ساختار سرمایه
The valuation effects of long-term
changes in capital structure
Ce´cile Carpentier
Faculty of Administrative Science,
Que´bec,
Abstract
Purpose – This paper aims to test the irrelevance proposition whereby changes in capital structure
do not affect firm value.
Design/methodology/approach – The long-run effect of changes in capital structure on firm value
is examined, using a sample of 243 French firms over the period 1987-1996.
Findings – The null hypothesis cannot be rejected. No evidence is found to support a significant
relationship between the changes in debt ratios and the changes in value. To assess the strength of this
finding, control for reversion towards the target debt level induced by the static trade-off theory is
introduced. Similar results were obtained.
Originality/value – This paper is one of the first to analyze the long-term relationship between
financial structure changes and value, and to propose a direct test for the irrelevance proposition.
Keywords Financing, Capital structure, Debt capital, Targets,
Paper type Research paper
The irrelevance proposition introduced by Modigliani and Miller (1958) states that in a
perfect market, capital structure has no impact on firm value. Although market
imperfections such as taxes, agency costs and asymmetric information have frequently
been cited in defense of the relevance of the capital structure, 40 years later we have
still not truly ascertained or clarified the relationship between capital structure and
firm value (Myers, 1993, 2001).
As Giner and Reverte (2001) noted, little empirical research has analyzed the
usefulness of leverage in equity valuation. However, numerous papers have explored the
short-term effects of various financing announcements. Notably, the survey conducted by
Harris and Raviv (1991) shows that stock market reaction to the announcement of
leverage-increasing (leverage-reducing) transactions tends to be positive (negative).
Research in this area predominantly adopts the event study methodology, and considers a
few transaction days surrounding the announcement date. More recently, the long-term
impact of new issues has been analyzed. Researchers generally agree that initial public
equity offerings and seasoned equity offerings are followed by long-run abnormal
underperformance. Long-run abnormal negative performance is also associated with
convertible debt offerings and public bond offerings (see Hovakimian, 2004, for a survey).
Nonetheless, the announcement of a debt or equity issue or an open repurchase
program can hardly be considered a permanent change in capital structure. Indeed,
according to Fama and French (2004), most firms issue, repurchase or do both, every
year. Several studies have shown that many firms use a “target debt ratio”. Dissanaike
et al. (2001) report that approximately 60 percent of the firms in their sample follow a
debt target; Frank and Goyal (2003) find strong evidence of mean reversion in leverage
in their sample, and the target leverage story is also confirmed by Hovakimian et al.
The current issue and full text archive of this journal is available at
www.emeraldinsight.com/1743-9132.htm
IJMF
2,1
4
International Journal of Managerial
Finance
Vol. 2 No. 1, 2006
pp. 4-18
q Emerald Group Publishing Limited
1743-9132
DOI 10.1108/17439130610646144
(2001). Fama and French (2002) put forth statistically reliable evidence of the mean
reversion of leverage, albeit at a low rate. Antoniou et al. (2002) conclude that firms in
structure. The abnormal returns following the announcement of debt or equity issues is
thus more easily associated with an information effect than with the impact of a change
in the financial structure. If the target leverage story adequately accounts for the firm’s
financial decisions, any change induced by a new issue would be offset by a
subsequent issue of the complementary financing instrument, a pattern affirmed by
Mayer and Sussman (2005). Thus, the long-term abnormal return on debt, IPO and
seasoned equity issue are also inconclusive with respect to the financial
structure-valuation relationship. The studies mentioned above rely on stock market
returns to assess the effect on financing decisions, and most researchers restrict their
investigation to a very short-term window. Neither event studies nor long-term
analysis of stock return after new issues yield compelling conclusions regarding the
relationship between financial structure and value. These studies generally do not
account for confounding events (simultaneous or subsequent public security offerings),
or for internal or private financing opportunities. The analysis of the valuation effect of
capital structure or changes therein thus necessitates an alternate approach.
Accordingly, Giner and Reverte (2001) propose a more direct test to analyze the
irrelevance proposition. By applying the Ohlson valuation model, they show that
deviation from the optimal debt level is perceived negatively by investors. Using panel
data, Giner and Reverte analyze the influence of debt level on share prices in relation to
several economic arguments. In this paper, I adopt the complementary perspective of
changes in both prices and debt level. I analyze the effect of capital structure changes
on firms’ relative stock prices, using economic arguments such as the target debt ratio.
Changes in the capital structure are considered in a long-term perspective. The
hypothesis that capital structure changes do not affect firm value is tested. Based on a
sample of 243 French firms during the 1987-1996 period, this hypothesis cannot be
rejected because both the decrease and the increase in leverage can be associated with
positive or negative changes in value. To assess the strength of this finding, the
reversion process of the debt ratio towards its target level is also taken into account
(according to the static trade-off theory). There is no evidence of a significant
relationship between the variation in debt and the variation in value.
To my knowledge, this paper is one of the first to analyze the long-term relationship
between financial structure changes and value, and to propose a direct test for the
irrelevance proposition. The remainder of the paper is organized as follows: the first
section is devoted to a brief survey of the two competitive theories of capital structure.
Part two presents the hypothesis and methodology. Part three describes the sample,
while Part four discusses the results. Part five contains the conclusion.
1. Literature review
The static trade-off theory maintains that firms select an optimal capital structure by
trading off the advantages of debt financing against its cost. The optimum debt level
maximizes firm value and should become a target debt level. According to
Shyam-Sunder and Myers (1999):
. . .this static trade-off theory quickly translates into empirical hypotheses. For example, it
predicts reversion of the actual debt ratio towards a target or optimum (. . .).
Changes in
capital structure
5
The target-adjustment pattern is not a specific feature of US firms. Using
Dissanaike et al. (2001) show that the firms adjust towards a target ratio. Hovakimian
et al. (2001) confirm that:
. . .when firms adjust their capital structures, they tend to move towards a target ratio that is
consistent with theories based on trade-off between the costs and benefits of debt.
They conclude that the static trade-off theory has a much greater time series and
cross-sectional explanatory power than the alternative theory of capital structure (the
pecking order theory), which states that firms rank financing sources by their
sensitivity to asymmetric information. Accordingly, firms prefer internal financing,
followed by debt and then by external financing by equity. Shyam-Sunder and Myers
(1999, p. 221) assert that in this model:
. . . changes in debt ratios are driven by the need for external funds, not by an attempt to
attain an optimal capital structure.
Remolona (1990) confirms that German, Japanese, British and American firms act in
accordance with the pecking order theory. Allen (1993) finds mixed evidence in
required in this area.
The opposition between these two models of financing is not clear-cut, in spite of the
extensive empirical research that attempts to determine which of these two models
better corresponds with reality. For example, Shyam-Sunder and Myers (1999) argue
that the pecking order theory is an excellent first order descriptor of corporate finance
behavior. However, Frank and Goyal (2003) contradict these results, and found no
out-of-sample validity for Shyam-Sunder and Myers’ propositions. Hovakimian et al.
(2004) suggest that these two conceptual frameworks should be integrated rather than
opposed in order to understand the firm’s financial decisions. As summarized by Fama
and French (2002, p. 20):
. . . in the trade-off and pecking order models, the exogenous driving variables for the level of
leverage are the profitability of assets in place, investment opportunities, non-debt tax shields
and volatility.
These variables are used to estimate target ratios, which are the central point of the
static trade-off theory. Based on evidence from the field, Graham and Harvey (2001)
find some support for both the pecking order and the static trade-off theory. In a
similar paper, Bancel and Mittoo (2004) observe that two main considerations drive the
behavior of European firm managers facing policy decisions: impact on the financial
statements and financial flexibility. Financial flexibility is achieved by selecting the
timing of issues. This observation is confirmed by Baker and Wurgler (2002), who
conclude that capital structure is the cumulative outcome of past attempts to time the
equity markets. Welch (2004) denies managers’ willingness to apply an active financial
policy. In his “inertia” story, the capital structure is determined primarily by external
stock market influences, not by internal corporate optimizing decisions. Assuming that
the timing or inertia proposition adequately describes financial strategies (or the lack
thereof), there should be no relationship between changes in debt ratios and changes in
value.
In this paper, firms simultaneously consider target ratios and factors linked to the
pecking order theory, as evidenced by field studies. More specifically, neither of these
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theories is excluded: firms establish a target ratio following the static trade-off theory,
but can temporarily diverge from the optimal level, either for historical reasons or for
considerations linked to the pecking order theory. Similarly, the reversion to the target
process may be affected by considerations linked to the pecking order theory.
2. Hypothesis and methodology
I test the irrelevance proposition whereby the capital structure has no impact on firm
value. A direct consequence of this proposition is that a change in the financial
structure should be neutral in terms of value, except for a short-term informational
effect. Therefore, according to the irrelevance proposition, within a long-term
perspective a change in capital structure has no significant effect on the value of the
firm. Consequently, the null hypothesis may be stated as follows:
H0. Capital structure changes do not affect firm value.
This proposition is assessed over a nine-year period, using bivariate tests and
multivariate regressions. However, since the sample comprises a mix of firms going
towards (away from) the target debt level, the analysis of the entire sample may be
biased, which would subsequently indicate that debt and value are unrelated. The
static trade-off theory posits that firm value increases (decreases) as the financial
structure moves closer to (away from) the target. Note that some authors consider that
the target can change (Hovakimian et al., 2001; Frank and Goyal, 2003). In this pattern,
an observed change in leverage can be either a target move or an adjustment of the
debt level to, or from, the unchanged target. In this paper, I do not try to disentangle
these various possibilities; the target ratio is assumed to remain unchanged throughout
the study period[1].
Given that the reversion process requires a measure for the target, Hovakimian et al.
(2001) and Fama and French (2002) use a two-step model in which the target debt ratio
is first estimated by regressing observed debt ratios on the variables used in the
classical cross-sectional studies of financial structure. Several of these variables are
generally associated with the pecking order theory. Although I applied a similar
approach to the data set, the coefficients of determination obtained were generally very
low, estimated coefficients were non-significant, and resulted in a spurious
relationship. Consequently, following Hovakimian (2004), the industry mean
leverage is used as a proxy for the target debt ratio[2].
3. Data and sample description
3.1 Data
Although most of the studies relative to capital structure focused on the American
market, out of sample analyses could be particularly informative when legal and
institutional contexts differ. Clayton et al. (1999) find that on a market value basis,
French companies tend to use a higher proportion of total debt and a higher proportion
of institutional debt (non-spontaneous funds) than US companies. La Porta et al. (1997)
underscore that the French legal structure is differentiated by less defence of investors’
rights compared with other legal systems. They show that countries with poorer
investor protections have smaller and narrower capital markets. In such markets,
equity offerings can be more limited and changes in capital structure should be more
complicated than in the
Changes in
capital structure
7
French firms can potentially have a more significant effect on value. Financing choices
of French firms have barely been examined, and the few such investigations analyzed
cross-sectional data exclusively (Rajan and Zingales, 1995).
To allow for a long-term test of the irrelevance proposition, a series of significant
changes in the capital structure is required, and periods of large stock market
fluctuations observed in many countries during the 1997-2001 period must be avoided.
The French firms met both conditions. Indeed, one can observe both increases and
decreases in leverage during this period, but no overall tendency can be detected. This
discrepancy of financial strategies warrants an empirical investigation, and is also
conducive to a study of the long-term relationship between leverage and value. The
sample of French firms seemed to satisfy the second condition as well, since 1987-1996
is a moderate-growth-in-returns period. The CAC 40 capital index advanced from 1,000
to 2,316 between 1987 and 1996 (annual rate of return of 9.7 percent), and then climbed
to 5,958 in 1999 (annual rate of return of 37.03 percent)[3].
The accounting and stock market data originate from the Corporate Information on
the World’s Leading Companies, provided by Worldscope/Disclosure. The sample
initially consisted of all firms recorded in the database for the 1987-1996 period. From
an initial 660 firms reporting consolidated financial statements, the sample is restricted
to firms with available market-to-book ratios for the whole period. The final sample
thus comprised 243 observations.
3.2 Measurement of variables
Following Rajan and Zingales (1995), debt is measured using book value[4], and the
capital structure is proxied by the total debt ratio. This total debt ratio is computed by
adding the long-term debt to the short-term debt and the current portion of the
long-term debt[5]; this amount is then divided by total assets. Financial debt, rather
than total liabilities, is used in this study owing to the preponderance of accounts
payable in the French firms’ financial statements, representing a portion of their
working capital (Rajan and Zingales). The estimated total debt ratio is very close to
that reported by Rajan and Zingales for 1991 (24.76 percent versus 25 percent).
Table I shows a mean total debt ratio of 23.45 percent. The mean equity ratio[6] is
33.29 percent[7]. Table II shows the industrial distribution of the sample and illustrates
the differences between the mean debt levels across the various industries. These mean
debt ratios at the industry level will be used as a proxy for the target debt ratio in the
following sections.
At times, the mean variation masks large variations at the firm level. Table III
shows that 113 firms are increasing their total debt ratios, whereas 130 are reducing
the ratio.
The variation in leverage for each firm (DTDi) was calculated using the growth rate
of leverage between the beginning (t ¼ 1) and the end of the period (t ¼ 9):
DTDi ¼
TDi9
TDi1 _ _2 1 ً1ق
Changes in value (DMBi) are estimated in the same manner as for debt:
DMBi ¼
MBi9
MBi1 _ _2 1 ً2ق
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Although Tobin’s Q is often used as a proxy for firm value, this variable cannot be
calculated for the French firms because it is not mandatory to report replacement cost
in France. Consequently, the market-to-book ratio (MB) defined as the ratio of market
capitalization to common shareholders’ equity is used. This variable is an indicator of
the goodwill that is created by the firm and recognized by the market. For example,
Fama and French (2002) use V/A to proxy firm value, where V and A are the market
and the book value of the total assets of the firm respectively. Since the debt is
estimated according to the book value, this ratio roughly equals the market-to-book
ratio. Harvey et al. (2004) use a similar proxy.
Industrial distribution SIC Total debt Total debt
Industry From To Number Mean Median
Primary and building 1 19.99 16 13.93 12.93
Consumer goods manufacturing 20 31.99 79 26.52 26.57
Industrial manufacturing 32 35.99 31 21.53 20.78
Technology 36 39.99 41 21.96 20.79
Transportation 40 47.99 11 34.26 31.53
Utilities 48 49.99 7 19.04 16.89
Trade 50 59.99 36 22.65 20.93
Services 70 87.99 22 22.25 18.94
Note: The industry classification is based on SIC codes
Table II.
Descriptive statistics
Capital structure ratios
Total debt ratio Long-term debt ratio Equity ratio
Year Number of firms Mean Mean Mean
% % %
1 243 21.50 13.68 32.47
2 243 23.14 13.63 32.20
3 243 23.78 13.79 32.58
4 243 24.33 13.96 32.93
5 242 24.76 14.65 32.83
6 243 24.62 14.39 33.66
7 240 23.49 14.20 34.16
8 242 22.65 12.94 34.21
9 243 22.75 13.15 34.54
Mean 23.45 13.82 33.29
Note: The capital structure ratios are calculated for 243 non-financial French firms for which
accounting and market data are available for the period of 1987 to 1996. Data come from the
Corporate Information on the World’s Leading Companies database, provided by
Worldscope/Disclosure. The total debt ratio is the sum of the long-term debt and the short-term
debt and the current portion of the long-term debt to the book value of assets. The long-term debt
ratio is the long-term debt to the book value of assets. The equity ratio is the common shareholders’
equity to the book value of assets
Table I.
Descriptive statistics
Changes in
capital structure
9
4. Empirical results
4.1 Bivariate tests of the irrelevance proposition
In order to show the impact of the firm’s debt choice on its market valuation, the
total sample is divided into four sub-samples, on the basis of debt and value
changes. Table III summarizes the distribution of the observations in the four
groups, based on changes in leverage and in market-to-book ratio. In each of the
two sub-samples, namely the increasing and the decreasing leverage sub-groups,
observations are also split in two other sub-samples distributed very closely to their
expected frequency under the null hypothesis of independence between debt and
value changes. The null hypothesis of a random distribution of data among the four
groups cannot be rejected.
This bivariate non-parametric test reveals that it is impossible to reject the
hypothesis of independence between changes in debt level and changes in value.
However, this method does not consider the magnitude of the changes.
Increase in the
market-to-book ratio
Decrease in the
market-to-book ratio Total
Increase in total debt:
Observed frequency 41 72 113
Theoretical frequency 44 69
Chi square contribution 0.17 0.11
Decrease in total debt:
Observed frequency 53 77 130
Theoretical frequency 50 80
Chi square contribution 0.15 0.09
Total absolute value 94 149 243
Total relative value (%) 39 61 100
Chi square 0.52
Notes: For each firm, the variation in leverage is measured by the total debt ratio at the end of the
period (t = 9) divided by the total debt ratio at the beginning (t = 1) minus one. For each firm, the
variation in value is measured by the market-to-book ratio at the end of the period (t = 9) divided by
the market-to-book ratio at the beginning (t = 1) minus one. Chi square test of the null hypothesis: the
changes in debt are independent from the changes in value. Chi square is equal to:
x 2 ¼X
2
i¼1X
2
j¼1
ًFOij 2 FTijق2
FTij
where FO and FT stand for the observed frequency (the actual number of firms in each part of the
Table: 41, 72, 53, 77) and the theoretical frequency (expected number of firms if the null hypothesis is
true), i and j stand for an increase (decrease) in debt and an increase (decrease) in the market-to-book
ratio. If the total debt variation distribution is independent from the market-to-book ratio variation
distribution, the expected theoretical frequency is 44 firms (94 *113/243), should both debt and value
increase. The Chi square contribution is the sum of the differences between observed frequencies and
theoretical frequencies. The null hypothesis is rejected at the 5 percent error level if the Chi square is
greater than 3.84. The calculated Chi square is 0.52
Table III.
Distribution of the 243
firms according to
changes in total debt and
value between 1987 and
1996
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4.2 Multivariate test of the irrelevance proposition
To assess the reliability of the hypothesis that capital structure changes are not related
to firm value, I use a multivariate parametric model. I control for profitability, growth,
size and asset tangibility, which are known to influence the value of the firm. Table IV
defines the variables, and Table V presents descriptive statistics and Table VI presents
the correlation coefficients.
A multivariate test of the irrelevance proposition can be performed based on an
ordinary least squares regression of the determinants of value, including the change in
leverage. The model is:
Abbreviation Definition
DTDi Change in leverage of company i
Growth rate of total debtb measured by (total debti9/total debti1) 2 1
DMBi Change in value of company i
Growth rate of market-to-book measured by (market-to-booki9/market-to-booki1) 21
PROFi Profitability (nine-year mean value) of company i
S net incomei/S shareholders’ equityi (nine years)
GROWTHi Growth rate of total assets between year 1 and 9 of company i
(total assetsi9/total assetsi1) 2 1
SIZEi Size (nine-year mean value)
Log (1/9 S net sales or revenuesi (nine years))
INTi Intangible ratio (nine-year mean value) of company i
1/9 S intangible ratioi (nine years)
With intangible ratioi ¼ intangible assetsi/total assetsi
DUMi Dummy variable
DUMi ¼ 1 if DGAPi ,0: Debt level of company i reverts towards the target
DUMi ¼ 0 if DGAPi .0 or if the absolute value of DGAP is more than 2:c Debt level
moves away from the target
With:
DGAPi ¼ (GAPi9/GAPi1) 2 1
GAPi9 ¼ debt ratio of the company i at the end of the period (year 9) – the industry
mean over the period
GAPi1 ¼ debt ratio at the beginning of the period (year 1) – the industry mean over
the period
Industry mean over the period ¼ mean of the total debt ratio for all the firms in the
gross sampled over the nine years
Notes: aThe ratios are estimated on an annual basis and the mean is then calculated, aside from
profitability. Net income and shareholders’ equity are added first, to avoid the influence of extreme
data on the mean ratio. Net income excludes special items. If these special items are taken into account,
the mean profitability increases but similar results are obtained; bThe total debt ratio is computed by
adding the long-term debt to the short-term debt and the current portion of the long-term debt. This
amount is then divided by total assets; cIf the change in GAP is negative, the debt ratio moves towards
its target debt level, except if the absolute variation in GAP is larger than two. In such case, the debt
ratio moves away from the target debt level. A negative relationship with value is consequently
expected, which is also true when the change in GAP is positive; dThe gross sample includes all the
French firms that are not in the financial, insurance or real estate sectors, and that have at least three
years of accounting data available (382 firms)
Table IV.
Definition of the variables
using accounts of the
Corporate Information on
the World’s Leading
Companies database,
compiled by
Worldscope/Disclosurea
Changes in
capital structure
11
DMBi ¼ b1 b2PROFi b3GROWTHi b4DTDi b5SIZEi b6INTi 1i ً3ق
When the change in debt affects the value of the firm, the coefficient of this variable
should be significant. The model is applied to three groups of firms: the whole sample,
the sample restricted to firms with positive changes in debt and the sample restricted
to firms with negative changes in their debt ratios. Normally, it is easier for a firm to
increase its indebtedness rather than increasing shareholders’ equity; this situation
could affect the relationship between the change in debt and the change in value.
Table VII shows that determination coefficients range from 6.12 percent in the case
of the sample restricted to positive changes in debt to 7.66 percent in the case of the
whole sample. The only significant coefficients are profitability and size, which are
positively related to changes in value in each sample. For the whole sample, and for the
nine-year period studied, when the mean profitability increases by 1 percent, the value
increases by 0.66 percent. There is no evidence of a significant relationship between the
change in debt and the change in value. In light of these multivariate results, the
irrelevance proposition cannot be rejected.
Variable Number Mean Median Standard deviation Minimum Maximum
DTD 242 0.9210 20.0480 5.4994 20.9943 68.5263
DMB 242 0.0087 20.2063 0.7789 23.5071 3.6071
PROF 242 0.0557 0.0950 0.2839 22.8031 0.6680
GROWTH 237 0.2124 0.0964 0.8226 20.0983 12.2819
SIZE 242 14.8081 14.7643 1.9016 10.2578 19.0631
INT 242 0.0776 0.0509 0.0834 0 0.4408
DUM 242 0.4793 0 0.5006 0 1
Note: One extreme observation (DTD of 662.33) comes from a non-operating firm in the beginning of
the period. This firm (Lagardere SCA) is subsequently excluded from the analyses
Table V.
Descriptive statistics for
the sample of 243 French
firms (Variables are
defined in Table IV)
Pearson correlation coefficients
DTD DMB PROF GROWTH SIZE INT DUM
DTD 1 20.0526 20.0174 0.0645 20.1287 0.0158 0.1561
(0.42) (0.79) (0.32) (0.05) (0.81) (0.02)
DMB 1 0.2326 20.0572 0.1652 20.0269 20.0694
(,0.01) (0.38) (0.01) (0.68) (0.28)
PROF 1 0.0308 20.0022 0.0674 0.0120
(0.64) (0.97) (0.30) (0.85)
GROWTH 1 0.0541 0.2248 0.0455
(0.41) (,0.01) (0.49)
SIZE 1 0.3162 0.0659
(,0.01) (0.31)
INT 1 0.1269
(0.05)
DUM 1
Notes: Numbers in parentheses are the probabilities that the correlation coefficients are different from 0.
One extreme observation (DTD of 662.33) comes from a non-operating firm in the beginning of the
period. This firm (Lagardere SCA) is subsequently excluded from the analyses
Table VI.
Descriptive statistics for
the sample of 243 French
firms (Variables are
defined in Table IV)
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To assess the strength of the lack of a significant relationship between debt and
value, I control for the static trade-off framework, including a dummy variable that
reflects the reversion towards the target, as defined in Table IV. The model is as
follows:
DMBi ¼ b1 b2PROFi b3GROWTHi b4DTDi b5SIZEi b6INTi
b7DUMi 1i ً4ق
I expect a positive relationship between the dummy variable and the change in value,
because the static trade-off theory posits that firm value should increase (decrease) as
the financial structure moves closer to (away from) the target. The model is tested on
three groups of firms: the whole sample, the sample restricted to firms reverting
towards the target debt level and the sample restricted to firms moving away from
the target. Table VIII shows the results. There is no other significant coefficient. The
null hypothesis that there is a lack of relationship between the change in debt and the
change in value cannot be rejected.
4.3 Robustness check
To assess the strength of these results, a multivariate non-parametric model is applied.
The logit estimation method links changes in values of the independent variables to
increasing or decreasing probability of occurrence of the event being modeled by the
dependent variable. Using a dichotomous variable as a dependent variable makes it
possible to bypass potential error of measures of this variable. With the logit, the
Whole sample
Positive variations in
the debt ratio
Negative variations in
the debt ratio
Parameters Coefficient Coefficient Coefficient
Intercept 21.1006 20.6646 21.4819
(22.80) * * * (21.30) (22.33) * * *
PROF 0.6638 0.7729 0.6337
(3.97) * * * (2.96) * * * (2.79) * * *
GROWTH 20.0530 20.0428 20.0496
(20.87) (20.72) (20.16)
DTD 20.0025 20.0045 0.1674
(20.28) (20.51) (0.59)
SIZE 0.0763 0.0490 0.1044
(2.82) * * * (1.37) (2.49) * * *
INT 20.7393 21.0726 20.4315
(21.17) (21.37) (20.39)
Number 237a 110 b 127 c
Adjusted R square 0.0766 0.0612 0.0698
Notes: Numbers in parentheses are the Student’s t and are significant for an accepted error risk of 10
percent *, 5 percent * *, and 1 percent * * *. a5 observations are lost due to the lack of dependent or
explanatory variables; b2 observations are lost due to the lack of dependent or explanatory variables;
c3 observations are lost due to the lack of dependent or explanatory variables. The model is:
DMBi ¼ b1 b2PROFi b3GROWTHi b4DTDi b5SIZEi b6INTi 1i
Table VII.
Linear regression results
for the model explaining
the change in value. The
sample comprises 242
non-financial French
firms between 1987 and
1996. The dependent
variable is the change in
value (DMBi) as defined
in Table IV
Changes in
capital structure
13
results are less sensitive to the distribution of value changes, since I assign a value of 1
to a positive change in the market-to-book ratio for any given change, and 0 otherwise.
Tables IX and X show the results. The Chi square is never significant, except for the
sample restricted to positive variations in the debt ratio. Profitability and size are
positively related to changes in value in each sample, but the coefficient is either not
significant or weakly significant, and the coefficient associated with the change in debt
is not significant[8].
In light of these multivariate results, the null hypothesis cannot be rejected. Hence, it
seems impossible to find a strong statistical link between changes in debt and the
variation in the market-to-book ratio, regardless of whether I control for reversion
towards the target.
5. Conclusion
This empirical investigation demonstrates that the irrelevance proposition cannot be
rejected. Bivariate and multivariate tests do not show a significant relationship
between changes in value and changes in leverage. With all things being equal,
changes in capital structure apparently do not explain changes in the value of the
sample of French firms. The lack of relationship is observed even when the direction of
change in financial structure is accounted for. The firm’s movement to or away from its
sectoral target level does not alter this conclusion.
Whole sample Reverting towards target Moving away from target
Parameters Coefficient Coefficient Coefficient
Intercept 21.0760 21.4631 20.6893
(22.74) * * * (22.87) * * * (21.10)
PROF 0.6657 0.6232 0.7021
(3.99) * * * (3.20) * * * (2.23) * *
GROWTH 20.0527 20.0458 20.2180
(20.87) (20.78) (20.80)
DTD 20.0006 0.0008 20.0244
(20.06) (0.10) (20.39)
SIZE 0.0780 0.0953 0.0530
(2.88) * * * (2.74) * * * (1.23)
INT 20.6485 20.6279 20.4875
(21.02) (20.73) (20.50)
DUM 20.1262
(21.27)
Number 237a 112b 125c
Adjusted R square 0.0790 0.1054 0.0322
Notes: Numbers in parentheses are the Student’s t and are significant for an accepted error risk of 10
percent *, 5 percent * *, and 1 percent * * *. a5 observations are lost due to the lack of dependent or
explanatory variables; b4 observations are lost due to the lack of dependent or explanatory variables;
c1 observation is lost due to the lack of dependent or explanatory variables.
For the whole sample, the model is:
DMBi ¼ b1 b2PROFi b3GROWTHi b4DTDi b5SIZEi b6INTi b7DUMi 1i
For each sub-sample, the model is:
DMBi ¼ b1 b2PROFi b3GROWTHi b4DTDi b5SIZEi b6INTi 1i
Table VIII.
Linear regression results
for the model explaining
the change in value. The
sample includes 242
non-financial French
firms between 1987 and
1996. The dependent
variable is the change in
value (DMBi) as defined
in Table IV
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The lack of a relationship between debt and value affirms the propositions of
Modigliani and Miller (1958) and Miller (1977). This result is also consistent with the
timing capital structure story (Baker and Wurgler, 2002), the inertia proposition
(Welch, 2004) and the evidence from the field. However, my empirical results contradict
the observations of Giner and Reverte (2001, p. 310), who conclude that the debt level of
a firm is taken into account by investors in order to determine stock prices. Several
observations can be put forth to explain this contradiction. The first explanation is
linked to the differing samples, periods under study and even countries under
examination. Second, the empirical methodology is quite different from that of the
above authors. Changes are analyzed over a long period, whereas Giner and Reverte
use a cross-sectional model. The valuation models are different, but one can observe
that dividing both sides of the simple form of the Ohlson valuation model used by
Giner and Reverte by the book value of equity yield the relation between the
price-to-book ratio and the return on equity, which is the basis of my analysis.
Furthermore, the contextual variables analyzed in this study are not identical to those
of Giner and Reverte, even though the return on equity (and for a robustness check, the
return on assets) is included in the model. The more plausible explanation is that while
a cross-sectional relationship between value and debt may exist, the numerous factors
that affect firm value in the long run overshadow the debt-value relationship. Clearly,
the relationship between leverage and value, in both the short run and the long run,
warrants more extensive analysis.
Whole sample Positive variations of debt ratio Negative variations of debt ratio
Parameters Coefficient estimate Coefficient estimate Coefficient estimate
Intercept 2.3444 2.8950 1.9919
(4.42) * * (3.16) * (1.43)
PROF 20.5940 23.6463 20.0553
(0.99) (2.02) (0.01)
GROWTH 0.1731 1.1163 20.6480
(0.26) (1.01) (0.63)
DTD 0.0196 0.0192 20.0439
(0.33) (0.27) (,0.01)
SIZE 2 0.1460 2 0.1926 2 0.1132
(3.62) * (2.87) * (1.07)
INT 3.2767 4.7429 2.5548
(2.98) * (2.86) * (0.75)
Number 237a 110b 127c
Chi square 8.1222 11.6263 * * 1.8390
Notes: The changes in leverage (DTDi) and the explanatory variables are defined in Table III.
Numbers in parentheses are the Wald coefficient of Chi square, which is significant for an accepted
risk level of * 10 percent, * * 5 percent, and * * * 1 percent. a5 observations are lost due to the lack of
dependent or explanatory variables; b2 observations are lost due to the lack of dependent or
explanatory variables; c3 observations are lost due to the lack of dependent or explanatory variables.
The estimated model is:
Li ¼ lnً Pi
12Piق ¼ b1 b2PROFi b3GROWTHi b4DTDi b5SIZEi b6INTi 1i
Pi is the probability of observing a variation in the market-to-book ratio of the firm (DMBi):
Pi = P (yi = 1), with yi = 1 if DMBi .0
Table IX.
Logit regression results
for the model explaining
the change in value.
A positive estimated
parameter is associated
with a more likely
decrease in value (group 0)
Changes in
capital structure
15
Notes
1. There is no significant variation in mean debt ratio for the entire sample, which comprises a
mix of increased, decreased and unchanged leverage ratios. Similarly, the mean industrial
ratio used as an estimator of the target ratio seems to be statistically unchanged between the
beginning and the end of the period studied.
2. Hovakimian uses medians. Reported results were obtained with the mean ratio as a proxy.
The use of medians rather than means does not change the results.
3. Moreover, a more recent period has not been used for the following reasons: The French
stock market exhibits strong variation in value during the 1997-1999 period (157.29
percent), and a 48.58 percent decline during the 2000-2002 period. The condition of stability
in value required for the model is clearly not met; The variations in value were stronger for
technology and communications companies, which represent 17 percent of the sample. The
sector effect thus induced can hardly be incorporated in the empirical pattern; The 2000-2001
period is known as a hot issue market period in France (Derrien, 2005). During these years,
numerous firms issued common shares, propelled by very high stock market valuations.
Concomitantly, high market values induced changes in capital structure. This phenomenon
can create spurious correlation in the model; During the 1997-2001 period, the target ratio
estimated as the mean of the sample can hardly be considered constant. However, this is one
of the hypotheses of the model; and updating the sample period would require accounting
Whole sample Reverting towards target Moving away from target
Parameters Coefficient estimate Coefficient estimate Coefficient estimate
Intercept 2.3056 3.7301 1.2807
(4.25) * * (5.19) * * (0.61)
PROF 20.6178 20.0909 24.1499
(1.01) (0.02) (2.10)
GROWTH 0.1876 0.1097 0.6702
(0.27) (0.14) (0.66)
DTD 0.0147 0.0096 20.1102
(0.20) (0.08) (0.26)
SIZE 20.1496 20.2352 20.0616
(3.78) * (4.45) * * (0.30)
INT 3.0741 4.1058 2.0588
(2.61) (2.00) (0.61)
DUM 0.2389
(0.73)
Number 237a 112b 125c
Chi square 8.8551 6.2715 6.0107
Notes: The changes in leverage (DTDi) and the explanatory variables are defined in Table III.
Numbers in parentheses are the Wald coefficient of Chi square, which is at a significant level for an
accepted risk level of * 10 percent, * * 5 percent, and * * * 1 percent. a5 observations are lost due to the
lack of dependent or explanatory variables; b4 observations are lost due to the lack of dependent or
explanatory variables; c1 observation is lost due to the lack of dependent or explanatory variables.
The estimated model for the whole sample is:
Li ¼ lnً Pi
12Piق ¼ b1 b2PROFi b3GROWTHi b4DTDi b5SIZEi b6INTi b7DUMi 1i
For each sub-sample, the model is:
Li ¼ lnً Pi
12Piق ¼ b1 b2PROFi b3GROWTHi b4DTDi b5SIZEi b6INTi 1i
Pi is the probability of observing a variation in the market-to-book ratio of the firm (DMBi):
Pi = P (yi = 1), with yi = 1 if DMBi .0
Table X.
Logit regression results
for the model explaining
the change in value.
A positive estimated
parameter is associated
with a more likely
decrease in value (group 0)
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and market data for a period of 15 years (1987-2001), but mergers, delistings and other
events during the tumultuous 1997-2001 period result in the disappearance of more than half
of the sample’s firms.
4. It is highly problematic to use market value to measure debt in France due to the small bond
market, which is restricted to the largest firms.
5. Long-term debt represents all interest-bearing financial obligations, excluding amounts due
within one year. Short-term debt and the current portion of long-term debt represent the
portion of debt payable within one year, including current portion of long-term debt, notes
payables arising from short-term borrowings, and various forms of financial debt.
6. The equity ratio is common shareholders’ equity divided by total assets. Common equity
represents common shareholders’ investment in a company, and includes common stock
value, retained earnings and capital surplus.
7. Firms with accounting data only for the eight years are included, when the fiscal year end
was modified. The number of firms consequently varies during the period.
8. To assess the robustness of the results using panel data but keeping a long-term approach, I
also split the sample into two five-year sub-periods (year 1-5 and year 5-9) and I replicated
the analysis on a total sample of 486 observations. Similar results were obtained. In order to
control for the possible endogeneity problem arising from the fact that the accounting rate of
return and the growth of total assets can be related simultaneously to the change in value
and the change in leverage, I supplemented the analysis with a two-stage least square
simultaneous equations model whereby the first equation explains the changes in value and
the second equation the changes in debt by the classical determinants of leverage (growth,
profitability and size). Similar results were obtained.
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Corresponding author
Ce´cile Carpentier can be contacted at: cecile.carpentier@fsa.ulaval.ca
IJMF
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