Does Equity Behave like a Component
of the Cost of Capital?
Evidence from Crossed Mixed Effects Panels
Anthony Bonen∗
March 2016
Abstract
Using a q theoretic framework to control for firm value and expected cash
flows, we test whether firms’ cost of equity capital rE depends on their choice
of payout mechanism. Firms are exclusively but not exhaustively categorized
as persistent share repurchasers and issuers, and compared. Two measures
of rE are estimated. In both specifications share issuing firms conform more
closely with standard capital structure and investment theory. Repurchasers
deviate from theoretical predictions suggesting these firms’ expected equity
returns do not accurately signal real-sector investment costs.
JEL classification: G32, C33
Keywords: q Theory, Weighted Average Cost of Capital, Linear Mixed Effects Models, Share Repurchases
∗
Economics Department, New School for Social Research
1
Introduction
Over the past three decades there has been a rapid rise in the rate of share repurchases
by US publicly-listed firms, and a concurrent decline in capital investment. This
trend has resulted in widespread concern that (excessive) share buybacks are reducing
corporations’ long-term value as net-positive investment projects are foregone in favor
of short-term payouts to shareholders (Lazonick, 2007; Mayer, 2013; Mackenzie,
Braithwaite, & Bullock, 2014; Hecht, 2014; Mason, 2015; Lazonick, 2015). This
would seem, on the face of it, counter to shareholders’ interest since stock markets
are supposed to price the risk-adjusted returns of firms’ investment opportunities.
Failing to undertake profitable capital projects should therefore lead to a fall in
equity’s value. On the other hand, with buybacks now outpacing new equity issuances
on average (see Fig. 1), the expected return on equity investment priced by the
typical shareholder is arguably a further step removed from setting the firm’s effective
cost of capital. This paper examines whether, and to what extent, persistent share
repurchasing firms’ market-based cost of equity deviates from standard theoretical
predictions of how equity covaries with the other canonical cost of capital, debt.
We investigate this issue through a q theoretic framework implemented in a linear
mixed effects model (LMM) on a panel of publicly-listed US firms. Using a crossed
(unnested) structure allows for covariation estimates in our variable of interest, the
cost of equity rE , to be simultaneously pooled toward idiosyncratic and macroeconomic tendencies. The results show that firms which are classified as repurchasers1
1
Defined as firms which repurchase a significant number of their shares (> 1%) in more commonly than they raise capital through equity issuances. See §4.4.
1
consistently deviate from theoretical predictions. Conversely, share issuing firms’
capital cost components covary closer to the expected behavior, and, when covarations do deviate from predicted tendencies, it is to a significantly lesser extent
than repurchasing firms’ deviations. The results reveal that, in addition to market
frictions and imperfect information, the weighted average cost of capital’s (WACC)
relevancy to investment decisions is contingent on the firm’s behavior vis-à-vis equity
markets. This suggests firms’ payout policy mechanisms are an important aspect to
consider in evaluating capital structure and q theories.
The paper is organized as follows. Section 3 presents a model of firm value based
on Abel and Blanchard’s (1986) VAR decomposition of marginal q into expected
cash flows and the WACC. After isolating the marginal costs of debt and equity,
we control for, inter alia, leverage and expected earnings to hypothesize – in line
with modern capital structure theory – that the marginal capital cost components
covary inversely. Section 4 presents the Compustat/CRSP data universe used for the
analysis. Section 5 provides a brief overview of the LMM approach to panel data.
Section 6 presents and discusses the empirical findings. Section 7 concludes. We
begin below with a review of the literature.
2
Related Literature
At least since the seminal Modigliani and Miller (1958) paper, firms’ cost of capital
has been canonically theorized as the tax-adjusted, weighted average of the rate of
interest on borrowed funds, rD , and the so-called “required return” to equity capital,
2
Figure 1: Average Investment and Shareholder Payouts relative to Total Assets
Compustat quarterly data, weighted average by firms’ total assets. Includes only firms based in the United States;
excludes utilities, public companies and financial sector companies. Quarterly figures include any quarterly financial
report in which the majority of the days are within the 3-month period (Jan-Mar, Apr-Jun, Jul-Sep, Oct-Dec).
Data are smoothed by a 4-period moving average. Investment, Investment, repurchases, issuances and dividends are
calculated from the year-to-date variables CAPXY, PRSTKCY, SSTKY and DVY, respectively. Net issuances are
SSTKY less PRSTKCY. Total asses are available quarterly in series ATQ.
rE , for which the weights are the leverage ratio and its complement, respectively.
This is commonly referred to as the weighted average cost of capital (WACC). While
it has long been recognized that firms more frequently turn to debt markets to
finance investment, Modigliani and Miller (1963, p. 441) argue this does not vitiate
the capital structure irrelevancy theorem because “over the long pull, all of the
firm’s assets are really financed by a mixture of debt and equity capital even though
only one kind of capital may be raised in any particular year.” However, for a
firm that expends more on the repurchase and retirement of shares than it raises
3
through new issuances, it is not clear what mechanism compels the firm to consider
expected equity returns as a component of its hurdle rate of investment. This raises
the question as to whether the appropriate measure of the cost of capital relevant
for investment decisions determined by the Modigliani-Miller (MM) theorem – the
WACC – is contingent on the firm’s payout and financing policies.
The question studied here differs from the bulk of capital structure literature
that considers deviations from the MM theorem in terms of real world imperfections
and frictions. For example, the dynamic tradeoff theory branch of the literature
focuses on the adjustment costs of moving to some managerially-determined target
leverage ratio that balances the interest tax-shield benefits of debt with the cost of
increased financial fragility (Jensen & Meckling, 1976; Fischer, Heinkel, & Zechner,
1989; Flannery & Rangan, 2006; Abel, 2015). In the financial hierarchy (viz. peckingorder) literature, emphasis is on the informational asymmetries that exist between
executive managers and outsiders. Although the former know the true value of
investment opportunities, they can only raise the required funds by issuing securities
at a discount – a discount which rises with the security’s riskiness (Myers, 1984;
Myers & Majluf, 1984; Oliner & Rudebusch, 1992; Myers, 2001; Leary & Roberts,
2010). In contrast, we consider deviations from the MM postulates based on firms’
policy mechanisms – specifically, on whether the firm primarily uses the stock market
as a source of capital financing or as a medium for shareholder payouts.
The q theory of investment provides a natural framework in which to address this
issue because it provides a straightforward model for relating the value of the firm,
investment and the cost of capital. Consider the relationship between the present
4
value of the firm V , its expected future cash flow π generated by investment I, and
the discount rate capitalizing these flows, ρ. Taking each as the expected value of
independent random variables, they are mechanically related by2
V = π(I)/ρ
(1)
Stripped down, q theory provides an optimal rule for selecting I to maximize V when
ρ is fixed: Invest in any project for which the present value of earnings π are greater
than the present value costs of investment, π 0 (I ∗ ) = ρ. This equalization of marginal
return to marginal opportunity cost is the reason for identifying the WACC as the
appropriate hurdle rate for investment decisions. From the perspective of capital
markets, the basis of MM theory is that investors determine V in response to changes
in π. Changes in capital structure independent of π(I) lead equity investors, per MM
Proposition II, to revalue their claims such that ρ is held constant in equilibrium.
This in turn requires the components of ρ – the marginal cost of debt and equity,
and leverage – balance out when V and π(I) are fixed.
When capital markets fail to accord with the MM postulates, the market-based
construction of q should not be expected to drive investment rates (Blanchard, Rhee,
& Summers, 1993; Schoder, 2014). Hence, it should not be surprising that, in spite
of its solid conceptual foundation, q theory has not performed well at predicting
aggregate and firm-level investment rates (e.g., Oliner, Rudebusch, & Sichel, 1995;
Gilchrist & Zakrajsek, 2007). However, there are two important caveats regarding the so-called ‘empirical failure’ of q, which provide support for investigating if
2
For expositional purposes the theory is greatly simplified.
5
that problem lies with the construction of the WACC as the appropriate metric for
investment costs.
First, q’s explanatory power is more robust in studies that move away from the
construction of q as the ratio of firms’ market value to book value of capital. For
example, Blanchard et al. (1993) focus on profitability as the relevant metric for
determining investment policy and find it to be a far more powerful predictor than
stock market valuations. Gilchrist and Himmelberg (1995) apply the Abel-Blanchard
methodology employed here and find the VAR-approximated q to perform better
than standard measures. Erickson and Whited (2000) find q to be more empirically
relevant than cash flow when GMM is used to control for higher moments in the
distribution.3 Phillipon (2009, p. 1012) argues this has led to an “uncomfortable
situation” of basing the benchmark investment equation on non-market data. He
overcomes the problématique by casting aside the equity market entirely and uses
the Merton (1974) debt pricing model to proxy q. The resultant “bond market q”
performs well under comparative testing (see Schoder, 2014).
Secondly, most empirical studies of q, including those just discussed, emphasize
investment decisions’ impact on expected earnings. However, as shown in equation
(1), the value of a firm is the product of expected earning and a discount factor
derived from the cost of capital. On the rare occasion the discount factor has been
tested directly, it has generated unexpected results. Using aggregate manufacturing
data, Abel and Blanchard (1986) find two surprising anomalies: a majority of the
cyclical variation in q is due to changes in the discount factor, and; the discount
3
In contrast to the seminal work of Fazzari, Hubbard, and Petersen (1988), Erickson and Whited
find that firms with cash flow constraints exhibit less investment sensitivity to cash flow variability.
6
factor (cost of capital) is positively (negatively) associated with changes in marginal
profit. In other words, they find capital costs substantially influence q in the opposite
direction predicted by theory. Frank and Shen (2015) apply the Abel-Blanchard (AB)
approach to firm-level data and find the cost of capital is a significant explanator
of investment behavior. However, their cost of equity measure based on a factor
model4 exhibits a positive correlation with investment. Conversely, the correlation is
negative – in accordance with standard theory – when equity costs are measured by
in an implied cost of capital model. They also regress investment on the cost of debt
and the cost of equity as separate covariates and find that interest cost coefficients
are consistently negative. Hence, their unexpected WACC results are entirely due to
the cost of equity measure.5
Given their similar empirical focus we follow Frank and Shen (2015) in constructing and testing two classes of equity cost estimates, one based on factor models such
as the capital asset pricing model (CAPM), and the other on implied cost of capital
(ICC) models. However, since our interest lies in whether these equity cost measures conform with capital structure theory predictions, we rearrange the investment
equation such that the covariation between the cost components of the WACC, rD
and rE , is studied directly. Building on a q model has the added benefit of providing a theoretical foundation for how to control for the value of the firm, investment
and expected cash flows. As discussed below, rD and rE are predicted to covary
negatively when these other variables are fixed, and covary positively otherwise.
4
See Section 4 for details on the two classes of equity cost measures.
In addition to the q theoretic analyses, the user cost of capital (UCC) literature demonstrates
debt costs are a highly significant driver of investment (e.g., Dwenger, 2014). Although the cost of
capital in UCC theory is also the WACC, empirical work typically relies on borrowing costs alone.
5
7
3
Theoretical Framework
The baseline model employed here is the Abel and Blanchard (1986) linearized estimation of marginal q, for which the the cost of capital components are then separated
as in Frank and Shen (2015). Part 3.2 discusses how the Merton (1974) bond pricing
model builds on the MM theorem to provide theoretical predictions of the covariation between between rD and rE . In part 3.3, we integrate these capital structure
postulates into the Abel-Blanchard (AB) q model to establish testable hypotheses.
3.1
q Theory of Investment
In a dynamic setting the value of the firm Vt at time t equals the expected value of
future earnings discounted by the cost of capital ρt = 1 + rt ,6
"
∞
X
πt+k (It+k , Kt+k )
Vt = E
Qk
j=0 (1 + rt+j )
k=0
#
(2)
subject to the capital accumulation dynamic
Kt+1 = (1 − δ)Kt + It .
where profit, πt+k (It+k , Kt+k ), is the firm’s net cash flow after operating expenses and
taxes, but before the deduction of interest. Profits are assumed to exhibit diminishing
returns to capital
∂πt
∂Kt
2
> 0, ∂∂Kπ2t < 0 and the cost of investment is positive and convex,
t
6
Although the AB model assumes the manager is risk-neutral, the WACC can be shown as
the appropriate discount rate under risk-aversion and tax-adjustment provisions (Liu, Whited, &
Zhang, 2009).
8
∂πt
∂It
2
< 0, ∂∂Iπ2t < 0. Capital depreciation 0 < δ ≤ 1 is assumed to be constant.
t
The solution to (2) yields marginal q as the sequence of marginal profit generated
by an additional unit of investment discounted by the cost of capital r,
"
qt = E
∞
X
Qk
k=1
where Mt+k ≡
∂πt+k
(1 − δ)k .
∂Kt+k
Mt+k
j=1 (1 + rt+j )
#
.
(3)
Abel and Blanchard (1986) decompose (3) with a first-
order Taylor expansion7 and solve for the linearized qt by assuming a convergent
VAR(1) process. Following this approach Frank and Shen (2015) show that if the
coefficient matrix is diagonal8 then the linearized value of q reduces to the sum of two
AR(1) series for marginal profit Mt+k and the cost of capital rt+j . The steady-state
of the AR(1) processes for the linearized marginal q yields the finite sequence (see
Appendix A for derivation).
L(qt ) :=
M̄ · ρr
β̄ · ρM
M̄ β̄
(Mt − M̄ ) −
+
(rt − r̄)
1 − β̄ 1 − β̄ρM
(1 − β̄)(1 − β̄ρr )
(4)
where β̄ ≡ (1 + r̄)−1 is the mean cost of capital, M̄ is average marginal profit,
0 < ρM , ρr < 1 are the lag coefficients for Mt and rt , respectively.
As is standard in this approach we assume linear-quadratic investment function,
∂πt
∂It
= −1 − φ KItt such that investment and L(qt ) are related by an error-adjusted
affine relationship,
It
Kt
=
1
φ
+ φ1 L(qt ) + t . Using the definition in (4) and rearranging,
7
They also test a second-order expansion but find differences between the linear and quadratic
approximations to be negligible.
8
For this simplification Frank and Shen (2015) state that the first element of the coefficient
matrix has an absolute value less than one and all other elements are zero. This is more restrictive
than necessary: one need only assume a diagonal coefficient matrix to derive AR(1) dynamics.
9
the investment equation becomes
−α
α
}|2
{
z
}|1
{
It
1
M̄ β̄
β̄ · ρM
M̄ · ρr
= +
−
M̄ +
r̄ +α1 rt + α2 Mt + t
Kt
φ 1 − β̄ φ(1 − β̄ρM )
φ(1 − β̄)(1 − β̄ρr )
|
{z
}
z
α0
Or simply,
It
= α0 + α1 rt + α2 Mt + t
Kt
(5)
where α1 < 0 and α2 > 0 and t is the NID disturbance term.
There are two things to note about equation (5). First, even though an autoregressive stochastic profile is a necessary intermediate assumption, the investment regression does not require the AR coefficients ρM , ρr to be determined independently
of the coefficients αi , i = 0, 1, 2. Third, the covariates Mt and rt are well-defined in
theory as marginal profit and the cost of capital. Although the cost of debt is defined
by the interest rate paid, there is no consensus on how to measure the cost of equity.
We will therefore follow Frank and Shen (2015) and construct two measures of the
required return to equity, rE .
3.2
Cost of Capital Components
The WACC is the weighted sum of returns payable to holders of debt and equity,
where the weights are given by the relative share of these securities in firm value:
rt := (1 − Lt )rE,t + (1 − τt )Lt rD,t
10
(6)
The market value leverage is given by Lt := Dt /(Et + Dt ) = Dt /Vt ∈ [0, 1] where
Dt is the stock of debt, and Et the value of equity. The marginal capital costs are
for equity and debt are rE,t and rD,t , respectively. Since interest payments are tax
deductible, the cost of debt is reduced by the tax shield 1 − τt .
The capital structure trade-off theory is driven by equity investors’ response to
leverage, as shown by rearranging (6),
rE,t = rt + (1 − τt )(rt − rD,t )
Dt
.
Et
(7)
Since rt capitalizes the firm’s stream of expected earnings, (7) suggests the components of the cost of capital should move inversely. However, Modigliani and
Miller’s theorem takes borrowing costs as exogenously determined by the risk-free
rate, thereby focusing attention on the stock market’s reaction to changes in leverage
and taxation. The relationship between rE and rD was not formalized until Merton
(1974) developed a debt pricing model atop the MM propositions.
Depending on the root cause of the variation, the Merton (1974) model posits
both positive and negative bond-stock correlations. This class of “structural models”
considers equity as a call option on the value of the firm where the strike price is
the face value of debt. Default ensues when equity matures ‘out of the money’, and
debt holders obtain the remaining – less than face – value of the firm. Debt claims
are therefore structurally equivalent to holding a short position on an American put
option with a face value strike price. For any increase (decrease) in the underlying’s
value, the price of bonds will rise (fall) and the yield will fall (rise). From this perspective, the value of both positions (short put, long call) will covary positively with
11
changes in present market value-cum-expected earnings.9 Conversely, an increase in
the volatility of the underlying’s value raises the value of both call and put options
(thus lowering the value of a short position on the put).10 Put another way, if expected earnings and the risk-free rate are controlled for, then rE and rD should be
inversely correlated as suggested by (7). Intuitively, the model says debt and equity
are both positively related to the firm’s expected stream of earnings, but as the variability of that income stream increases those holding only up-side risk gain, whereas
those earning a fixed income, but face the downside risk, lose.11
On the basis of current market price and expected earnings, Merton’s extension
of the MM framework provides a theoretical foundation for the inverse rD , rE relationship asserted in (7). In the “corrected” version of their paper, Modigliani and
Miller (1963) derive the value and earnings relations to the WACC as,
rt =
π̄t − τt rD,t Dt
Vt − τt Dt
9
(8)
Under log-normal dynamics an increase in the present market value or in the risk-free rate
raises the value of a call option and reduces value of a put option. In terms of “The Greeks”, calls
(puts) have a positive (negative) ∆ and positive (negative) ρ, which are the partial derivatives of
the options’ value to, respectively, the underlying’s value and the risk-free rate.
10
In finance parlance, the ν – the derivative of the option’s value with respect to the standard
deviation of returns – is positive for both calls and puts under log-normality.
11
Empirical studies of firm-specific returns covariance are surprisingly scarce. This is in spite of
the fact there is an expansive literature on the relationship between aggregate stock returns and
average (or risk-free) interest rates (e.g., Barsky, 1986; Campbell & Ammer, 1993; Fama & French,
1993; Chordia, Sarkar, & Subrahmanyam, 2003; Choi, Richardson, & Whitelaw, 2014). The limited
firm-level evidence does seem to confirm the predictions of the Merton model. Nieto and Rodriguez
(forthcoming) find evidence of the theorized positive correlation between a firm’s stock and bond
prices, the strength of which varies with firm specific characteristics (e.g., correlations increase with
leverage) and time-specific/ macroeconomic factors (e.g., correlations decrease with the volatility
of consumption growth). On the other side, Alexander, Edwards, and Ferri (2000) find evidence
of negative covariation between rE and rD among firms with high-yield bonds, for which returns
variance is an important driver.
12
i
h
PJ
−1
is the the average expected future earnwhere π̄t := Et limJ→∞ J
j=1 πt+j
ings.12 Substituting (8) into (7) and rearranging produces the off-setting relationship
between rE and rD discussed above in terms of expected earnings:
rD,t =
π̄t
Et
− rE,t .
Dt
Dt
(9)
Equation (9) is a simple reformulation of the weighted average cost of capital that
Modigliani and Miller (1963, p. 441) argue is the relevant cost consideration for
investment planning. To this point we have merely imbued it with the insights and
intuition from Merton’s later work.
3.3
A Combined Model
Returning to the regression equation (5) and replace rt with the WACC from (7),
It
= α0 + α1 (rE,t (1 − Lt ) + (1 − τt )rD,t Lt ) + α2 Mt + t .
Kt
Proxying marginal profit by average profit as in Abel and Blanchard (1986), permits
us to replace Mt by π̄t /Vt . Isolating the cost of capital components yields
(1 − τt )rD,t = α̃0
Et
π̄t
It /Kt
Vt
+ α̃1 rE,t
+ α̃2
+ α̃3
Vt + t
Dt
Dt
Dt
Dt
(10)
The coefficients α̃i , i = 0, 1, 2 are equal to the coefficients in (5) scaled by −α1 > 0.
This implies that α̃1 = −1, α̃2 > 0 and α̃3 =
1
α1
< 0. Although one would expect
12
the WACC
should also be defined by its average expected value rt =
i
h To be exact
PJ
−1
Et limJ→∞ J
j=1 rt+j .
13
the inverse of market leverage, Vt /Dt , to be negatively related to interest costs (i.e.,
α̃0 < 0), the model is ambiguous about the sign of α0 and, therefore, also of α̃0 .
Equation (10) is essentially the same as the pure theory trade off relationship in
the Merton model (9), but with the explicit controls for leverage, investment and
expected earnings introduced through q theory.
Implementing (10) is challenging because there is no consensus on the correct
measure of equity costs rE and it is not possible to perfectly proxy for expected profitability π̄. We test two types of equity cost estimates: rE,CAPM based on the capital
asset pricing model (CAPM), and; rE,ICC derived from residual income value models
(RIVM). For expected profitability, we draw on the empirical finance literature to
develop a breadth of current and expectational variables known to reasonably project
movements in firm value. Thus, for each firm i year t observation, we test
(1 − τit )rD,it = α0int ξit + α̃0
(rE,ζ Eit )
Iit /Kit
Vit
+ α̃1
+ α̃3
+ α02 Xit + it
Dit
Dit
Lit
(11)
where Xit is a vector of firm-specific value controls such as cash flow and expected
earnings, each of which is normalized by the firm’s stock of debt in year t−1 per (10).
ξit is a set of classification controls that can include size, industry, corporate policy
indicators and a macroeconomic variable. ζ = {CAPM, ICC} indicates which equity
cost measure is tested. In either case we expect α̃1 < 0 when sufficient controls are
introduced through X and ξ, but without such controls α̃1 is expected to be positive.
(j)
The model also predicts α̃3 < 0 and α2 > 0 for any X (j) ∈ X that is positively
associated with expected earnings.
14
4
Data
Our dataset consists of the Compustat/CRSP merged universe of publicly listed
companies in the United States from fiscal year 1984 (when the daily CRSP data
series begins) through 2014. The Daily CRSP dataset provides end of day stock prices
and factor adjustment returns (for in-year splits and dividends). As in Fazzari et al.
(1988) and Schoder (2014) we exclude observations in which merger or acquisition
expenses (or losses) are greater (less) than 20% of a firm’s operating income. To
control for the influence of outliers the remaining data remain are winsorized at 1%
on both tails. We further require tax-adjusted interest rate (1 − τ )rD and all rE
estimates to be between 0 and 1. To take advantage of the panel nature of the data,
we require firms to appear in the merged dataset for at least 5 consecutive years.
Details of data construction are provided in Appendix B.
4.1
Capital Cost Calculations
Cost of Debt. The cost of debt is proxied by total interest expenses over the stock
of short-term and long-term debt. This measure has the advantage of scaling interest
expenses by the same factor used for all dollar-value covariates in (11), namely total
debt at the start of the fiscal year. To account for the tax deductibility of interest
charges we adjust the interest rate by the average tax rate τ . The effective borrowing
cost measure is therefore the average interest after tax, aiat, for firm i in year t,
aiatit := (1 − τit )rDit .
15
(12)
We keep values of τit and rDit between 0 and 1, thus 0 < aiatit ≤ 1 ∀i, t.
Factor-based Cost of Equity. From daily returns data we calculate standard the
standard 1-factor CAPM and the Fama and French (1992) 3-factor extension for
each firm-year.13 Linear projections of the year’s average returns on these factors
produces two factor-based cost of equity estimations, the average of which we denote
by rE,CAPM . As is standard we require that each year has at least 60 in-year daily
return observations from which to calculate the loading factors.
ICC-based Cost of Equity. The implied cost of equity capital (ICC), denoted
by rE,ICC , equalizes the firm’s stock market value M Vτ at time τ to its expected
dividends, Dτ +t , t = 1, 2, . . . as in the discounted dividend model (Gordon, 1959).
Gebhardt, Lee, and Swaminathan (2001) were among the first to translate this into
a residual income value model (RIVM). RIVMs use “clean surplus” accounting in
which net income N It is allocated either to payouts Dt or added to book equity Bt
(Ohlson, 1995). Book equity therefore evolves according to Bt = Bt−1 + N It − Dt .
Substituting N It − ∆Bt for Dt into the discounted dividend model yields,
M Vτ =
∞
X
Eτ [N Iτ +t − Bτ +t + Bτ +t−1 ]
(1 + rE,ICC )t
∞
X
Eτ ROEτ +t − rE,ICC Bτ +t−1
= Bτ +
(1 + rE,ICC )t
t=1
t=1
13
(13)
The 1-factor model regresses firms’ monthly excess returns (over the 1-month Treasury bill
daily return) on the excess return of a value-weighted portfolio of NYSE, AMEX and NASDAQ
stocks. The 3-factor regression additionally includes: (a) the difference in returns between a highvalue and low-value portfolio (HML, high-minus-low), and; (b) the difference in returns between a
small-cap and large-cap portfolio (SMB, small-minus-big).
16
The implied cost of equity capital, rE,ICC , solves (13).14 The difference between the
return on equity, ROE, and the cost of equity is the firm’s ‘residual income’.
To convert the infinite series in (13) to observable metrics with proxies for expected earnings, we employ the methodology developed by Hou, van Dijk, and Zhang
(2012). They project firms’ cash earnings for up to five years ahead using current balance sheet data.15 In comparing these estimates with analysts’ forecasts, the authors
demonstrate that their method reduces forecast bias, but at the cost of lower forecast
accuracy.16 More importantly, their projections are associated with a significantly
larger earnings response coefficient (ERC), implying the balance sheet projections
better approximate investor expectations. Implementation details are provided in
Appendix C.17 For consistency and convenience we calculate rE,ICC for the same five
residual income models tested in Hou et al. (2012), and add a 5-period finite-horizon
Gordon model.18 Following Hou et al. (2012), we define rE,ICC as the median of the
available ICC estimates for each firm-year observation.
14
Note that the second equality holds with the return on equity defined as ROEt ≡ N It /Bt−1
and by assuming the ‘normal’ growth rate of Bt is equal to investors’ required return.
15
Typically, expectations are proxied by analysts’ earnings predictions available in the I/B/E/S
database. The data loss involved in merging these data with the Compustat/CRSP universe is
substantial; furthermore I/B/E/S coverage is skewed toward larger, well-known firms.
16
Bias is measured difference between forecasted earnings and realized earnings; accuracy is the
absolute value of forecast bias.
17
The original RIVM-based ICC estimates are based on (see Gordon & Gordon, 1997; Gebhardt
et al., 2001; Claus & Thomas, 2001; Easton, 2004; Ohlson & Juettner-Nauroth, 2005). Details of
the RIVMs are in Appendix D.
18
Most models define rE as an implicit polynomial. We use the rootSolve package in R to solve
for rE . We constrain the solution space to rE ∈ [0, 1]. If multiple solutions obtain we select the
result with the smallest absolute difference from that ICC model’s mean estimate.
17
4.2
Summary Statistics
The summary statistics for the tax-adjusted average interest rate aiat, the two
CAPM-based and six RIVM-based estimates of the cost of equity are reported in
Table 1. Because the equity cost estimates, rE,CAPM and rE,ICC , are averages of the
available model-specific measures, aggregation increases the total number of valid
firm-year observations (N = 27, 600). In line with previous studies, ICC estimates
of equity’s cost are generally lower than the factor-based models. Mean estimates
for the ICC rE ’s range from 4.4% for the Claus and Thomas (2001) model to 21%
for the 5-period Gordon and Gordon (1997) model. The rE,ICC mean of 11.0% is
close to the 11.7% rE,CAPM mean, but this largely because of the former’s skewness
(the median values are 6.6% and 10.7%, respectively) and greater variance (12.6%
vs. 6.1%). Indeed, with the exception of the rE,CT model, each of the ICC measures
exhibit this higher variance and skewness. The variability of the model’s response
variable, aiat, is comparable to the rE measures with a mean value of 6.4% and a
standard deviation of 5%.
In the model the marginal cost estimates are scaled by the equity/debt ratio for
which the firm’s stock market value is used for E.19 Table 2 reports correlations of
the full cost of capital estimates, rE E/D, and the marginal cost of debt. As expected
we find a significant positive relationship between aiat and each rE metric. Within
the class of ICC models, there is robust positive correlation amongst the estimates
and correlations of 0.57 and above with average rE,ICC estimate. The average ICC
19
There is no qualitative difference in the results when rE is included as an additional term or
E
in place of rE D
in equation (11). This indicates that our results are driven by the marginal equity
cost measure and not the equity/debt ratio.
18
Table 1: Cost of Capital Summaries
Variable
N
Mean
St. Dev.
Pctl(25)
Median
Pctl(75)
Source
Average Interest After Tax-Deduction
aiat
27,600
0.064
0.050
0.040
0.054
0.073
Implied Cost of Equity Capital Models
rE,GLS
26,073
0.114
0.124
0.042
0.080
0.135
Gebhardt, Lee,
and Swaminathan (2001)
rE,CT
25,841
0.044
0.034
0.030
0.041
0.055
Claus and
Thomas (2001)
rE,OJ
22,113
0.115
0.148
0.032
0.062
0.130
Ohlson and
JuettnerNauroth
(2005)
rE,East
18,799
0.164
0.159
0.065
0.111
0.201
Easton (2004)
rE,G-1
21,794
0.107
0.143
0.029
0.057
0.118
Gordon and
Gordon (1997)
(1 Period)
rE,G-5
21,330
0.212
0.210
0.065
0.135
0.281
Gordon and
Gordon (1997)
(5 Period)
rE,ICC
27,600
0.110
0.126
0.041
0.066
0.126
Median of the
above
Factor-based Cost of Equity Capital Models
rE,1 factor
27,438
0.097
0.042
0.068
0.092
0.122
Standard
CAPM
rE,3 factor
26,947
0.137
0.096
0.082
0.116
0.161
Fama and
French (1992)
rE,CAPM
27,600
0.117
0.061
0.079
0.107
0.142
Mean of the
above
estimate has a correlation of approximately 0.3 with each factor model estimate. The
factor-based models also correlate as expected with aiat, but at a lower magnitude
(≈ 0.08) than the ICC measures.
19
Table 2: Pearson’s Correlations: Equity (rE E/D) and Marginal Debt Costs (aiat)
rE,GLS
rE,CT
rE,OJ
rE,East
rE,G-1
rE,G-5
rE,GLS
rE,CT
rE,OJ
rE,East
rE,G-1
rE,G-5
rE,ICC
aiat
0.11∗
0.16∗
0.25∗
0.26∗
0.25∗
0.26∗
0.22∗
0.43∗
0.28∗
0.36∗
0.63∗
0.68∗
0.57∗
0.31∗
0.77∗
0.35∗
0.55∗
0.78∗
0.50∗
0.97∗
0.63∗
0.64∗
0.60∗
0.81∗
0.84∗
0.87∗
0.76∗
0.87∗
rE,1 factor
rE,3 factor
rE,CAPM
0.08∗
0.07∗
0.08∗
0.11∗
0.17∗
0.16∗
0.71∗
0.66∗
0.71∗
0.11∗
0.11∗
0.11∗
0.43∗
0.49∗
0.49∗
0.11∗
0.12∗
0.12∗
0.25∗
0.30∗
0.29∗
∗
4.3
rE,ICC
rE,1 factor
rE,3 factor
0.31∗
0.32∗
0.33∗
0.81∗
0.91∗
0.98∗
p < 0.01.
Control Variables
To avoid the use of noisy market capitalization values, annual share values are determined by the average of the firm’s daily closing prices in each year smooth by a
low-pass filter. Market capitalization is this value scaled by the number of outstanding shares. Total enterprise value, V in (11), is the sum of market capitalization and
book value assets less the value of preferred equity and deferred taxes (see Frank &
Shen, 2015). As with all other continuous variables, the inverse of market leverage
is enterprise value scaled by the start-of-year debt load,
V
.
D
The investment rate
I/K is measured by capital expenditures over the net value of plant, property and
equipment at the start of the fiscal year and is scaled up by the former ratio per
equation 11. A full description of variable construction is in Appendix B.
A multitude of proxies for expected profitability, M , are embedded in X. The
20
baseline earnings controls are current net income N I and the next three year’s expected earnings N It+j , j = 1, 2, 3 generated by the Hou et al. (2012) methodology.
In an extended version of the model we include operating income cash flow cf , total accruals of short-term assets, AC, and total shareholder payouts (buybacks plus
dividends). All seven of these variables are normalized by start-of-period debt.
In addition, full controls in X include growth in sales from the previous year
∆SALE, growth in total assets gT A, and year-on-year shareholding capital gains
dP . Two binary variables, N oDLC and recession indicate if the firm has no shortterm debt and/or if the economy is in contraction, respectively.
Three standard risk metrics are also included. From the empirical finance literature, expected profitability is expected to correlate negatively with systemic risk,
proxied by the log of the book equity to market equity (BM ) (Fama & French, 1992,
1993; Hahn, O’Neill, & Swisher, 2010) and the Ohlson (1980) score of bankruptcy
risk, OH.20 Thirdly, following Kogan and Papanikolaou (2013), firms’ idiosyncratic
volatility ivol is derived from residuals from the 1 factor CAPM regression. That is,
as described in §4.1, from the rolling regressions
(realized return premium)it = αit + βit (market return premium)t + it
(14)
we obtain the market-β factor loadings to estimate rE,CAPM , as well as the metp
ric ivol = var(it ). Thus, the data used to estimate rE,CAPM and ivol are, by
construction, orthogonal.
20
Despite its age, OH is still used to explain portfolio returns (e.g., Griffin & Lemmon, 2002;
Fama & French, 2006).
21
4.4
Subsetting by Observed Equity Market Policy
Repurchases have become an important mechanism for payout policy (Allen & Michaely,
2002; Bonaimé, Hankins, & Jordan, 2015), but it is unclear how – if at all – they affect firms’ weighted average cost of capital.21 While it is tempting to simply compare
aggregate share repurchases to issuances over any particular time period (e.g. van
Rixtel & Villegas, 2015), such an approach is unlikely to capture a firm’s persistent
interactions “over the long pull” since a single large repurchase program can easily
swamp the sum of occasional seasoned equity issuances. To avoid these outlier-type
issues of firm’s typical behavior we develop an ordinal categorization to uniquely
group each firm in the sample.
Firms are categorized as share “repurchasers” or “issuers” as follows. In each
year the number of shares repurchased (issued) is estimated by dividing the amount
spent (raised) by the smoothed annual share price. The number of years the firm
buys back and/or issues more than 1% of its outstanding shares are counted. Firms
for which the number of significant share repurchasing years are greater than the
number of significant share issuing years are classified as “repurchasers”; they are
“issuers” if the converse holds. Firms with no or an equal number of significant
issuing/repurchasing years are classified as “neither”. To save space we do not report
results for the “neither” group here.22
21
As one recent example, Chay, Park, Kim, and Suh (2015) test pecking order theory. In doing
so, they remove all observations in which firms repurchase more equity than they issue because
“negative values of internal and external funds do not represent financing and thus including them
could hamper proper interpretation of the relative role of internal and external funds in financing
investments” (p. 150). This assumes repurchases should not be seen as a negative cost and implies
that equity somehow differs qualitatively when it is issued versus when it is repurchased by the firm.
22
These results are available upon request
22
5
The Structure of Linear Mixed Effects
Mixed effect (ME) coefficients allow selected covariates differ by factor groups (e.g.,
firm ID and year). This is achieved by treating k covariate coefficients as random
variables. The vector-valued random variable coefficients b ∈ B produce the conditional distribution of the n × 1 response variable vector Y|B, which is aiat in our case
and n is the number of firm-year observations (Bates, Mächler, Bolker, & Walker,
forthcoming). For a multivariate Gaussian distribution this is
Y|(b = B) ∼ N Xβ + Zb, σ 2 I ,
where B ∼ N (0, Σθ ).
(15)
X is the n × p matrix of fixed effect, or pooled, coefficients as in a standard linear
model.23 Z is n × q matrix of random effects. For any covariate in Z that is also
included in X, a mixed-effects coefficient is obtained. Since mixed-effects are specified for each group j ∈ J, Z consists of J non-zero blocks each with k columns of
covariates and nj rows (i.e., the number of members i in group j). Thus, q = J · k
and the j[i]th row of Z is zero in all columns corresponding to J \ j.
The minimization of the residuals from (15) maximizes the joint distribution of
Y and B (see Bates, 2010, Chapter 5). Gelman and Hill (2007, ch. 12-13) offer an
intuitive interpretation of the k resultant β, b coefficients as “shrinkage” or “pooling”
toward toward the grand mean. Consider a univariate model with a pooled covariate
23
Gelman (2005) argues that the terms ‘fixed effect’ and ‘random effect’ have become unmanageably muddled. We use ‘pooled’ and ‘unpooled’ to refer to, respectively, ‘fixed’ and ‘random’ effects,
in the sense of a standard OLS estimate versus an analysis of variance model (i.e., not in the sense
of a random intercept vs. a random slope, which are both random effects in an LMM structure).
23
xi and a mixed-effect intercept, which can be written as
yi = αj[i] + βxi + i
where, i ∼ N (0, σy2 ) and αj ∼ N (µα , σα2 ). Here, β is the pooled slope coefficient and
αj[i] is the group-specific intercept drawn from an uncentered normal distribution.
Each intercept is approximated by a weighted average between the in-group mean
(ȳj − x̄j β) and the grand mean (µα ),
αj ≈
nj /σy2
1/σα2
·
(ȳ
−
x̄
β)
+
· µα
j
j
nj /σy2 + 1/σα2
nj /σy2 + 1/σα2
(16)
where nj is the number of observations in the j th group. From (16) it is evident
that for relatively smaller groups more weight is put on the overall mean; for higher
inter-group variability (σα2 large) more weight is placed on the in-group mean.
In terms of equation (15), each αj in (16) is equivalent to the sum of the corresponding j[i]th elements in vectors β and b. The intuition in (16) applies to any
number of ME intercept and slope coefficients, but the weighting factors become
increasingly complex. Even though each group-level ME coefficient is determined
in the LMMs below, the ME coefficients reported are the mean of these estimates,
P
namely ᾱ = J −1 j αj . The R package lme4 is used with the restricted-estimation
maximum likelihood (REML) algorithm to compute all mixed effects models.
Crossed Effects Mixed Models. In the mixed effects models specified below,
all intercept terms are the average of partially pooled firm-specific constants. In
24
terms of equation (16), x̄j = 1 for each j th firm and nj is the number of years
the firm appears in the merged dataset. The cost of equity estimates, rE,CAPM or
rE,ICC , are implemented as crossed, or un-nested, mixed effects. This means the
rE slope coefficients are partially pooled across each firm over time and across all
firms within each year. In other words, the crossed mixed effect structure provides for
simultaneous idiosyncratic (i.e., firm-specific) and macroeconomic (i.e., time-specific)
variations in our estimate of the covariance of the components of the weighted average
cost of capital.
The generic form of the crossed effects models tested is
aiati,t = Xit β + Zj[i,t] bj + it
∀i, t
(17)
where it ∼ N (0, σ), ∀i, t and bj ∼ N (0, Σθ ), ∀j as in equation (15). Equation (17)
restates equation (11), but with all covariates bundled into Xit . The random effects
matrix Zj[i,t] matrix has q columns equal to the total number of factors (no. of firms +
no. of years). The unreplicated crossed design of the data gives the sparse Z matrix
a block diagonal structure in which the firm-specific blocks allow for covariation
between the intercept and rE random effects (see Bates, 2010, ch. 2 for details).
Finally, the mixed models approach also allows for group-level predictors since
their coefficient estimate will simply assign a weight of zero to the in-group variability
(Gelman & Hill, 2007, §12.6). Hence, in addition to the theoretical control variables,
we include tbond to control for annual changes in the 10-year risk-free rate of interest
in all specifications. In certain specifications, we include either a dummy of the firm’s
average total assets quintile, sizeIV , or a 5-sector industry dummy SIC.
25
6
Results
6.1
Repurchasing vs. Issuing Firms
The four tables below report the crossed effects model results for six specifications
for share issuing firms (Tables 3, 5) and repurchasing firms (Tables 4, 6), depending
whether the factor-based model (Tables 3, 4) or ICC measure (Tables 5, 6) of equity
costs is specified. In each case, the linear model is fit to the log of aiat.24 Intercept
estimates are partially pooled toward firm-specific information and the grand mean
E
coefficients are generated by a partial cross pooling of
estimate. Similarly, the rE D
firm-specific, year-specific and full sample estimates (see Sec. 5). Note, that all other
continuous variables are normalized by their ungrouped sample mean and variance
so as to aid convergence of the REML algorithm.
The ME Models 1 through 6 employ an increasing number of covariates. Model
1 looks at the direct covariation of rE with log(aiat), controlling only for the constant term and risk-free interest rate, tbond. Model 2 adds the inverse of market
leverage
V
D
and the investment-leverage ratio
I/K
L
as determined in (10). Model 3
adds current earnings N I, and expected earnings N It+1,2,3 estimated by the Hou
24
The log transformation of aiat renders a better fit with the Gaussian distribution assumed by
the REML algorithm as compared to aiat (see Appendix E). Identical tests have been run on aiat
directly, and do not differ substantially from the log(aiat) results presented here. These are available
upon request. It is further worth noting that the sample distribution of aiat approximates the Log
Normal distribution more closely than the log-transformed normal distribution, or Weibull (e.g.,
exponential) distributions. However, the Generalized Linear Mixed Model (GLMM) algorithm
in lme4 required for a Log Normal maximum likelihood estimation is plagued with convergence
problems – GLMM optimization routine failures are persistent for large samples and/or multifactor
models, as we have here. Many of the GLMM results are therefore unreliable. They are, with
caution, also available upon request.
26
et al. (2012) methodology, and firms’ idiosyncratic volatility ivol as baseline proxies
for π̄t . Recognizing these proxies will fail to fully control for firms’ intrinsic value
and expected marginal profit, Models 4 through 6 introduce ten additional variables
typically found in the financial forecasting literature.
In addition, Model 5 includes the industry SIC dummy variable, whereas Model
6 adds a sizeIV dummy for firms’ average asset quintile. These two firm-invariant
controls can be included in LMMs (unlike standard variance-component approaches)
because the indicator simply gets embedded in each firm’s intercept estimate. However, including two (or more) group-level variables would lead to overdetermination
of the group-specific estimates (i.e., within the firm, or within the year). These classification variables are important because Modigliani and Miller (1958, p. 267, fn. 9)
are explicit that their theorem applies to firms within the same class, which they
note is closely related, but not identical, to the firm’s industry of operation. We
return to this issue in §6.2 below.
Capital Cost Component Correlations. The theoretical model predicts that
with few value and expectational controls, the costs of debt and equity should covary
positively. This is indeed the case across Models 1-3 in which positive covariation
cov(rE , rD ) > 0 is found to be significant at the 1% level in each specification (save
for share issuing firms in Model 3 for which the rE,ICC coefficient is significant at
the 5% level). As expected, the baseline proxies do not sufficiently control for firm
value and expected profitability. It is notable that for both equity costs measures
in Models 1 to 3, share issuing firms exhibit a lower magnitude of covariation with
log(aiat) than do their repurchasing counterparts: 0.007 compared to 0.035 for the
27
CAPM measure, and 0.11 versus 0.16 for the ICC measure. Yet, in each case the
rE,ICC specifications exhibit greater covariation than the rE,CAPM estimates.
The rE,CAPM correlation with log(aiat) among share issuing firms falls from 0.007
in Model 1 to 0.001 in Model 3 (see Table 3). In Models 4 through 6, the average
correlation coefficient becomes negative as predicted, but is too small in magnitude
to be significantly below zero. Among share repurchasing firms in Table 4, a similar
but less pronounced pattern is observed. The rE,CAPM coefficient falls from 0.035
in Model 1 to 0.025 in Model 3 and remains significant at the 1% level. Through
Models 4-6 the correlation again loses significance, but the point estimate remains
positive for the repurchasers. Preliminarily, we note that the equity cost covariation
with debt costs is an order of magnitude greater among buyback firms versus share
issuing firms in each model.
Share repurchasing firms under the rE,ICC specification also exhibit a higher magnitude of covariation with log(aiat) than do issuers (cf. Tables 6 and 6). However,
for both subsets the covariation remains positive and significant at the 1% level in
all models. Nevertheless, there is again a noticeable difference in the rate of decline
in the correlations in moving from Model 1 to Models 4-6. For share issuing firms
the rE coefficient’s magnitude is 70% lower when all controls are introduced versus a
relative decline of only 40% for the share repurchasing firms. These imperfect results
suggest further refinements to the dataset or better proxies many help uncover the
tradeoff relationship between rE and rD posited by standard capital structure theory.
Before turning to this, we discuss the other covariate estimates.
28
Table 3: Share Issuing Firms, log(aiat) ∼ rE,CAPM
(Intercept)
rE,CAPM E/D
tbond
Model 1
Model 2
Model 3
Model 4
Model 5
Model 6
−2.8457∗∗
(0.0113)
0.0065∗∗
(0.0009)
0.1960∗∗
(0.0072)
−2.8401∗∗
(0.0113)
0.0037∗∗
(0.0007)
0.1948∗∗
(0.0072)
−0.0095
(0.0148)
0.0508∗∗
(0.0108)
−2.8568∗∗
(0.0108)
0.0010∗
(0.0004)
0.2002∗∗
(0.0070)
−0.0309∗
(0.0138)
0.0618∗∗
(0.0097)
−0.0593∗∗
(0.0071)
0.0819∗∗
(0.0178)
−0.1465∗∗
(0.0282)
0.1391∗∗
(0.0178)
0.0536∗∗
(0.0061)
No
No
No
−2.8570∗∗
(0.0111)
−0.0005
(0.0007)
0.1870∗∗
(0.0068)
−0.0096
(0.0134)
0.0226∗
(0.0090)
−0.2579∗∗
(0.0106)
0.0918∗∗
(0.0170)
−0.1116∗∗
(0.0268)
0.0714∗∗
(0.0171)
0.0554∗∗
(0.0058)
0.0488∗∗
(0.0098)
−0.0294∗∗
(0.0073)
0.1941∗∗
(0.0106)
0.0712∗∗
(0.0045)
0.0584∗∗
(0.0047)
−0.0222∗∗
(0.0044)
0.0186∗∗
(0.0066)
−0.1106∗∗
(0.0206)
No
−2.7916∗∗
(0.0344)
−0.0005
(0.0006)
0.1871∗∗
(0.0069)
−0.0095
(0.0134)
0.0226∗
(0.0091)
−0.2575∗∗
(0.0106)
0.0915∗∗
(0.0170)
−0.1122∗∗
(0.0268)
0.0722∗∗
(0.0171)
0.0548∗∗
(0.0059)
0.0490∗∗
(0.0098)
−0.0300∗∗
(0.0073)
0.1937∗∗
(0.0106)
0.0710∗∗
(0.0045)
0.0583∗∗
(0.0047)
−0.0224∗∗
(0.0044)
0.0192∗∗
(0.0066)
−0.1167∗∗
(0.0208)
SIC
−2.8057∗∗
(0.0233)
−0.0005
(0.0007)
0.1842∗∗
(0.0070)
−0.0095
(0.0133)
0.0227∗
(0.0090)
−0.2582∗∗
(0.0106)
0.0922∗∗
(0.0170)
−0.1083∗∗
(0.0268)
0.0666∗∗
(0.0172)
0.0526∗∗
(0.0060)
0.0498∗∗
(0.0098)
−0.0267∗∗
(0.0074)
0.1942∗∗
(0.0106)
0.0713∗∗
(0.0045)
0.0580∗∗
(0.0047)
−0.0216∗∗
(0.0044)
0.0182∗∗
(0.0066)
−0.1118∗∗
(0.0206)
sizeIV
0.1158
0.0000
0.0000
0.2067
0.1168
0.0000
0.0000
0.2069
0.1021
0.0000
0.0000
0.2025
0.1026
0.0000
0.0000
0.1798
0.1018
0.0000
0.0000
0.1798
0.1024
0.0000
0.0000
0.1797
V
D
I/K
L
NI
N It+1
N It+2
N It+3
ivol
SHpay
BM
cf
∆AT
AC
dP
OH
N oDLC
IV included
Variances
Firm’s Intercept
Firm’s rE
Annual rE
residual
∗∗ p
< 0.01 (bold face), ∗ p < 0.05. Each model contains 9,648 observations across 1,164 firms and 31 years. Standard
Errors in parentheses.
29
Table 4: Buyback Firms, log(aiat) ∼ rE,CAPM
(Intercept)
rE,CAPM E/D
tbond
Model 1
Model 2
Model 3
Model 4
Model 5
Model 6
−3.0405∗∗
(0.0108)
0.0348∗∗
(0.0043)
0.2092∗∗
(0.0061)
−3.0307∗∗
(0.0109)
0.0323∗∗
(0.0043)
0.2091∗∗
(0.0061)
0.1049∗∗
(0.0293)
−0.0182
(0.0241)
−3.0163∗∗
(0.0110)
0.0254∗∗
(0.0044)
0.2084∗∗
(0.0061)
0.0929∗∗
(0.0292)
−0.0086
(0.0240)
0.0183
(0.0114)
−0.0520
(0.0284)
−0.0008
(0.0466)
0.1053∗∗
(0.0322)
0.0179∗∗
(0.0066)
No
No
No
−2.9786∗∗
(0.0114)
0.0057
(0.0045)
0.1873∗∗
(0.0064)
0.0755∗∗
(0.0286)
−0.0284
(0.0229)
−0.1759∗∗
(0.0155)
−0.0786∗∗
(0.0271)
0.0889∗
(0.0444)
0.0119
(0.0308)
0.0289∗∗
(0.0064)
0.0548∗∗
(0.0041)
0.0045
(0.0082)
0.1358∗∗
(0.0128)
0.1174∗∗
(0.0070)
0.0584∗∗
(0.0053)
−0.0158∗∗
(0.0053)
0.0030
(0.0116)
−0.1276∗∗
(0.0202)
No
−2.9328∗∗
(0.0541)
0.0059
(0.0045)
0.1887∗∗
(0.0064)
0.0769∗∗
(0.0286)
−0.0298
(0.0229)
−0.1760∗∗
(0.0155)
−0.0775∗∗
(0.0271)
0.0884∗
(0.0444)
0.0117
(0.0308)
0.0291∗∗
(0.0064)
0.0547∗∗
(0.0041)
0.0044
(0.0082)
0.1359∗∗
(0.0128)
0.1168∗∗
(0.0070)
0.0583∗∗
(0.0053)
−0.0159∗∗
(0.0053)
0.0038
(0.0116)
−0.1291∗∗
(0.0202)
SIC
−2.9600∗∗
(0.0325)
0.0058
(0.0045)
0.1889∗∗
(0.0064)
0.0785∗∗
(0.0286)
−0.0292
(0.0229)
−0.1770∗∗
(0.0155)
−0.0779∗∗
(0.0271)
0.0889∗
(0.0444)
0.0111
(0.0309)
0.0313∗∗
(0.0064)
0.0547∗∗
(0.0041)
0.0069
(0.0082)
0.1365∗∗
(0.0128)
0.1174∗∗
(0.0070)
0.0586∗∗
(0.0053)
−0.0161∗∗
(0.0053)
0.0107
(0.0118)
−0.1249∗∗
(0.0202)
sizeIV
0.0719
0.0033
0.0000
0.1631
0.0706
0.0032
0.0000
0.1630
0.0709
0.0029
0.0000
0.1617
0.0745
0.0025
0.0000
0.1452
0.0728
0.0025
0.0000
0.1453
0.0730
0.0025
0.0000
0.1452
V
D
I/K
L
NI
N It+1
N It+2
N It+3
ivol
SHpay
BM
cf
∆AT
AC
dP
OH
N oDLC
IV included
Variances
Firm’s Intercept
Firm’s rE
Annual rE
residual
∗∗ p
< 0.01 (bold face), ∗ p < 0.05. Each model contains 8,619 observations across 864 firms and 31 years. Standard Errors
in parentheses.
30
Table 5: Share Issuing Firms, log(aiat) ∼ rE,ICC
(Intercept)
rE,ICC E/D
tbond
Model 1
Model 2
Model 3
Model 4
Model 5
Model 6
−2.9034∗∗
(0.0113)
0.1142∗∗
(0.0108)
0.1971∗∗
(0.0070)
−2.9023∗∗
(0.0113)
0.1089∗∗
(0.0108)
0.1957∗∗
(0.0070)
−0.0326∗∗
(0.0121)
0.0518∗∗
(0.0100)
−2.9196∗∗
(0.0113)
0.1097∗∗
(0.0112)
0.1955∗∗
(0.0069)
−0.0383∗∗
(0.0120)
0.0594∗∗
(0.0100)
−0.0620∗∗
(0.0084)
0.0861∗∗
(0.0210)
−0.1404∗∗
(0.0326)
0.0801∗∗
(0.0218)
0.0557∗∗
(0.0059)
No
No
No
−2.8786∗∗
(0.0118)
0.0318∗∗
(0.0088)
0.1832∗∗
(0.0068)
−0.0215
(0.0117)
0.0267∗∗
(0.0095)
−0.2707∗∗
(0.0128)
0.0943∗∗
(0.0199)
−0.1029∗∗
(0.0308)
0.0497∗
(0.0204)
0.0563∗∗
(0.0058)
0.0476∗∗
(0.0108)
−0.0199∗∗
(0.0073)
0.2012∗∗
(0.0129)
0.0727∗∗
(0.0045)
0.0552∗∗
(0.0049)
−0.0237∗∗
(0.0043)
0.0183∗∗
(0.0064)
−0.0995∗∗
(0.0203)
No
−2.8154∗∗
(0.0343)
0.0314∗∗
(0.0088)
0.1834∗∗
(0.0068)
−0.0209
(0.0117)
0.0267∗∗
(0.0095)
−0.2703∗∗
(0.0128)
0.0945∗∗
(0.0198)
−0.1043∗∗
(0.0308)
0.0510∗
(0.0204)
0.0559∗∗
(0.0058)
0.0477∗∗
(0.0107)
−0.0205∗∗
(0.0073)
0.2008∗∗
(0.0129)
0.0726∗∗
(0.0045)
0.0551∗∗
(0.0049)
−0.0239∗∗
(0.0043)
0.0188∗∗
(0.0064)
−0.1054∗∗
(0.0205)
SIC
−2.8320∗∗
(0.0239)
0.0311∗∗
(0.0088)
0.1810∗∗
(0.0069)
−0.0212
(0.0117)
0.0268∗∗
(0.0095)
−0.2715∗∗
(0.0128)
0.0948∗∗
(0.0198)
−0.0994∗∗
(0.0308)
0.0455∗
(0.0205)
0.0540∗∗
(0.0059)
0.0485∗∗
(0.0108)
−0.0178∗
(0.0074)
0.2013∗∗
(0.0129)
0.0729∗∗
(0.0045)
0.0551∗∗
(0.0049)
−0.0231∗∗
(0.0043)
0.0180∗∗
(0.0064)
−0.1002∗∗
(0.0203)
sizeIV
0.1062
0.0262
0.0007
0.1828
0.1059
0.0247
0.0007
0.1825
0.0965
0.0257
0.0006
0.1805
0.0993
0.0103
0.0003
0.1674
0.0987
0.0101
0.0003
0.1674
0.0992
0.0103
0.0003
0.1673
V
D
I/K
L
NI
N It+1
N It+2
N It+3
ivol
SHpay
BM
cf
∆AT
AC
dP
OH
N oDLC
IV included
Variances
Firm’s Intercept
Firm’s rE
Annual rE
residual
∗∗ p
< 0.01 (bold face), ∗ p < 0.05. Each model contains 9,648 observations across 1,164 firms and 31 years. Standard
Errors in parentheses.
31
Table 6: Buyback Firms, log(aiat) ∼ rE,ICC
(Intercept)
rE,ICC E/D
tbond
Model 1
Model 2
Model 3
Model 4
Model 5
Model 6
−3.0851∗∗
(0.0120)
0.1573∗∗
(0.0196)
0.1985∗∗
(0.0066)
−3.0835∗∗
(0.0120)
0.1554∗∗
(0.0196)
0.1986∗∗
(0.0066)
0.0317
(0.0245)
−0.0118
(0.0220)
−3.0922∗∗
(0.0132)
0.1990∗∗
(0.0232)
0.1984∗∗
(0.0066)
0.0267
(0.0244)
−0.0043
(0.0221)
−0.0125
(0.0131)
−0.0669∗
(0.0313)
−0.0413
(0.0517)
0.0836∗
(0.0373)
0.0172∗∗
(0.0064)
No
No
No
−3.0195∗∗
(0.0137)
0.0940∗∗
(0.0234)
0.1783∗∗
(0.0070)
0.0350
(0.0241)
−0.0165
(0.0213)
−0.1611∗∗
(0.0172)
−0.0633∗
(0.0301)
0.0134
(0.0496)
0.0566
(0.0358)
0.0242∗∗
(0.0063)
0.0491∗∗
(0.0044)
0.0100
(0.0078)
0.0943∗∗
(0.0151)
0.1151∗∗
(0.0068)
0.0610∗∗
(0.0055)
−0.0158∗∗
(0.0052)
0.0035
(0.0115)
−0.1284∗∗
(0.0200)
No
−2.9814∗∗
(0.0557)
0.0948∗∗
(0.0235)
0.1798∗∗
(0.0070)
0.0360
(0.0241)
−0.0176
(0.0213)
−0.1612∗∗
(0.0172)
−0.0616∗
(0.0301)
0.0119
(0.0496)
0.0563
(0.0358)
0.0244∗∗
(0.0063)
0.0491∗∗
(0.0044)
0.0102
(0.0078)
0.0944∗∗
(0.0151)
0.1145∗∗
(0.0068)
0.0608∗∗
(0.0055)
−0.0157∗∗
(0.0052)
0.0035
(0.0115)
−0.1298∗∗
(0.0200)
SIC
−2.9976∗∗
(0.0350)
0.0940∗∗
(0.0234)
0.1802∗∗
(0.0070)
0.0367
(0.0241)
−0.0167
(0.0213)
−0.1621∗∗
(0.0172)
−0.0617∗
(0.0301)
0.0126
(0.0497)
0.0557
(0.0359)
0.0265∗∗
(0.0064)
0.0491∗∗
(0.0044)
0.0123
(0.0078)
0.0944∗∗
(0.0151)
0.1151∗∗
(0.0068)
0.0612∗∗
(0.0055)
−0.0159∗∗
(0.0053)
0.0104
(0.0116)
−0.1259∗∗
(0.0200)
sizeIV
0.0839
0.0682
0.0039
0.1506
0.0837
0.0681
0.0039
0.1505
0.0832
0.0714
0.0048
0.1493
0.0808
0.0524
0.0043
0.1380
0.0804
0.0526
0.0043
0.1379
0.0805
0.0523
0.0043
0.1379
V
D
I/K
L
NI
N It+1
N It+2
N It+3
ivol
SHpay
BM
cf
∆AT
AC
dP
OH
N oDLC
IV included
Variances
Firm’s Intercept
Firm’s rE
Annual rE
residual
∗∗ p
< 0.01 (bold face), ∗ p < 0.05. Each model contains 8,619 observations across 864 firms and 31 years. Standard Errors
in parentheses.
32
Value and Expectational Control Variables. The risk-free interest rate exhibits a persistent correlation with log(aiat) at around 0.2 across each model and
specification. The investment and leverage variables, included in Model 2 onwards,
have greater similarities across policy groups than between equity cost specifications.
While there is no formal prediction on the sign of
V
,
D
the ‘common sense’ negative
relationship is consistently found for both sets of share issuing firms, though it does
not achieve significance at the 5% level in Models 4 through 6. Among share repurchasing firms,
V
D
is consistently positive and, for rE,CAPM , significant at the 1% level
in all models. Conversely, the predicted negative relationship between aiat and
I/K
L
is found consistently among buyback firms, but with no instance of significance. The
opposite holds for issuers:
I/K
L
is significant and positively related to interest costs
in each model. Although these result are somewhat mixed, consistent differences
between the share repurchasing and issuing firms supports the argument that there
are important valuation differences between these qualitatively distinct groups.
Current earnings, N I, are consistently negatively related to current interest costs
across Models 3-6 in each specification, and significant at the 1% level in all but
two cases (namely, Model 3 for repurchasing firms). This result is not unexpected
as higher earning firms are less cash constrained. The expected earnings measures
N It+1,2,3 are positively related to log(aiat) as predicted in (11). Although the signs
for these three estimates vary, the sum of each model’s coefficients is positive.
In the full control Models 4-6 shareholder payouts (SHpay), cash flows (cf ), asset
growth (∆AT ), and accruals (AC) are taken as signals of future firm performance.
Consistent with the theoretical predictions in (11), each of these forecasting vari-
33
ables are positively and significantly related to interest costs across all models and
specifications. The stock market capital gains, ∆P , is also in line with expected
results: The negative correlation between share price growth and interest costs in
each specification implies a positive covariation between the the value of bonds and
stocks as in Merton’s theory (see §3.2). The Ohlson score measure of bankruptcy
risk is also positive and significant across the models as expected, but significant only
among share issuing firms. Sales growth is the only variable insignificant across all
models and specifications, and has therefore been suppressed in the tables.
Finally, the ordinal and binary indicators generally behave as expected. The
indicator for no short-term debt is associated with a lower interest rate burden,
significant at the 1% level in all models. The sizeIV levels (Model 6; not shown)
have mixed coefficients, but only negative coefficients are significant at the 5% level
or less in each specification. That is, we find firm size is either not statistically
significant for interest costs or is associated with lower borrowing rates. We have no
prior expectation for which industries typically face lower or higher interest costs,
but the categorical variable SIC (Model 5) has some significance in each case except
for share repurchasing firms under the rE,ICC specification.
Model Comparison. As mentioned, MM theory is applicable to firms of the same
“class”, but we are limited to one firm-specific classification variable in the LMM
structure. We would therefore like to subset the dataset further into their true
classes. It also important to verify that the SIC and/or sizeIV classifications contain relevant information. Since Models 1-4 are sequentially nested, and Models 5
and 6 are nested within 4, we conduct ANOVA tests that also allow us to ensure
34
the data are not overfit. Tables 7 and 8 display the test results for the rE,CAPM and
rE,ICC models, respectively. In spite of the large number of covariates included in
Model 4, there is consistent and robust support for implementing this full model as
compared to the simpler version in Model 3.
Table 7: Anova Tests for Models with rE,CAPM
Issuance Firms
Model
AIC
BIC
logLike
1
2
3
4
SIC
sizeIV
14312.40
14284.24
13904.89
12897.77
12893.99
12896.08
14369.79
14355.98
14012.51
13069.96
13094.88
13096.97
-7148.20
-7132.12
-6937.45
-6424.88
-6419.00
-6420.04
BIC
logLike
deviance
Chisq
Chi Df
Pr(>Chisq)
14296.40
14264.24
32.16
13874.89 389.35
12849.77 1025.12
12837.99
11.78
12840.08
9.68
2
5
9
4
4
0.0000
0.0000
0.0000
0.0191
0.0461
Buyback Firms
Model
1
2
3
4
SIC
sizeIV
AIC
deviance
Chisq
Chi Df
Pr(>Chisq)
10679.40 10735.90 -5331.70 10663.40
10659.18 10729.80 -5319.59 10639.18
10589.37 10695.30 -5279.68 10559.37
9765.49 9934.97 -4858.75 9717.49
9755.47 9953.20 -4849.73 9699.47
9755.68 9953.40 -4849.84 9699.68
24.23
79.81
841.88
18.02
17.82
2
5
9
4
4
0.0000
0.0000
0.0000
0.0012
0.0013
The F-tests for Models 5 and 6 are against Model 4 in which both are nested.
The ANOVA tests confirm that firms’ industry classification contains important
information: In all four cases the informational content of Model 5 is significantly
better than 4 at the 5% level for share issuing firms, and at the 1% level for share
repurchasers. The sizeIV ordinal measure provides a marginal improvement over
35
Model 4. For share buyback firms, the informational improvement is robust with p
values less than 1%. For share issuing firms, however, the informational content of
sizeIV has a p-value of 4.6% for the rE,CAPM specification, and over 10% for rE,ICC .
Therefore, in refining the analysis below, we keep the firm-size indicator, but find
more utility with industry classification. We therefore subset firms into four SIC
groups, and include a sizeIV for quintile within each industry. This has the added
benefit of being closer to the theoretical position of MM theory.
Table 8: Anova Tests for Models with rE,ICC
Issuance Firms
Model
AIC
BIC
logLike
1
2
3
4
SIC
sizeIV
13704.95
13677.77
13511.71
12677.11
12673.54
12677.38
13762.34
13749.51
13619.33
12849.30
12874.42
12878.26
-6844.47
-6828.88
-6740.86
-6314.56
-6308.77
-6310.69
BIC
logLike
deviance
Chisq
Chi Df
Pr(>Chisq)
13688.95
13657.77 31.18
13481.71 176.05
12629.11 852.60
12617.54 11.58
12621.38
7.73
2
5
9
4
4
0.0000
0.0000
0.0000
0.0208
0.1018
Chisq
Chi Df
Pr(>Chisq)
10310.31 10366.81 -5147.16 10294.31
10310.66 10381.28 -5145.33 10290.66
3.65
10263.29 10369.22 -5116.64 10233.29 57.37
9580.77 9750.25 -4766.38 9532.77 700.52
9573.78 9771.50 -4758.89 9517.78 14.99
9571.70 9769.42 -4757.85 9515.70 17.07
2
5
9
4
4
0.1609
0.0000
0.0000
0.0047
0.0019
Buyback Firms
Model
1
2
3
4
SIC
sizeIV
AIC
deviance
The F-tests for Models 5 and 6 are against Model 4 in which both are nested.
36
6.2
Mixed Effects by Industry Groups
The subsamples of repurchasing and share issuing firms are here further divided into
four industry classifications: Manufacturing (Man); Business and Consumer Services
(Svc); Transportation, Communication and Energy (TCE); and, Wholesale and Retail Trade (WRT). Furthermore, given the imperfect fit of the log-transformed sample
distribution of aiat, we refine the admissible set of interest rates. In the above analysis any positive, tax-adjusted average interest rate less than 100% was admissible.
By limiting average interest rates to the far more reasonable the range of 1-30%,
the log-transformed Gaussian distribution of aiat is now the best fit (see Appendix
E).25 These restrictions reduce the fifth industry group – agriculture, mining and
construction (AMC) – to fewer than 140 unique firms, of which only 31 are share
repurchasers. We have therefore omitted the AMC group from the analysis. The
remaining four industry groups are tested according to Model 6. To save space, only
the coefficients of interest are reported in Tables 9 through 12.
E
and log(aiat) are posiAs before, the industry-specific correlations between rE D
tive for all share repurchasing firms for both equity cost measures. Repurchasers in
the Manufacturing, WRT and TCE sectors retain highly significant rE,ICC estimate
correlations with the cost of debt. In the service sector, share repurchasers’ rE,CAPM
estimate covaries significantly (at the 1% level) with the cost of debt. Thus, for each
industry group, we find at least one instance of persistent and statistically significant
deviations from the MM postulates discussed in Section 3.
25
The distribution of aiat ∈ [0.01, 0.3] itself remains too skewed and heavy-tailed to be well
approximated by the Gaussian distribution directly.
37
Table 9: Model 6 for SIC Manufacturing
Response Variable: log(aiat)
rE,CAPM
rE,ICC
Repurchasers
Issuers
Repurchasers
Issuers
sizeIV included
0.0047
(0.0038)
0.0836∗∗
(0.0259)
−0.0301
(0.0204)
yes
0.0003
(0.0011)
−0.0217
(0.0230)
0.0213
(0.0152)
yes
0.1118∗∗
(0.0229)
0.0236
(0.0224)
0.0032
(0.0199)
yes
0.0122
(0.0097)
−0.0358
(0.0196)
0.0301∗
(0.0142)
yes
Log Likelihood
Total Obs.
No. Firms
No. Years
-1673.7298
4412
444
31
-2244.7773
3898
502
31
-1595.5542
4412
444
31
-2227.0184
3898
502
31
rE E/D
V
D
I/K
L
Table 10: Model 6 for SIC Services
rE,CAPM
rE,ICC
Repurchasers
Issuers
Repurchasers
Issuers
sizeIV included
0.0561∗∗
(0.0193)
−1.1005∗
(0.4571)
0.2856∗
(0.1329)
yes
−0.0003
(0.0009)
−0.0396
(0.0266)
0.0338
(0.0204)
yes
0.0677
(0.0735)
−0.1115
(0.2287)
0.1181
(0.1964)
yes
0.0148
(0.0084)
−0.0335
(0.0214)
0.0352
(0.0187)
yes
Log Likelihood
Total Obs.
No. Firms
No. Years
-360.5251
727
86
31
-629.7538
865
118
31
-351.9017
727
86
31
-627.6228
865
118
31
rE E/D
V
D
I/K
L
Standard errors in parentheses. ∗∗ p < 0.01, ∗ p < 0.05. Intercept, tbond and value control variables
suppressed for clarity. See Model 6 in Tables 3 through 6.
38
Table 11: Model 6 for SIC WRT
Response Variable: log(aiat)
rE,CAPM
rE,ICC
Repurchasers
Issuers
Repurchasers
Issuers
sizeIV included
−0.0008
(0.0070)
0.1338∗
(0.0561)
−0.1178∗∗
(0.0413)
yes
−0.0078∗
(0.0032)
0.1787
(0.1140)
0.0009
(0.0640)
yes
0.1044∗∗
(0.0372)
0.1607∗∗
(0.0469)
−0.1452∗∗
(0.0425)
yes
0.0455
(0.0314)
0.0587
(0.0601)
−0.1100∗
(0.0519)
yes
Log Likelihood
Total Obs.
No. Firms
No. Years
-730.0629
1957
181
31
-701.9330
1316
164
31
-691.1709
1957
181
31
-681.9675
1316
164
31
rE E/D
V
D
I/K
L
Table 12: Model 6 for SIC TCE
rE,CAPM
rE,ICC
Repurchasers
Issuers
Repurchasers
Issuers
sizeIV included
0.0710
(0.0374)
−2.5162∗
(1.0393)
0.2041
(0.3647)
yes
−0.0081
(0.0125)
−0.1956
(0.1563)
0.0141
(0.0500)
yes
0.4311∗∗
(0.1508)
−0.1857
(0.2964)
−0.1010
(0.4070)
yes
0.4092∗∗
(0.0869)
−0.1838
(0.1269)
0.0620
(0.0330)
yes
Log Likelihood
Total Obs.
No. Firms
No. Years
-143.5696
851
80
30
-203.6063
2152
208
31
-119.9375
851
80
30
-126.8134
2152
208
31
rE E/D
V
D
I/K
L
Standard errors in parentheses. ∗∗ p < 0.01, ∗ p < 0.05. Intercept, tbond and value control variables
suppressed for clarity. See Model 6 in Tables 3 through 6.
39
Among share issuing firms, the rE,ICC coefficient remains positively correlated
in each sector, but is significant only for firms in the TCE group. Conversely, the
rE,CAPM equity cost measure exhibits the predicted negative covariation for firms
in the service sector, TCE, and wholesale and retail trade (Tables 10, 12 and 11,
respectively). For this latter group the cov(rE,CAPM , aiat) < 0 is significant at the
the 5% level. These results support the central hypothesis, albeit tentatively, that
firms which persistently use the stock market as a medium for shareholder payouts
– as opposed to a source of capital – deviate from the basic dynamics of capital
structure theory. For these repurchasing firms, the estimated “required return to
equity” does not behave, over the long pull, like a component of the cost of capital.
Of course, the rE metrics for share repurchasing firms remain tied to the value of
the underlying assets and hence the firm’s free cash flows. However, the “required
stock returns” for repurchasing firms are more akin to a bet on these returns than
on the long-term returns to real investments, because those claims should be – and
are for share issuing firms – sensitive to the shifts in cash flow distribution generated
by changes in borrowing costs.
An intuitive sense of this separation from capital investment pricing can be obtained from inspecting the trend of year-specific rE coefficient estimates. The most
clear cut example of the theoretically expected results are plotted in Figure 2 for
equity issuing firms in the WRT sector. The time series point estimates are means
of the cov(rE,CAPM , log(aiat)) coefficients across the firms in each sample year – controlling, of course, for value and earnings expectations to the extent possible. Fig. 2
shows that the negative correlation is persistent and relatively stable over time. The
40
noticeable deviations from the green fixed effect estimate (≈ −0.008) are during the
stock market booms in the late 1980s and 1990s, which coincided expansionary monetary policy, which reduced the overall cost of borrowing.
Figure 2: Whole and Retail Trade Issuers in rE,CAPM , Model 6
0.02
rE(CAPM) coefficient
0.01
0.00
−0.01
16
20
14
20
12
20
10
20
08
20
06
20
04
20
02
20
00
20
98
19
96
19
94
19
92
19
90
19
88
19
86
19
19
84
−0.02
These estimates are based on Model 6. Errors bars are year-specific ±2standard deviations around the mean estimate.
The green line indicates the average “fixed effect” coefficient estimate from the crossed effects of firms and years as
reported in Table 11. The grey bars are US recessionary periods.
It is also telling to compare the these time series coefficient plots between payout
policy groups. For instance, manufacturing firms’ rE,ICC fixed effects estimates in
41
Table 9 provide minimal information about the how well or not the data corresponds
to the theory. However, by comparing the annual estimates of repurchasers and
issuers, as is done in Figure 3, the relative stability of the latter group’s rE correlation
with debt costs becomes apparent. In all but three years, issuers’ 2-s.d. error bars
encompass both positive and negative correlations at the firm level (see Panel b).
For share repurchasers in Panel (a) a cyclical pattern comes to the fore. In the
years following a recessionary period, these firms’ capital cost components become
more strongly correlated in the subsequent boom period. As share repurchases are
highly procyclical (see Fig. 1), this finding suggests that buyback programs generate
increased deviations from equity markets’ role in signaling firms’ cost of investment.
Although procyclicality in the coefficients among share issuing Manufacturers can be
seen, it is far more muted than that for persistent share repurchasers.
Figure 3: Manufacturing Firms in rE,ICC , Model 6
rE(ICC) coefficient
0.3
0.2
0.1
0.1
(a) Repurchasers in rE,CAPM Model
16
14
20
12
20
10
20
08
20
06
20
04
20
02
20
00
20
98
20
96
19
94
19
92
19
90
19
88
19
86
19
84
19
16
14
20
12
20
10
20
08
20
06
20
04
20
02
20
00
20
98
20
96
19
94
19
92
19
90
19
88
19
19
19
19
86
0.0
84
0.0
0.2
19
rE(ICC) coefficient
0.3
(b) Issuers in rE,CAPM Model
These estimates are based on Model 6. Errors bars are year-specific ±2standard deviations around the mean estimate.
The green line indicates the average “fixed effect” coefficient estimate from the crossed effects of firms and years as
reported in Table 9. The grey bars are US recessionary periods.
42
6.3
Discussion
The results presented above demonstrate distinct empirical tendencies between firms
that persistently use the stock market as a source of capital financing and those
using it as a medium for shareholder payouts. Unconditional and weakly controlled
covariance coefficients between firms’ equity cost estimates (both rE,CAPM and rE,ICC )
and the log of marginal debt costs were positive and significant for each policy group
(see Models 1-3 in §6.1). As debt and equity are claims on the same underlying set of
assets, these results are consistent with the predictions of Merton’s extension of MM
theory. Conversely, attempts to control for intrinsic firm value and expected earnings
did not produce robust evidence of the predicted negative covariation between the
components of the cost of capital for either group of firms. However, share issuing
firms tended much closer to the theoretical expectations than did share repurchasing
firms. Results from the sector-specific tests in §6.2 support the inference that (more)
exact expectational proxies would uncover the fundamental rE -rD trade-off for share
issuing firms, but likely not for persistent share repurchasers.
Negative coefficient point estimates were found among share issuing firms in the
full sample rE,CAPM specifications (Models 4-6 in Table 3) and in three of the four
SIC subgroups (see Tables 10, 12, 11). Only the estimate for the Wholesale and Retail Trade sector proved significant. The single case of a negative coefficient estimate
among share repurchasing firms was for the WRT sector under the rE,CAPM specification, though it too lacked significance. That the fundamental tradeoff relationship
between rD and rE is difficult to isolate should come as no surprise. Our empiri-
43
cal specifications, like all models, necessarily fail to hold “all else equal”. Yet, by
controlling for a wide range of variables commonly used in earnings forecasting, we
have accounted for much of the information available to capital markets investors.
Moreover, the crossed mixed effects structure employed enabled us to control for
latent effects specific to individual firms and to particular years.
With these caveats in mind, the persistently positively correlated rE,ICC estimates reveal that share issuing firms’ equity costs behave more like a component of
the WACC than their repurchasing counterparts. As mentioned above, the relative
decline between Model 1 and 4-6 in §6.1 was much greater for issuers than repurchasers. Looked at another way, the repurchasers-to-issuers rE,ICC coefficients ratio
was 1.38 (=0.157/0.114) in Model 1 but, after controlling for expected earnings, the
divergence more than doubled to 3.02 (=0.094/0.031) in Models 5 and 6 (see Tables 5
and 6). Similarly, under the rE,ICC specification, share repurchasers had significantly
positive covariations with log(aiat) in two sectors for which share issuers had no
significant covariation (Manufacturers and WRT).26 Overall, we conclude that share
issuing firms under the ICC measure of equity costs deviate substantially less from
the theoretical predications as compare to share repurchasing firms.
The various comparative LMM results provide preliminary support for our hypothesis that how firms interact with capital markets affects these markets’ pricing
and signaling function. Thus, in addition to the well-known noisiness of stock prices
(e.g., Shiller, 1981), even smoothly rising equity valuations by themselves do not
signal falling capital costs for persistent share repurchasers. It follows that, among
26
In the other two sectors, either both (TCE) or neither (Services) payout policy groups had
significant correlations.
44
such firms, rising share prices are of little value to the broader economy. On the
other hand, for firms that regularly turn to equity markets for capital financing,
rising share prices can be expected to reflect rising investments in real capital and
employment.
If further substantiated, these findings argue that new qualifications be added to
real world analyses of capital structure and q theory. Both dynamic trade-off and
pecking order theories should account for firms’ long-term interaction with equity
markets as the expected pricing behavior will depend on the these policies. Secondly, the explanatory weakness of q can now be, in part, ascribed to the direct
construction of q from stock market values and/or returns. The findings suggest
that this construction is valid only for share issuing firms. Because the required
returns to equity for share repurchasing firms fail to accurately price real capital
projects, rE should not enter into q’s discount factor. The basic logic of q theory,
however, remains intact: Firms should invest whenever the cost of capital is less than
the returns it will generate. Our results merely argue for a reconsideration of those
capital costs as that which is actually borne by the firm (e.g., interest costs), and not
what would be borne were firms to have a different payout and financing policies.
7
Conclusion
Widespread concern that the rapid rise in share repurchases in the United States is
reducing corporations’ long-term value motivated an investigation of whether firms
engaged in such payout policies differ substantial from other firms. As noted, the
45
weakness of such critiques is that if corporate value were being reduced by buybacks
then investors would be expected to punish managers by selling out (Easterbrook &
Fischel, 1989). Such a self-correcting response would fail were the returns to equity
amongst share repurchasing firms to behave in a manner inconsistent from capital
structure theory, which ties rE to firms’ real sector investment. This led us to ask
how rE is expected behave vis-à-vis capital investment and firm value, and whether
share repurchases perturb the expected results. To operationalize the issue, Frank
and Shen’s (2015) update to the Abel and Blanchard (1986) model of marginal q was
particularly useful in its disaggregation of rE from the other variables, while being
built within a well-founded theory of investment. In order to isolate the fundamental
relationship between rE and rD , we employed a wide range of value controls in a LMM
framework that allowed for idiosyncratic and macroeconomic variability.
Although the results remain tentative, we found evidence that persistent share
repurchasers’ rE is tied less directly to firms’ capital investment than is the case for
other firms. The results suggest that share repurchases can denude the stock market
of its real sector signaling function, thereby enabling changes in long-term firm value
to go unaccounted for by investors. More immediately, our results imply firms’ payout
policy mechanisms are an important qualifier for investment and capital structure
theory. In particular, we argued that rE is properly considered a component firms’
cost of capital only if they regularly rely on issuances to finance investment projects.
These results are poignant but require further validation with larger datasets and
improved controls, which must be left for future research.
46
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51
Appendix A
Derivation of Linear q and I/K Equation
Take a first-order Taylor expansion of (3) around around M̄ and β̄ ∗ ,
"
#
∞
∞
X
X
M̄ β̄ ∗
M̄
∗ k
∗ k−1
Ωt
qt ≈ E
+
(
β̄
)
(M
−
M̄
)
−
(
β̄
)
(r
−
r̄)
t+k
t+k
1 − β̄ ∗ k=1
1 − β̄ ∗ k=1
(A.1)
The third term replaces the discount rate with the cost of capital according to βt∗ ≈
1 − rt − δ and defining β̄ ∗ = 1 − r̄ − δ. To render (A.1) finite, a VAR(1) process is
assumed.
ψ
Let Ztψ be an S ψ × 1 VAR(1) process in which the first element Z1,t
= ψt , for
ψ
ψt = {Mt , βt } and the remaining S − 1 elements are macro- and idiosyncratic
variables relevant to the value of the firm. Then the stochastic process is
ψ
Ztψ − Z¯ψ = Aψ (Zt−1
− Z¯ψ ) + t
(A.2)
where s,t ∼ N (0, σs2 ), ∀ s ∈ S and the constituent elements of q are the first elements
in the respective VAR. That is, Mt = a0 ZtM and βt∗ = b0 Ztβ where a and b are S M ×1
and S β × 1 vectors with the first element equal to 1 and all others zero.27
Assuming the coefficient matrix Aψ is diagonal,28 then the marginal profit and
cost of capital dynamics reduce to the independent AR(1) processes:
Mt+1 = M̄ + ρM (Mt − M̄ ) + M
rt+1 = r̄ − ρβ (rt − r̄) + β
27
2
M ∼ N (0, σM
)
(A.3)
β ∼ N (0, σβ2 )
(A.4)
This construction, due to Frank and Shen (2014, Appendix A.2), differs from Abel and Blanchard’s in which the VAR vector Zt is identical for both Mt and βt . The latter method requires
that observable data are augmented by the VAR coefficient matrix, whereas the former allows us
to avoid this intermediate step (see below).
28
For this simplification Frank and Shen (2014) state that the first element of Aψ is ρψ > 0 and
all others are zero. Although correct, one need only assume a diagonal coefficient matrix to derive
AR(1) dynamics.
52
The last equality comes from βt∗ ≈ 1 − δ − rt and defining β̄ ∗ = 1 − r̄ − δ. Equation
(A.4) makes explicit that the cost of capital rt in (A.1). Recursively substituting
(A.3) and (A.4) into (A.1) produces the convergent sequence
L(qt ) :=
β̄ ∗ · ρM
M̄ β̄ ∗
M̄ · ρβ
+
(M
−
M̄
)
−
(rt − r̄)
t
1 − β̄ ∗ 1 − β̄ ∗ ρM
(1 − β̄ ∗ )(1 − β̄ ∗ ρβ )
(A.5)
which is equation (4).
Following Abel and Blanchard (1986, sec. 6) we adopt a linear homogenous investment cost function, which reduces the relationship with q to a positive affine
t
= −1 − φ KItt ,
transformation. As in Frank and Shen’s application, we assume ∂π
∂It
which implies
It
1 1
= + L(qt ) + t
Kt
φ φ
Using the definition in (A.5) and rearranging, the investment equation becomes
−α
α
}|2
{
}|1
{
z
It
1
M̄ β̄ ∗
β̄ ∗ · ρM
M̄ · ρβ
= +
−
M̄ +
r̄ +α1 rt + α2 Mt + t
Kt
φ 1 − β̄ ∗ φ(1 − β̄ ∗ ρM )
φ(1 − β̄ ∗ )(1 − β̄ ∗ ρβ )
|
{z
}
z
α0
It
= α0 + α1 rt + α2 Mt + t
Kt
which is (5).
53
(A.6)
Appendix B
List of Variables
Annual accounting data is from the Compustat database covering the period 1984-2014. Daily returns data
are from the CRSP database. Market portfolio and monthly short-term risk-free borrowing figures are from
Kenneth French’s website. The 10-year Treasury bond figure is from the Federal Reserve Flow of Funds
account. Item names in Table B.1 refer to Compustat variable names unless otherwise noted.
Table B.1: Model Variables – Capital Cost and Value Controls
Variable Name
Equity Value
Symbol
Description
E
Daily closing stock prices within each fis-
Restrictions
E>0
cal year are smoothed by a Baxter-King
54
filter (freq. 2-1000; 10 lead/lags). Share
price P is the mean of the smoothed series. Multiply this by year-end shares
outstanding. P × Item CSHO
Total Debt
D
Start of period short-term plus long-term
D>0
debt. Item DLC + Item DLTT
Total Assets
K
Total Assets (Item AT)
K>0
Enterprise Value
V
Sum of assets and market capitalization,
V >0
less shareholder internal equity and deferred taxes. K + E− Item SEQ - Item
TXDB
Variable Name
Investment
Tax-adjusted interest rate
Symbol
I
aiat
Description
Restrictions
Capital expenditures (Item CAPX)
I≥0
Total interest expenses over total debt
Average interest and tax
(Item XINT / D) multiplied by average
shield rate each trimmed to
tax shield on pretax income (1 - Item
∈ [0, 1]
TXT / Item PI)
Implied Cost of Equity
rE,ICC
See §4.1
Trimmed to rE,ICC ∈ [0, 1]
rE,CAPM
See §4.1
Trimmed to rE,CAPM ∈ (0, 1)
Capital (ICC)
Factor model-based Cost
of Equity
Market Leverage (Inverse)
55
Idiosyncratic Volatility
Share repurchases
V
D
ivol
bb
Two-tail winsorized at 1%
see §4.3
Two-tail winsorized at 1%
Total expenditure on repurchases less
bb ≥ 0
and positive change in the value of preferred shares. Item PRSTKC−(Item
PSTKRV − Item PSTKRVlag )+ .
Current earnings
Expected Earnings
NI
Net income scaled by debt (Item IB)
Two-tail winsorized at 1%
N It+1,t+2,t+3
Determined by the Hou et al. (2012)
Two-tail winsorized at 1%
projections and scaled by debt. See Appendix C for details
Book equity-to-market
BM
equity
Total Payouts
Log of book equity B (Item AT - Item
B>0
LT) over stock value E.
SHpay
Cash flow dividends (Item DVT) plus
Non-negative and top-tail
share repurchases bb scaled by debt.
winsorized at 1%
Variable Name
Symbol
Sales Growth
∆SALE
Description
Year-on-year change in sales (∆ Item
Restrictions
Two-tail winsorized at 1%
SALE)
Asset Growth
∆T A
Year-on-year change in total assets (∆
Two-tail winsorized at 1%
Item AT)
Capital Gains
dP
Log of year-on-year change in equity
Trimmed to dP ∈ [−10, 2)
value (log (∆P ) )
Cash Flow
cf
Operating income before depreciation
Trimmed to cf /D ∈ (−5, 5)
and taxes (Item OIBDP).
Accurals
AC
From Fama and French (2006): Change
Two-tail winsorized at 1%
in short-term assets (∆ Item ACT) plus
56
change in short-term debt (∆ Item DLC)
minus change in cash, short-term investments and short-term liabilities (∆ Item
CHE, ∆ Item LCT).
No Short-term Debt Indi-
N oDLC
Equals 1 if Item DLC = 0, otherwise 0.
cator
Ohlson Score
OH
OH
=
−1.32 − 4.07 log (Item AT) +
6.03(Item LT / Item AT) − 1.43(Item ACT - LCT) +
0.0757(Item LCT / Item ACT) − 2.37(Item NI / AT) − 1.72N egB −
0.521( Item NI - Item NI-1 ) /abSumN I +0.285N egN I −1.83(Item IB+
Item TXDB)/Item LT). Where N egN I and N egB are indicator
variables for negative net income and negative book equity and
abSumN I is the sum of the absolute values of current and lagged Item
NI. See Ohlson (1980), Fama and French (2006) for further details.
Variable Name
Risk-free interest rate
Symbol
tbond
Description
Restrictions
Constant maturity monthly 10-year Treasury bond yield average over
12-month period according with each firm’s fiscal year. Series RIFLGFCY10 N.M from the H15 flow of funds series.
Size Quintiles
sizeIV
Quintiles of firm’s sorted on total assets (Item AT) in each fiscal year.
Size quintiles are determined within each industry when applicable.
Industry Classification
SIC
AMC firms have SIC code less than 2000; Manufacturing is in the
2000-4000 range; TCE are in the 4000s; WRT are between 5000 and
6000; Service sector is between 7000 and 8000.
57
Appendix C
Calculation of Earnings Expectations
Following Hou et al. (2012) we conduct a series of regressions on 10-years of pooled
annual data from the Compustat universe. The regression is
Eit+τ = α0 + α1 Ai,t + α2 Di,t + α3 + DDi,t + α4 Ei,t + α5 N egEi,t + α6 ACi,t + i,t+τ (C.7)
The right-hand side variables are pooled data for the current year plus the prior nine
years. For each firm-year observation in the pooled samples the covariates are
• Ei,t , Ei,t+τ are the earnings/net income (Item IB) in year t or year t + τ . For
the τ th -year ahead forecast the left-hand side variable leads all other variables
by τ years.
• Ai,t is total assets (Item AT).
• Di,t is total dividends paid (Item DVT).
• DDi,t is an indicator variable which 1 if the firm did pay dividends and is zero
if not.
• N egEi,t is an indicator variable which is 1 if the firm has negative earnings,
and zero otherwise.
• ACi,t is total accruals which we calculate on the basis of Fama and French
(2006) as the change in current assets plus the change in short-term debt, less
the change in cash holdings and change in short-term liabilities (cf. Table B.1).
i,t+τ is the residual for the τ ’s regression. The τ th -year ahead expected earnings is
firm i’s fitted-value given its current year covariates and the coefficients αi associated
with the τ th regression from in (C.7).
58
Appendix D
Implied Cost of Capital Calculations
Table D.1: Description of Implied Cost of Capital (ICC) Models
Gebhardt et al.
(2001)
M C t = Bt +
11
X
Et [(ROEt+i − rE ) · Bt+i−1
i=1
(1 + rE )i
+
Et [(ROEt+12 − rE ) · Bt+11
rE · (1 + rE )11
M Ct is the current market value, ROEt+i is the projected return on equity,
Bt+i is the book value of equity and rE is the implied cost of equity. The first
3 earnings projections Et [N It+i ], i = 1, 2, 3 are based on the Hou et al. (2012)
methodology (see Appendix C). Expected book equity is then determined by
Et [Bt+i ] = Et [Bt+i−1 ] + (1 − k)Et [N It+i ] where k is the payout ratio (1 − k the
retention ratio) and is equal to the current year’s payout ratio if N It > 0 or as
6% of the dividends-total asset ratio if the firm has negative earnings, N It ≤ 0.
For years t + i, i = 4, . . . 12, ROE converges to the industry-specific historical
It+i
average by t + 12 by a linear interpolation. Note that since ROEt+i ≡ BNt+i−1
the interpolated points uniquely determine Bt+i for i = 4, . . . 12.
Claus and Thomas
(2001)
M C t = Bt +
5
X
Et [(ROEt+i − rE ) · Bt+i−1
(1 + rE )i
i=1
+
Et [(ROEt+5 − rE ) · Bt+4 · (1 + g)
(rE − g) · (1 + rE )11
M Ct is the current market value, ROEt+i is the projected return on equity,
Bt+i is the book value of equity and rE is the implied cost of equity. Earnings projections Et [N It+i ], i = 1, . . . 5 are based on the Hou et al. (2012)
methodology (see Appendix C). Expected book equity is then determined by
Et [Bt+i ] = Et [Bt+i−1 ] + (1 − k)Et [N It+i ] where k is the payout ratio (1 − k the
retention ratio) set equal to the current year’s payout ratio if N It > 0 or as 6%
of the dividends-total asset ratio if the firm has negative earnings, N It ≤ 0.
g is the risk-free rate of return proxied by the current 10-year Treasury bond
yield minus a 3% premium.
Easton (2004)
M Ct =
Et [N It+2 ] + rE · Et [Dt+1 ] − Et [N It+1 ]
2
rE
M Ct is the current market value, N It+i is projected earnings, Dt+i is dividend
paid in year t + i and rE is the implied cost of equity. Earnings projections
Et [N It+i ], i = 1, 2 are based on the Hou et al. (2012) methodology (see Appendix C). Expected dividends
is determined by Et [Dt+1 ] = k·Et [N It+i ] where
59
k is the payout ratio (1 − k the retention ratio), set equal to the current year’s
payout ratio if N It > 0 or as 6% of the dividends-total asset ratio if the firm
has negative earnings, N It ≤ 0.
Continued on next page
Table 1 (cont.): Description of Implied Cost of Capital (ICC) Models
Ohlson and
Juettner-Nauroth
(2005)
s
A2 +
rE = A +
Et [N It+1 ]
· g − (γ − 1)
M Ct
where
A=
1
2
· (γ − 1) +
Et [Dt+1 ]
M Ct
1
2
and g =
Et [N It+3 ]−Et [N It+2 ]
Et [N It+2 ]
+
Et [N It+5 ]−Et [N It+4 ]
Et [N It+4 ]
M Ct is the current market value, ROEt+i is the projected return on equity,
Bt+i is the book value of equity and rE is the implied cost of equity. Earnings projections Et [N It+i ], i = 1, . . . 5 are based on the Hou, van Dijk, and
Zhang (2012) methodology (see Appendix C). Expected book equity is then
determined by Et [Bt+i ] = Et [Bt+i−1 ] + (1 − k)Et [N It+i ] where k is the payout
ratio (1 − k the retention ratio) set equal to the current year’s payout ratio
if N It > 0 or as 6% of the dividends-total asset ratio if the firm has negative
earnings, N It ≤ 0. g is the risk-free rate of return proxied by the current
10-year Treasury bond yield minus a 3% premium.
Gordon and
Gordon (1997)
(1 Period)
M Ct =
Et [N It+1 ]
rE
M Ct is the current market value, N It+1 is projected earnings and rE is the
implied cost of equity. Earnings projections Et [N It+1 ] is are based on the Hou,
van Dijk, and Zhang (2012) methodology (see Appendix C).
Gordon and
Gordon (1997)
(5 Period)
M Ct =
5
X
Et [Dt+i ]
Et [N It+5 ]
+
i
(1 + rE )
rE · (1 + rE )5
i=1
M Ct is the current market value, Dt+i is the projected dividend payout, N It+5
is expected income in t + 5 and rE is the implied cost of equity. Earnings
projections Et [N It+i ], i = 1, . . . 5 are based on the Hou, van Dijk, and Zhang
(2012) methodology (see Appendix C). Expected dividends is determined by
Et [Dt+1 ] = k · Et [N It+i ] where k is the payout ratio (1 − k the retention
ratio), set equal to the current year’s payout ratio if N It > 0 or as 6% of the
dividends-total asset ratio if the firm has negative earnings, N It ≤ 0.
This table is adapted from appendix in Hou, van Dijk, and Zhang (2012).
60
Appendix E
Theoretical and Sample Distributions of aiat
Figure 4: Unrestricted aiat sample distributions
log(aiat)
−4
−2
0
2
−8 −6 −4 −2
0.4
0.0
aiat
0.8
0
Issuance Group
4
−4
−2
2
4
0.8
aiat
0.4
0.0
0.4
0.0
aiat
0
norm quantiles
0.8
norm quantiles
0
10
20
30
40
50
0.0
0.1
lnorm quantiles
0.2
0.3
gamma quantiles
(a) Share Issuing Firms
−2
−10
−6
log(aiat)
0.4
0.0
aiat
0.8
Buyback Group
−4
−2
0
2
4
−4
−2
2
4
0.8
aiat
0.4
0.0
0.4
0.0
aiat
0
norm quantiles
0.8
norm quantiles
0
10
20
30
40
0.00
lnorm quantiles
0.05
0.10
0.15
gamma quantiles
(b) Repurchasers in rE,ICC Model
61
0.20
0.25
Figure 5: Restricted aiat ∈ [0.01, 0.30] sample distributions
−1.5
−3.0
log(aiat)
−4.5
aiat
0.00 0.10 0.20 0.30
Issuance Group (aiat in 0.010−0.298)
−4
−2
0
2
4
−4
−2
aiat
0
10
20
0
2
4
norm quantiles
30
40
0.00 0.10 0.20 0.30
aiat
0.00 0.10 0.20 0.30
norm quantiles
0.00
0.05
0.10
lnorm quantiles
0.15
0.20
0.25
gamma quantiles
(a) Share Issuing Firms
−1.5
−3.0
log(aiat)
−4.5
aiat
0.00 0.10 0.20 0.30
Buyback Group (aiat in 0.010−0.298)
−4
−2
0
2
4
−4
−2
aiat
0
10
20
30
0
2
4
norm quantiles
40
lnorm quantiles
0.00 0.10 0.20 0.30
aiat
0.00 0.10 0.20 0.30
norm quantiles
0.00
0.05
0.10
gamma quantiles
(b) Repurchasers in rE,ICC Model
62
0.15
0.20