 20%, but in 2001, 2002 and 2004 there were

some companies whose debt levels exceeded 90% over total market value. For

instance, Coltejer in 2001, 2002 and 2004 reported leverages of 94.39%, 92.53%

and 92.91% respectively, while Aceras had a leverage of 92.29% in 2002. Table A4

shows that the average leverage at market prices is 19.22%. This leverage is less

than half of those presented by Baker and Wrgler (2002). The average debt at

market prices of firms analyzed is between 40.22% and 54.6% (see Baker and

Wrgler (2002), p. 6). In 2006 there were lower levels, since no firm borrowed

above 55% and in 2010 again there were reports of high levels of debt 8. This can be

explained by observing the behavior of the preferential rate offered by banks as

shown in Figure 1.

A question arises: is it possible that Colombian firms are not creating value

because they use a very low leverage? According to MM (1958, 1963) it can be

accepted that firms are losing value. Explaining the MM (1963) position,

Wrightsman (1978) says:

"Modigliani and Miller (1963) were the first to value the tax shield astB, []. Under conditions of riskless debt, the value of the tax shieldincreases as financial leverage is increased. The substitution of debt forequity in the capital structure raises the value of the firm's debt. Since

the corporate tax rate is independent of leverage, the value of the taxshield increases proportionally with debt. This leads to the conclusionthat the value of the firm is maximized by maximizing debt. Thetheoretically optimal capital structure, in this case, is an all debtstructure.(Wrightsman (1978) p. 651).

8Despite this, many companies have a very low D%. This can be evidenced by the concentration of companies

below the level of 20%.


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Figure 3.Behavior of leverage of 23 companies between 2001 and 2010.

Source:Authors' calculations.

On the other hand, Fama and French (1998), suggest a negative relationship

between debt and total value:

thus, controlling for after-tax earnings, the relation between debt

and value is negative. In contrast, MM (1963) predict that the relation

between value and leverage is positive in regressions that control forpretax earnings because pretax earnings do not capture the debt tax

shield. If profits are measured after taxes, they capture the benefit of

the interest deduction (Fama and French (1998), p 829)

Following Fama and French (1998), statistical tests on data were applied in

order to determine whether the market recognizes tax shields and debt as variables

that add value to firms. Linear regressions using data panel to determine the

relationship between the total value (TV), tax shields (TS) and debt were ran.

Regressions considered the data with and without lag of one year. The numerical

results are reported in Tables A5 to A8. The following table 3, based on the tables

A4-A7, shows the impact of each independent variable on the dependent, with and

without lag.

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011

D/TV

Year


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Panel estimates were calculated using fixed effects models (FE), in some

cases and random effects (RE) in others, depending on results from the Hausman

test. The FE model has the virtue that is statistically consistent and, unlike the EA

model is efficient. Efficiency denotes less variance in the estimators of the model

over any other model estimators, while the consistency is that the value of the

estimator tends to be equal to the population estimator with increasing sample size.

The numerical results can be examined in Tables A5 to A8. The following

Table 3, based on the tables A5-A8, shows the impact of each independent variable

on the dependent, with and without lag.

Table 3.Relations between TS, D and Ln(TV) and TVNo lag Lagged

For Ln (TV)TS Non significant PositiveD Positive Non significantFor TVTS Negative Non significantD Non significant Non significant

The assumption is that the market does not react instantly to changes in

capital structure of companies, but it does observe it and takes some time to react

with respect to past information about debt and its consequences. It is expected that

debt D which lags one year will send a signal to the market about the existence of

TS. However, as shown in Table 3, D (lagged or not) is not significant and does not

affect total value. On the other hand, TS is obtained from debt at previous period

and earned in the current year is expected to affect the total value, but it is a non-

significant variable or have negative effect. However, the TS from the prior year

show a positive effect on value.

The above results indicate that the available information shows no evidence

of what was proposed by MM (1958, 1963). This is that there is a strong positive

relationship between debt and TV. On the contrary, data show some evidence, as

reported by Fama and French (1998), that value is negatively related to debt or at

least, that TV has no relation at all with D.


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The results above appear to be internally consistent; however, further work

has to be done.

1. Concluding Remarks

After addressing the concept and calculation of the VTS and weight in

relation to TV and market equity for each firm, some considerations should be

highlighted. First, the weight of VTS for the 23 companies when TS is discounted at

Ke is on average, 9.65% of firm value and 24.75% on equity. When Ku is the

discount rate for TS, the weight of VTS was on average 12.01% of the total value of

the firm and 33.60% of the value of equity. Similarly, when Kd is the discount rate

for TS, the weight of VTS is 56.73% of the total value of firms and 201.57% of the

value of equity.

Secondly, the calculations for average weight of VTS without outliers

(Coltejer and Aceras) yield the following results: using Ke as the discount rate for

TS, the weight of VTS was 7.62% of total value and 10.39% of equity. Using Ku as

the discount rate, the average weight of VTS on the total value of the firm is 9.33%,

while for equity is 13.36%. With Kd as the discount rate, the average weight of VTS

represented 37.02% of the value of the firm, and 51.11% of equity.

When VTS is calculated according to the proposal by MM ((1958, 1963) or,

TDt-1, the result is 6.57% on TV and 20.65% on equity. When outliers are excluded,

the weights are similar: 5.40% and 9.28%.

Thirdly, with reference to the market leverage of companies, in general it was

low, less than 20%, during the study period, with some exceptions for Coltejer and

Aceras. The cost of debt also remained low, fluctuating around 10% compared with

Ku and Ke.

The analysis of the Debt-TV using data panel techniques, shows evidence of

a negative relationship between debt and total value, similar to that found by Fama

and French (1998).


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2. References

Baker, M. and Wurgler, J. (2002). Market Timing and Capital Structure. The Journal

of Finance, Vol. 57, No. 1 (Feb., 2002), pp. 1-32.

Benninga, S. Z. and Sarig, O. H. (1997). Corporate Finance. A Valuation Approach.

New York: McGraw-Hill.

Brealy, R.A., Myers, S.C. (2003). Principles of Corporate Finance. New York:

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Appendix

Table A1. Value of Tax Shields 2001-2010 (Ke) (Millions Pesos)

Firm 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

ACERIAS PAZ DEL RIO 34,147.8 38,226.2 25,272.0 28,267.1 34,524.1 44,624.0 56,976.4 60,251.7 80,001.6 80,001.6

ALMACENES EXITO 206,807.1 242,759.3 283,967.7 366,507.9 527,586.9 650,180.0 707,961.8 583,513.2 498,711.0 498,711.0

BAVARIA 696,795.7 723,134.0 844,971.2 826,664.0 884,585.0 858,393.8 729,925.6 NA NA NA

CARTON DECOLOMBIA 33,108.7 34,258.8 32,973.2 27,042.4 25,485.1 25,555.9 27,124.1 24,669.9 22,385.0 22,385.0

CEMENTOS ARGOS NA NA NA NA 566,897.8 622,839.9 795,408.0 784,197.3 803,237.5 803,237.5

COLTEJER 5,408.3 10,037.8 15,207.2 13,694.8 43,712.7 93,523.3 191,831.5 206,864.0 259,433.8 259,433.8

CORFERIAS 908.4 1,069.2 1,070.0 1,206.3 1,372.9 1,636.3 2,080.6 2,560.0 2,617.4 2,617.4

ECOPETROL NA NA NA NA NA NA 6,473,006.4 5,511,667.1 4,844,726.1 4,844,726.1

ENKA DE COLOMBIA NA NA NA NA NA NA 6,070.6 7,879.8 9,150.1 9,150.1

ETB 0.0 0.0 103,996.5 100,330.3 132,763.0 150,309.0 148,157.6 124,976.4 98,866.7 98,866.7

FABRICATO 39,035.5 45,373.6 45,348.2 41,625.3 45,343.0 51,431.6 57,781.8 59,076.1 82,374.4 82,374.4

GAS NATURAL NA NA NA NA 14,274.6 14,524.4 15,045.9 13,280.6 10,137.9 10,137.9

IMUSA 8,621.6 8,946.7 10,674.9 10,341.8 12,509.3 14,442.8 17,643.7 16,316.1 14,861.9 14,861.9

INDUSTRIAS ESTRA 2,548.2 2,617.0 2,665.6 2,700.8 3,320.5 3,567.8 3,452.7 3,275.4 3,889.2 3,889.2

ISA 248,686.7 239,108.2 256,140.2 265,072.6 288,011.5 222,810.4 241,533.3 192,749.9 173,170.8 173,170.8

ISAGEN NA NA NA NA NA NA 117,460.6 111,799.4 104,402.3 104,402.3

MANCEMENTOS 1,866.3 1,971.2 2,362.1 2,558.8 2,905.4 3,071.6 3,317.0 3,202.4 2,962.1 2,962.1

MINEROS 8,724.8 8,590.0 9,438.9 10,706.2 13,274.0 11,992.2 13,967.9 13,730.4 13,230.5 13,230.5

NAL. DE CHOCOLATES 9,937.6 861.9 961.5 976.1 1,130.1 1,522.4 2,000.2 2,261.0 2,216.1 2,216.1

ODINSA NA NA NA NA NA 21,462.0 29,615.2 27,155.5 25,803.8 25,803.8

PRODUCTOS FAMILIA 23,471.0 23,181.7 24,234.3 27,324.6 31,913.2 33,888.7 36,252.2 31,766.6 27,131.1 27,131.1

PROMIGAS NA NA 52,589.3 56,997.1 71,405.8 85,057.0 109,865.6 110,846.2 91,115.6 91,115.6

TABLEMAC 4,530.4 3,721.7 3,799.2 5,866.3 5,186.4 4,871.1 5,052.4 4,417.2 4,472.4 4,472.4

Source: Authors' calculations.


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Table A2. Value of Tax Shields 2001-2010 (Ku) (Millions Pesos)

Firm 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010


ALMACENES EXITO 253,391.9 300,465.4 360,357.5 410,240.4 517,148.4 646,220.5 797,875.0 757,833.1 633,997.9 534,337.5

BAVARIA 832,820.1 1,045,990.8 1,069,893.4 1,127,768.1 968,935.3 930,992.0 849,859.1 NA NA NA

CARTON DE COLOMBIA 36,620.3 33,592.6 33,915.9 33,798.3 27,503.6 28,902.6 32,043.3 28,508.1 25,995.0 24,050.5

CEMENTOS ARGOS NA NA NA NA 577,197.0 710,223.3 832,477.5 926,192.8 905,021.3 919,146.6

COLTEJER 106,479.1 119,228.0 141,609.7 147,401.0 161,854.1 185,045.9 203,492.8 250,625.7 313,028.0 375,017.1

CORFERIAS 877.5 918.2 1,087.4 1,075.5 1,297.9 1,457.4 1,723.0 2,080.4 2,578.0 2,617.4

ECOPETROL NA NA NA NA NA NA 6,313,456.6 6,722,860.8 5,458,903.9 4,844,726.1


ETB NA NA 129,758.8 105,563.2 121,862.1 158,638.1 173,877.3 162,735.2 133,372.3 105,223.9

FABRICATO 58,826.8 62,279.9 68,251.5 62,019.4 59,237.8 65,702.7 79,369.5 83,717.5 90,906.1 114,166.6


IMUSA 11,467.7 12,890.4 14,151.9 16,329.0 18,132.8 21,297.7 25,373.1 26,059.1 22,921.6 22,007.4


ISA 314,959.1 316,638.5 285,278.1 283,172.5 285,023.9 297,200.2 249,898.6 242,972.6 183,374.3 175,777.7


MANCEMENTOS 2,234.9 2,322.3 2,422.7 2,627.2 2,944.1 3,225.3 3,631.5 3,781.7 3,635.7 3,465.9

MINEROS 7,415.4 8,970.6 8,939.7 9,261.5 10,908.1 13,311.3 12,972.2 14,230.1 13,561.4 13,231.0

NAL. DE CHOCOLATES NA 9,544.1 866.5 984.6 1,032.5 1,261.1 1,733.5 2,018.7 2,282.6 2,216.1

ODINSA NA NA NA NA 19,952.5 22,330.8 27,837.8 32,779.2 29,098.1 28,730.1


PROMIGAS NA NA 58,893.8 61,884.9 72,645.9 93,045.2 113,487.5 119,876.1 120,286.6 100,253.1

TABLEMAC 10,125.9 10,819.1 10,161.2 10,323.2 6,998.8 5,802.4 5,903.1 5,074.5 4,384.6 4,479.1



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Table A3. Value of Tax Shields 2001-2010 (Kd) (Millions Pesos)

Firm 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010


ALMACENES EXITO 1,221,328.1 1,342,831.9 1,464,875.1 1,570,591.0 1,683,919.7 1,808,346.8 1,950,197.0 2,030,351.1 1,952,061.8 1,845,719.

BAVARIA 2,206,195.4 2,432,251.5 2,433,163.6 2,458,567.4 2,165,510.1 1,984,506.8 1,791,389.2 NA NA NA

CARTON DE COLOMBIA 89,950.4 88,723.0 90,883.9 90,941.5 84,237.6 82,680.6 82,769.1 84,493.8 84,685.3 82,803.6

CEMENTOS ARGOSNA NA NA NA 2,526,910.4 2,666,738.8 2,815,900.4 3,113,495.3 3,203,068.1 3,232,522.

COLTEJER 702,408.4 771,703.2 846,615.3 912,502.2 980,602.9 1,040,294.2 1,121,327.1 1,287,556.5 1,419,410.6 1,498,420.

CORFERIAS 6,190.9 6,645.5 7,225.7 7,645.8 8,202.9 8,637.7 9,456.0 10,717.6 11,693.8 11,789.7

ECOPETROL NA NA NA NA NA NA 24,542,282.8 26,223,764.8 25,521,778.1 24,859,983


ETB NA NA 385,067.3 373,091.9 381,995.7 402,771.0 412,603.2 414,750.1 391,279.6 360,630.3

FABRICATO 254,048.2 273,213.9 292,287.6 302,284.5 313,768.0 329,381.4 360,301.7 399,678.5 426,952.4 456,164.5


IMUSA 53,147.0 57,637.7 61,544.8 66,279.2 68,424.8 70,822.3 73,606.4 77,094.1 76,405.0 75,671.2


ISA 872,006.9 910,277.9 913,930.9 945,375.2 949,683.3 956,864.8 910,745.1 964,506.8 941,313.4 935,616.7


MANCEMENTOS 10,777.7 11,340.6 11,873.5 12,703.1 13,416.9 13,979.2 14,819.2 16,005.5 16,423.4 16,283.5

MINEROS 39,644.2 43,227.1 44,803.1 47,540.2 50,866.8 54,419.3 55,463.5 60,797.2 62,308.7 62,161.4

NAL. DE CHOCOLATES NA 14,347.4 4,711.2 5,099.7 5,357.9 5,706.0 6,390.9 7,216.8 7,747.0 7,702.5

ODINSA NA NA NA NA 92,796.4 97,400.4 104,270.0 116,659.0 117,603.9 117,651.6


PROMIGAS NA NA 265,308.9 279,273.2 292,051.6 303,668.1 316,092.6 342,567.6 351,887.4 330,533.5

TABLEMAC 22,244.9 23,131.5 22,464.6 22,154.9 18,133.6 15,876.9 15,275.2 15,419.5 15,249.9 15,421.1



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Table A4. Descriptive statistics of the sample (Obs. = 192) (In millions of pesos)

Variable Mean Standard dev.Minimu

m Maximum

Tax shields 85,600.2 353,264.5 0.0 3,387,470.0

Assets 194,000,000.0 921,000,000.0 35,394.8 5,050,000.0

Market value of equity 4,243,371.0 16,200,000.0 2,582.1 166,000,000.0

Short term debt 64,699.6 128,341.2 0.0 980,484.7

Long term debt 146,635.6 305,111.1 0.0 1,713,036.0

Bonds 129,238.0 459,283,5 0.0 3,259,826.0

Total debt 340,573.2 779,430.3 0.0 4,707,060.0

Total value (D+Equity) 4,583,944.0 16,300,000.0 12,352.1 166,000,000.0

D% (Market) 19.22% 21.72% 0.00% 94.39%

P% (Market) 80.78% 21.72% 5.61% 100.00%

The following tables show the output for the data panel regressions. Each

row represents a different model. Numbers in parentheses are standard errors. ***,

** and * denotes statistical significance of 1%, 5% and 10% respectively. RE:

Random effects estimation. FE: Fixed effects estimation.

Tabla A5. Results of the regressions in Panel Data (No lag)

Dependent Variable: Tax Shieldst Debtt

Ln (VTt) (FE) 3.62E-07(5.01E-07) -

Ln(VTt) (RE) -3.90E-07

(1.70E-07)***Relation Non significant Significant

Table A6. Results of the regressions in Panel Data (with lag)

DependentVariable

Tax shieldst-1 Debtt-1

Ln(VTt) (RE)

7.21E-06

(5.59E-07)***

Ln(VTt) (FE) -1.61E-07

(1.71E-07)Relation Significant Non significant


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Tabla A7. Results of the regressions in Panel Data (no lag)

DependentVariable

Tax shieldst Debtt

VTt (FE) -26.123(3.329189)***-

VTt (RE) -1.23754(1.360)

Relation Significant Non significant

Tabla A8. Results of the regressions in Panel Data (with lag)

DependentVariable

Tax shieldst-1 Debtt-1

VTt (FE)4.500

(4.746) -

VTt (RE) -1.248

(1.408)Relation Non significant Non significant

Table A9. Total value per year (23 firms) and share on TV

Year TV VTS (TD)VTS(T*D)/TV

VTS (Kd)VTS(Kd)/TV

VTS (Ku)VTS(Ku)/TV

VTS (Ke)VTS(Ke)/TV

2001 9,519,026 0 5,788,389 60.81% 1,686,868 17.72% 1,324,598 13.92%

2002 14,482,360 993,269 6.86% 6,317,212 43.62% 1,982,240 13.69% 1,383,857 9.56%2003 17,634,887 1,955,835 11.09% 7,217,547 40.93% 2,251,822 12.77% 1,715,672 9.73%

2004 24,022,379 2,741,761 11.41% 7,484,856 31.16% 2,333,556 9.71% 1,787,882 7.44%

2005 52,399,494 2,589,981 4.94% 10,103,373 19.28% 2,945,321 5.62% 2,706,201 5.16%

2006 58,798,235 2,670,693 4.54% 10,332,264 17.57% 3,294,094 5.60% 2,915,704 4.96%

2007 152,045,002 2,898,639 1.91% 35,704,928 23.48% 9,988,829 6.57% 9,791,531 6.44%

2008 131,794,919 1,608,344 1.22% 36,384,684 27.61% 9,647,853 7.32% 7,896,456 5.99%

2009 173,099,846 2,061,466 1.19% 35,870,674 20.72% 8,203,206 4.74% 7,174,897 4.14%

2010 246,321,075 2,095,275 0.85% 35,208,276 14.29% 7,547,968 3.06% 7,174,897 2.91%


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Table of ContentsValue of Debt Tax Shields in Colombia: An Empirical Study ................................................... i

Abstract ...................................................................................................................................... i

1. Introduction ....................................................................................................................... 1

2. Literature Review ............................................................................................................. 1

3. Data and Sample.............................................................................................................. 4

4. Methodology ..................................................................................................................... 5

4.1. Determining the correct amount of Tax Shields ........................................................... 5

4.2. Estimating the Market Cost Debt (Kd) ......................................................................... 6

4.3. Estimating Risk Free Rate and Market Return ............................................................ 7

4.4. Estimating the Unlevered Cost of Equity, Ku ............................................................... 9

4.5. Estimation of Cost of Levered Equity, Ke .................................................................. 10

4.6. The Value of Tax Shields from Debt .......................................................................... 10

5. Empirical Results: Value of Tax Shields ........................................................................ 11

5.1. Ratio of VTS to Total Firm Value and Equity ............................................................. 11

5.2. Market Leverage ......................................................................................................... 15

6. Concluding Remarks ...................................................................................................... 18

7. References ..................................................................................................................... 19

Appendix ................................................................................................................................ 22

Documents

Value of Debt Tax Shields in Colombia an Empirical Study