National Tax Journal
Vol 51 no. 4 (December 1998) pp. 653-73
CAPITAL GAINS TAXATION AND NEW FIRM INVESTMENT
CAPITAL GAINS
TAXATION AND NEW
FIRM INVESTMENT
M. KEVIN MCGEE
*
Abstract - This paper simulates the
impact of a capital gains tax cut on new
and established firms, assuming that
new firms differ from their older
counterparts because of the dividend
trap. For all parameter values, the tax
cut increases the mature firms’ desired
capital stock, holding interest rates
constant. In nearly every case, however,
the tax cut is more beneficial to mature
firms than to new startups. Indeed, in
many of the cases portrayed, the tax cut
actually reduces new firm investment.
Hence, this paper contradicts the widely
held view that a capital gains tax cut
would be a well-targeted approach for
encouraging new firm capital formation.
The problem with this logic is that it
treats as given both the initial value of
the firm and the accretions to value that
follow. But certainly neither the firm’s
current market value, nor its expected
future increases in value, is independent
of either the firm’s current level of
investment or the tax treatment of its
investment return. Any analysis that
treats them as such should be suspect.
This paper presents a “Trapped Equity”
model of firm behavior, that endogenously determines both the firm’s initial
value and its optimal initial level of
investment. New firms differ from older,
established firms in this model because
of the dividend trap: since corporations
can at the margin only return equity to
their shareholders through taxable
dividends, making new share issues a
more expensive source of equity than
retained earnings, new corporations are
created with less equity than would
otherwise be optimal. All their earnings
are then retained, and firm equity grows
internally, until the marginal value of
additional equity is low enough to
justify paying (taxable) dividends. New,
equity-poor firms don’t pay dividends;
old, equity-rich firms do.
An oft-stated dictum of journalists and
politicians is that a cut in capital gains
taxation will increase economic growth,
by encouraging investment in new firms.1
Much of the initial return on these newly
formed firms, the reasoning goes, is in
the form of increases in firm value, i.e.,
capital gains; a lower tax rate on this
return would help direct more investment
dollars into these nascent enterprises.
*
I find in this model that a reduction in
the capital gains tax always increases
University of Wisconsin–Oshkosh, Oshkosh, WI 54901.
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NATIONAL TAX JOURNAL VOL. LI NO. 4
investment demand by old firms, and
usually increases investment demand by
new firms as well. As such, the capital
gains tax cut competes with a variety of
other policy instruments, such as a
reduction in the corporate tax rate,
changes in depreciation allowances, and
movement to a cash flow tax, all of
which would similarly increase investment demand in models such as these.
wisdom: that firm behavior is not
modeled, but simply assumed.
The subsequent sections address that
shortcoming, by presenting a model of
firm behavior. In the second section, I
develop the dynamic optimization
problem, based on the prior section’s
asset market equilibrium, that the firm
must solve, deriving the conditions for
an optimal firm capital stock and
financing mix. Functional forms,
adopted to generate both analytic and
numerical results, are presented in the
third section. The fourth section
develops analytically the impact of the
capital gains tax cut on firm behavior in
the trapped equity model, when firms
are fully equity financed. The conditions
under which the tax cut results in less
relative investment in new firms than in
old firms are derived. Readers who wish
to skip the technical details may jump
from the second section directly to the
fifth section, where I present my
simulation results. These simulations
show that new firm investment falls
relative to that of mature firms for all
reasonable parameter values, and
indeed falls absolutely for some parameter values, both in an all-equity model
and when debt financing is also
allowed. The final section summarizes
these results.
The alleged advantage of the capital
gains tax cut, however, its advocates
avow, is not just that it encourages
investment, but that it targets that
investment toward new enterprises
where it is needed most. I find, however, that a reduction in the capital
gains tax consistently increases investment proportionately more in old firms
than it does in new firms. Although it
has been for some time intuited that
this result should arise in a trapped
equity model—i.e., that a lower capital
gains tax will merely deepen the equity
trap—before now this result had never
been formally established.2 And the
possibility that the tax cut might actually
reduce investment in new firms has to
the best of my knowledge never before
been suspected, let alone demonstrated. This paper therefore shows, at
least from the trapped equity view of
corporate taxation, that if the policy
goal is not just to promote corporate
investment, but to target that investment toward new enterprises, a capital
gains tax cut is definitely not the policy
option of choice.
THE ASSET MARKET EQUILIBRIUM
Capital gains are just one form of investment income. To attract investors, therefore, appreciating assets must yield an
after-tax return at least as great as other
assets, paying dividend or interest
income. Hence, to assess how capital
gains taxation impacts investment behavior, we must begin with the investor’s
asset market equilibrium, first modeled
by Pye (1972) and Stapleton (1972), and
discussed by King (1974), Poterba and
Summers (1983), and Sinn (1987).3
In the first section, I discuss the role of
capital gains taxes in the equilibrium
that must arise in the asset market. As
will be seen, the result of that analysis,
at least at first glance, closely parallels
the popular wisdom, that a capital gains
tax cut will encourage new firm
formation. The limitation of that analysis
is also the limitation of the popular
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Vol 51 no. 4 (December 1998) pp. 653-73
CAPITAL GAINS TAXATION AND NEW FIRM INVESTMENT
Investors will be indifferent between
alternative investments when they yield
identical after-tax rates of return.4 A
corporation with a current market value
of Vt must generate sufficient dividend
.
income .Dt and capital gain (Vt – VNt),
where Vt is the change in firm value and
VNt represents new share issues,5 to
yield the same after-tax return as an
interest-paying security:
The firm’s market value is the present
value of the stream of after-tax payments to its shareholders: its dividends
after the income tax is levied and its
share repurchases (negative new issues),
which are untaxed. Since no tax liability
is incurred until the dividends are
actually paid, the share’s income stream
is discounted by the investor at the
after-tax interest rate.
Since the ordinary personal income tax
reduces both the after-tax value of
dividend payments and the rate at
which the firm’s payments are discounted, its impact on firm value is
ambiguous. If the firm were to only
issue a single dividend payment at some
future time T, its current value would be
1
.
(1 – θ)rVt = (1 – θ)Dt + (1 – c)(Vt – VNt).
The parameters θ and c are the effective
tax rates on ordinary and capital gains
income, respectively, and r is the interest
rate.6 Integrating subject to a
transversality condition gives the current
market value of the firm:7
5
V0 = DT (1 – θ )e–r(1 – θ )T.
2
∞
∫ [(
V0 = e –ρt
Its derivative, measuring the change in
firm value as the ordinary tax rate
increases, is
1–θ
1 – c Dt – VNt dt
)
]
0
where the firm’s discount rate ρ is
6
dV0
V0
=
[rT(1 – θ ) –1]
1–θ
dθ
3
ρ=r
( 11 –– θc ).
which will be positive only for sufficiently large T, i.e., for dividends
sufficiently distant into the future. Any
increase in the ordinary personal income
tax, therefore, presumably will be more
likely to reduce or leave unchanged the
current market value of established
firms, whose stream of dividend
payments may remain relatively constant
over time, and increase the value of
firms with strong growth prospects (and
no current dividends).8
To interpret equation 2, observe that, in
the absence of a capital gains tax, it
simplifies to
4
∞
V0 = ∫ e–r (1 – θ )t [(1 – θ)Dt – VNt ]dt.
0
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8
The tax on capital gains income similarly
affects the current market value of a
given future stream of dividends and
repurchases in two ways. First, the
capital gains tax increases the after-tax
value of any dividend payment at time t,
since that dividend creates a capital loss
(or avoids a capital gain) and hence
reduces current or future capital gains
tax liabilities. This effect partly offsets
the dividend tax; if c = θ, the tax on the
dividend payment and the tax reduction
on the capital loss exactly offset, and
the dividend’s value to the investor at
time t is the same as when no taxes are
imposed.
dV0
V0
=
1–c
dc
which will be negative for large T. An
increase in the capital gains tax therefore presumably will be more likely to
increase or leave unchanged the current
market value of established firms,
whose stream of dividend payments
may remain relatively constant over
time, and reduce the value of firms with
strong growth prospects. Since newly
formed firms are presumably in the
latter category, the asset market
equilibrium suggests that a reduction in
the capital gains tax rate will indeed
encourage investment in new firms, by
increasing the market value of their
shares relative to other investment
instruments.
Second, an accrual capital gains tax will
continuously result in immediate tax
liabilities, rather than liabilities that are
delayed until the actual dividend
payments or share repurchases.9
Because of this partial (or if c = θ,
complete) elimination of the share’s
ability to delay tax liabilities, the
investor’s discount rate approaches the
before-tax interest rate, which is also
taxed on an accrual basis.
This analysis of the asset market
equilibrium is in a sense a formalization
of the popular wisdom, and it shares the
same shortcomings of the popular
wisdom. The impact on the market
value of a given flow of dividends and
repurchases was examined, without
determining whether that flow of
payments would remain unchanged.
Mature firms were assumed to pay
dividends (or repurchase shares) now,
and new firms only later, without
justifying those behavior patterns. And
the discussion of tax impacts focused
entirely on the firm’s total market value,
without determining whether or how
those taxes affect the marginal value of
additional investment in the firm.
Like the ordinary income tax, the capital
gains tax’s impact on firm value therefore is, as a result of these two effects,
ambiguous. For a firm paying only a
single dividend at time T, the firm’s
current value when capital gains are
taxed is
7
V0 = DT 1 – θ e –r(1 – θ )T/(1 – c)
1–c
(
[1 – rT(11 –– θc)]
)
The next sections address those shortcomings. A dynamic optimization
model, taking as its beginning point this
asset market equilibrium, will be used to
describe the firm’s optimizing behavior,
and the change in V0 due to the tax rate
is
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CAPITAL GAINS TAXATION AND NEW FIRM INVESTMENT
to identify differences between new and
established firms, and to examine how a
reduced capital gains tax translates into
investment demand.
outlays, and agency costs (1 –
u)Ψ(B,K).10 These agency costs are
assumed to depend upon the ratio of
debt to capital, to reduce the firm’s
taxable income (and hence are effectively tax deductible), and to reflect both
the agency and bankruptcy costs
associated with excessive debt, as well
as the agency costs associated with
excessive equity.11 The agency cost
function Ψ therefore will reach its
minimum at some optimal debt/capital
ratio γ, which will be the ratio the firm
would choose in the absence of
taxation.12
THE EQUITY TRAP FIRM OPTIMIZATION
MODEL
The dynamic optimization model used
here expands upon the firm growth
dynamics presented in Sinn (1991a), by
incorporating a debt/equity financing
choice. Its results are similar to those of
Hayashi (1985).
The firm maximizes its current share
value, developed in the prior section,
subject to two dynamic constraints: the
investment constraint that capital
growth equals investment minus capital
depreciation,
Two additional constraints are imposed
on the optimization problem:
11
Dt ,VNt ≥ 0.
9
The former, that dividends are nonnegative, is natural; the latter, that new share
issues are nonnegative, rules out share
repurchases and allows the model to
reflect the “New View” (or trapped
equity view) of dividend taxation
developed by Auerbach (1979),
Bradford (1981), and King (1974).13
.
Kt = It – δKt
where δ is the real rate at which capital
assets depreciate; and a budget
constraint, equating the firm’s cash
inflows and outflows,
10
Attaching the costate variables qte –ρt
and zte –ρt to the two dynamic constraints and the multipliers µDe –ρt and
µV e –ρt to the inequality constraints, and
maximizing the resulting Hamiltonian
function, yields the following firstorder conditions (suppressing time
subscripts):
.
Bt + VNt + (1 – u)[R(Kt ,Lt) – wLt] + uδKt
= Dt + (1 – u)rBt + It + (1 – u)Ψ(Bt,Kt).
.
Inflows are net new bond issues B, new
share issues VN, after-tax operating
income (1 – u)[R(K,L) – wL], and tax
depreciation allowances uδK; K and L
are firm capital and labor, w is the wage
rate, and u is the corporate tax rate.
Outflows are dividends, deductible
interest payments (1 – u)rB, investment
12
HI = e–ρt[q + z] = 0
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NATIONAL TAX JOURNAL VOL. LI NO. 4
16
13
HD = e–ρt
[(11 –– θc ) + µ
D
.
z = z [ ρ – r (1 – u) – (1 – u)ΨB ]
]
+z =0
17
14
.
q = q (δ + ρ) + z[(1 – u)(RK – ΨK) + uδ ].
HVN = e [ µv – 1 – z] = 0
–ρt
15
. .
Since equation 12 implies that z + q = 0,
combining these equations gives the
firm’s cost of capital:
HL = – (1 – u) ze–ρt [ RL – w] = 0.
18
RK – δ = r + Ψ B + Ψ K
The costate variables qt and zt measure
the change in the firm’s value due to
incremental increases in Kt and Bt ,
respectively; qt will be positive and zt
negative. Equation 12 states that, at the
optimal level of investment, they will
sum to zero, which implies that the
marginal cost of capital will equal the
marginal cost of debt, or that, at the
margin, the firm cannot increase its
market value through additional
purchases of debt-financed capital.
which depends both on the marginal
agency costs of debt (ΨB) and equity
(ΨK).15 In general, these marginal costs
will be of opposite sign; e.g., when the
firm is excessively debt financed, ΨB will
be positive, since more debt will
exacerbate the problem of excessive
debt, but ΨK will be negative, since
additional equity will reduce the agency
costs due to excessive debt. If the
agency cost function is convex, implying
for example that the increased bankruptcy risk of more debt is greater when
the debt/equity ratio is already high,
then these marginal costs will not be of
equal magnitude (e.g., ΨB will exceed
ΨK, when the firm is excessively debt
financed), so agency costs due to an
inefficient debt/equity ratio in general
will raise the cost of capital and reduce
investment.16
Equations 13 and 14 determine when
dividends or new shares will be issued:
by equation 13, dividends will be paid
( µD = 0) whenever –z, and hence q
equals (1 – θ)/(1 – c); by equation 14,
new shares will be issued ( µV = 0) when
q = 1.14 Equation 15 states that labor
will be employed until its marginal
revenue product equals the wage rate.
All of these results are standard.
FUNCTIONAL FORMS
The canonical equations, which describe
the rate of change in these two costate
variables over time, are
To draw out the implications of the
above model, it will be useful to adopt
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CAPITAL GAINS TAXATION AND NEW FIRM INVESTMENT
functional forms for the revenue
function R(K,L) and the agency function
Ψ(B,K). In this section, I describe the
adopted functions.
which gives a marginal revenue product
of capital of
20
I assume that the revenue function is
Cobb–Douglas and homogenous of
degree (1 – β). Two stories could justify
this less than unit homogeneity. One
would be a decreasing returns to scale
production function. The other would
be a degree of market power, giving the
firm a downward sloping demand for its
product. In particular, if the firm faces a
constant elastic demand for its product,
Q = P –1/β, where P is the firm’s price,
then the firm’s revenue R = Q1–β will be
homogeneous of degree (1 – β) when
the production function is linearly
homogeneous. Either story is sufficient
to guarantee that the firm’s size (i.e.,
output level or capital stock) is determinate in the long run.
RK = AK –β.
The agency cost function is assumed to
take the form19
21
Ψ=
v
(λ – γ )2K
2
where λ is the debt/capital ratio B/K.
Agency costs are normalized to equal
zero at their minimum point, where
λ = γ. A marginal increase in debt
increases agency costs by
The market power story implies that
corporate enterprises earn significant
inframarginal rents, that increase at a
diminishing rate as output increases. It is
the existence of these potential rents that
makes new firm creation worth taking on
in the face of the dividend trap.17 This
story is also consistent with the images of
potential new enterprises that proponents of lower capital gains taxes put
forward: innovative, high technology
startups, with a great idea or a new
discovery to exploit. These firms are not
perfect competitors, not indistiguishable
providers of some homogeneous product.
22
ΨB = v (λ – γ )
while an increment in equity increases
them by
23
ΨK = – v (λ2 – γ 2).
2
For subsequent ease of notation, I
assume the real revenue function net of
labor costs takes the form18
These functional forms will be incorporated into the previous analysis, to help
illustrate the impact of the capital gains
tax on firm formation.
19
CAPITAL GAINS AND THE NEW VIEW
R(K,L) – wL =
A
K 1–β
(1 – β )
In the trapped equity model developed
by Auerbach (1979), Bradford (1981),
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NATIONAL TAX JOURNAL VOL. LI NO. 4
and King (1974), established firms pay
dividends, but newly created firms do
not. As Sinn (1991a) demonstrates, new
firms go through three stages: an
instantaneous birth stage, in which new
shares are issued; a growth phase,
during which all earnings are retained;
and maturity, when the firm pays
dividends. In the New View model,
share repurchases are not possible.20
where equation 3 has been used to
substitute for ρ.
Equations 24 and 25 both imply that a
reduction in the capital gains tax rate,
by decreasing the investor’s discount
rate, will decrease the firm’s optimal
debt/equity ratio. Earnings retained
within the firm, that generate the
capital gains, will be less heavily taxed;
the firm responds by retaining more
earnings, thereby replacing some of its
debt with equity.
To analyze the impact of the capital
gains tax in this model, I must examine
each of the three growth phases of the
firm: infancy, expansion, and maturity. It
will be most convenient to examine
them in reverse order.
Those increased retained earnings will
not be used solely to decrease debt.
Since the reduced debt/equity ratio
reduces the firm’s total agency costs, by
equation 18, the reduction in the capital
gains tax rate in turn will reduce the
cost of capital, increasing the firm’s
desired capital stock. The assumed
functional forms make this relationship
more explicit: substituting equations 23
and 24 into equation 18, and then
solving equation 20 for K, gives the
firm’s optimal capital stock:
Mature Firms
Mature firms issue dividends, so µD = 0,
and q = –z = (1 – θ)/(1 – c). Therefore,
both costate variables q and z are
constant over time, and the canonical
equation 16 reduces to
24
ΨB =
[
ρ – r (1 – u)
(1 – u)
26
]
K=
which says that the firm will choose a
debt/capital ratio that equates the
after-tax cost of additional debt
(ΨB + r)(1 – u) to the discount rate ρ.
When the quadratic agency cost function (equation 21) is assumed, this in
turn implies that the debt/capital ratio λ
will be
[( )
r
ν (1 – u)
1–θ
1–c
A
ρ
– ν (λ2 – γ 2)
(1 – u) 2
}
.
Since equation 24 was used to eliminate
ΨB, the firm must be choosing its costminimizing debt/capital ratio. Therefore,
equation 26 describes the optimal
capital stock as a function of the
optimal amount of equity, with the
denominator of equation 26 measuring
the required rate of return on equity net
of the marginal agency cost of equity.
The capital gains tax cut reduces the
discount rate ρ but, by reducing the
25
λ=γ+
{
δ+
1
β
]
– (1 – u)
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CAPITAL GAINS TAXATION AND NEW FIRM INVESTMENT
optimal debt/capital ratio λ, raises the
marginal agency cost of equity. As
equations 3 and 25 make clear, the
former effect is dominant, and a lower
capital gains tax rate increases the
mature firm’s optimal capital stock.21 A
capital gains tax cut will reduce the
desired debt/equity ratios of mature
firms and increase their demand for
capital.
have sufficient earnings on hand to pay
dividends, after meeting their investment needs, expanding firms are equity
cash starved and must borrow too much
to finance too little investment.
To examine the impact of the capital
gains tax on these growing firms,
consider first the simpler case, where
the firm
is fully equity financed. Letting
.
B = B = 0 in equation 10, and z = 0, the
remaining canonical equation becomes
Expanding Firms
Expanding firms neither issue shares nor
pay dividends, so both µD and µV > 0. By
equations 13 and 14,
29
.
q = q [δ (1 – u) + ρ – (1 – u)RK]
27
(11 –– cθ) < (11 –– θc ) + µ
D
which, using equation 14, gives the
mature firm’s capital stock:
= – z = 1 – µv < 1
30
so – z and therefore q are between
(1 – θ)/(1 – c) and 1. Since, as Sinn
(1991a) shows, expanding firms must
eventually become mature firms, and
therefore q and – z must eventually
equal (1 – θ)/(1 – c), q must be falling
and z rising during this stage. Then,
.
.
q < 0 and z > 0, so by equation 16,
KT =
ρ – r (1 – u)
[
(1 – u)
δ+
ρ
(1 – u)
.
During the growth stage, dividends and
new share issues are both zero, so
substituting the budget constraint
(equation 10) for I into equation 9 gives
the firm’s capital growth equation:
28
ψB >
1
β
{ }
A
]
31
.
K = (1 – u)
which says that the debt/capital ratio
will be higher in the expansion stage
than at maturity, which by equation 18
implies that total agency costs, and
hence the cost of capital, will be higher,
and the stock of capital lower, than at
maturity. Unlike mature firms, which
(1 1– β )AK
1–β
–δ (1 – u) K.
Defining as t = T the moment the firm
reaches the mature stage, equations 30
and 31 together imply that the expanding firm’s capital growth path prior to
time T will be
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NATIONAL TAX JOURNAL VOL. LI NO. 4
32
Kt =
{
A
d(1 – β)
e
[ (
1–
]}
βδ (1–u)(T–t)
1
β
βδ (1 – u) + ρ
δ (1 – u) + ρ
absolute rate (the extra output has
increased after-tax income and hence
investment) but at a slower relative rate
(the additional inframarginal rents will
be relatively smaller). Therefore, the
capital stock during those periods will
be a larger fraction of the ultimate level.
)
.
When debt financing is brought back
into the model, an analytical solution is
no longer possible. It is clear that,
during the expansion phase, the firm’s
capital stock will be rising; Hayashi
(1985) demonstrated that its debt/
equity ratio during that phase will be
falling. The impact of the capital gains
tax cut on expanding firms in this model
will be explored through numerical
simulation in the next section.
In this all-equity model, the capital gains
tax rate affects Kt only through the
discount rate ρ; since from equation 32
dK/dρ is clearly negative, a reduction in
the tax increases K over the entire
growth stage, holding constant the date
of maturity at time T.
Perhaps, more interestingly, reducing
the discount rate flattens the relative
optimal capital stock profile over the
growth period. Reformulating equation
27 produces
Infant Firms
Infant firms, i.e., new startups, or
existing firms whose investment
prospects have suddenly expanded issue
new shares: µV = 0 and q = – z = 1. Sinn
(1991a) has shown that, since infant
firms become expansion firms, their
capital stock must be suboptimal, so the
flow condition (equation 17) cannot
hold. Similarly, the above analysis shows
that the debt/capital ratio must be
suboptimal, so equation 16 cannot hold
either. Both statements imply that
infancy is a momentary phenomenon:
the infant firm issues some beginning
stock of shares and bonds and proceeds
immediately into the expansion phase.
33
Kt
β
( )[
KT
=
δ (1 – u) + ρ
(1 – β)δ (1 – u)
]
(1 – eβδ (1–u)(T–t))
+ eβδ (1–u)(T–t),
which increases as ρ falls: with a lower
discount rate, the firm’s optimal Capital
stock n periods before maturity will be a
larger fraction of its mature optimal
capital stock than at the higher discount
rate. During the growth stage, all the
firm’s after-tax income is reinvested; as
its capital stock and hence output rises,
that income increases at a decreasing
rate (for β < 1), so productive capacity
similarly grows at a decreasing rate.
Since with the lower discount rate the
ultimate mature optimal capital stock
will be larger, during the last n periods,
it will have been growing at a greater
To determine the size of these initial
stocks, equation 16 or 17 must be
integrated backward over time, from
the moment maturity is reached (when
q = – z = (1 – θ)/(1 – c)) through the
expansion phase, until q = – z = 1. The
sizes of the initial stocks will depend
upon the exact paths of q and z, which
in turn depend upon the exact form of
the revenue function F(K,L) and the
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CAPITAL GAINS TAXATION AND NEW FIRM INVESTMENT
agency cost function Ψ. Since any
reasonable function forms will be
nonlinear, no analytic solution for the
size of the initial capital stock can be
obtained.
market power to exploit and earns very
few inframarginal rents. Its rate of capital
accumulation therefore is very slow, and
its length to maturity can be quite long—
perhaps a century or more. Discounting
to the present, any decline in the
eventual qT so many years away has but
a negligible impact on the initial investment decision, and the effects of the
lower discount rate alone dominate.
However, it may be reasonably questioned whether firms with so little market
power, that would as corporations fail to
pay dividends for so long, would ever be
formed as corporations in the first place
in the face of the dividend trap.
Notice however that a reduction in the
capital gains tax rate reduces the value
of q at maturity, without affecting its
initial value at formation. A lower capital
gains tax increases the impact of the
dividend tax, “deepening” the equity
trap. Therefore, unless the tax cut
.
increases q, the length of time the firm
spends in the expansion phase will
increase. This implies, ceteris paribus, a
lower initial optimal capital stock, since
it now takes longer to grow to its
mature size; for example, in equation
33, Kt falls as T, the date at which
maturity is reached, increases. The
question then is, will this longer growth
to maturity, decreasing the initial capital
stock, be large enough to offset both
the flatter relative growth profile and
the higher ultimate capital stock at
maturity, which both suggest a larger
initial K0.
Figure 1 illustrates the results when β is
reasonably large.22 In the New View
model, firms acquire an initial capital
stock in infancy, expand by investing
their cash flow during the growth
phase, and maintain some steady-state
capital stock in maturity. Holding
constant the maturity date, the capital
gains tax cut increases the firm’s desired
capital at maturity and throughout the
growth phase; since that growth phase
is longer, however, the optimal initial
level of investment is nearly unchanged.
The relative capital stock (K0 /KT), holding
interest rates constant, is as a result
significantly smaller.
The Appendix demonstrates that, in the
all-equity model, with interest rates
fixed, a capital gains tax cut may either
increase or decrease the ratio of new
firm capital to mature firm capital, (K0 /
KT). When β is very small, i.e., when the
firm produces with a nearly (or exactly)
constant returns to scale technology
and faces a nearly horizontal demand
curve, a capital gains tax cut will
increase the initial capital stock relative
to its level at maturity. With a larger β,
the tax cut works in the opposite
direction, reducing (K0/KT).
Interest rates however are unlikely to
remain fixed. The tax cut increases both
new and existing firms’ demand for
capital; unless the supply of capital to
them is perfectly inelastic, the interest
rate must rise. But an increase in the
interest rate raises the firm discount
rate ρ, which as the Appendix shows
will necessarily reduce (K0 /KT). On
balance then, the all-equity New View
model suggests that, unless the corporate sector is made up of nearly perfectly competitive firms, with a very
elastic supply of savings to it, a capital
gains tax cut will direct capital away
These differing results reflect the fact
that, for very small values of β, a lower
qT has a comparatively small impact on
the initial optimization decision. When β
is very small, the firm has almost no
663
National Tax Journal
Vol 51 no. 4 (December 1998) pp. 653-73
NATIONAL TAX JOURNAL VOL. LI NO. 4
FIGURE 1.
The Evolution of the Firm’s Capital Stock
from rather than toward new enterprises.
dividend stream are constant over time.
The market value of a new firm,
immediately after its initial share issues
(which occur at time zero), will be
Similarly, the capital gains tax cut will
reduce the market value of new firms
relative to old firms. In the trapped
equity model, with no share repurchases, the market value of a mature
firm will be
35
∞
1–θ
1–θ
∫ (1 – c ) D dt = (1 – c ) ρ
Vn = e
∞
V =
t
e
– ρt
T
34
m
Dt
– ρt
∫e (
– ρt
The tax cut increases the eventual
dividend payments by both firms equally,
while increasing T, the years to maturity;
hence, V n must fall relative to V m.
1 – θ D dt = 1 – θ Dt
t
1–c
1–c ρ
)
(
)
T
where the second equality assumes that
the steady, state capital stock and hence
It may seem paradoxical that a capital
gains tax cut, which in the first section
664
National Tax Journal
Vol 51 no. 4 (December 1998) pp. 653-73
CAPITAL GAINS TAXATION AND NEW FIRM INVESTMENT
appeared to increase the market value
of new firms relative to old, is now
shown to do just the opposite. Keep in
mind however that, in the initial section,
we examined how the market values a
given stream of dividends and repurchases, concluding that, with a lower
capital gains tax, it would reward capital
growth over immediate dividends. While
the market value of firm shares was
allowed to change in that model, the
actions of those firms whose share
values were changing were held rigidly
constant.
internal finance to maturity, increasing
over time their capital stock, while
decreasing their debt/capital ratios. This
section simulates such firms, both at the
point when they are created and at the
time they reach maturity, before and
after the capital gains tax cut.23
In this section, we have examined how
both old and new firms would optimally
adjust their patterns of capital investment and dividend paying to that lower
tax. Older firms, already mature in size
and generating more revenue than their
investment needs, would expand
investment somewhat with the tax cut,
until the marginal return on their
investments matched the new, lower
discount rate. New firms, on the other
hand, would respond by choosing a
smaller initial investment level, thereby
delaying maturity and the eventual
payment of dividends. By rewarding
growth over repayments, the lower
capital gains tax discourages initial
investment in these new enterprises,
reducing rather than enhancing their
current market value relative to their
mature counterparts.
The values for the inflation rate π and
the real interest rate r are widely used;
the depreciation rate δ is a weighted
average of the depreciation rates
estimated by Hulten and Wycoff (1981).
The tax rates reflect the current top
corporate tax rate (u), the current 36
percent marginal tax rate at $200,000
adjusted gross income (θ ), and a top
capital gains tax rate of 28 percent,
divided by 4 to convert it into its accrual
equivalent (c).24 As a sensitivity test, a
14 percent effective capital gains tax
rate is also simulated.
To simulate the impacts of the tax cut, I
assume the following baseline parameter values:
π = 0.04
r = 0.03
δ = 0.095
u = 0.34
θ = 0.36
c = 0.07
A range of values for β, from 0.1 to 0.5,
were used to simulate the model. This
parameter measures both the firm’s
returns to scale in production and the
firm’s market power in pricing its
product, increasing as both returns to
scale and market power increase. The
range of values could depict a firm with
a constant returns to scale production
technology, facing a demand elasticity
ranging from –10 to –2. This range
should be broad enough to include
nearly all the new and existing firms
observable in less than perfectly
competitive industries. The revenue
function scale parameter A can be
arbitrarily chosen; it was always set so
mature firms would have 100 units of
capital when c = 0.07.
I turn now to numerical simulation, to
determine whether the endogenous
firm financing model leads to a similar
conclusion.
NUMERICAL SIMULATION
The previous three sections have
presented a Trapped Equity model, in
which new firms are created with a
limited amount of capital and a high
debt/capital ratio, to then grow through
665
National Tax Journal
Vol 51 no. 4 (December 1998) pp. 653-73
NATIONAL TAX JOURNAL VOL. LI NO. 4
Table 1 reports the simulation results,
when firms are assumed to be entirely
equity financed. Before the capital gains
tax cut, new firms begin with from 18.6
to 27.7 percent as much capital as
mature firms, depending on the values
of β and c.25 It then takes the firm from
9 to 62 years to reach maturity, with the
greater time lengths associated with the
lower values of both c and β.
new firms. As the previous section
noted, the tax cut has two opposite
impacts on the value of K0: since the tax
cut increases the desired level of capital
at maturity, KT , the optimal initial level of
capital will increase; but, since the tax
cut also increases the length of time until
maturity is reached, T, the optimal initial
level of capital will fall. For small values
of β, the former impact is dominant, but,
as β rises, the latter impact comes to
dominate. In general then, a capital
gains tax cut, while necessarily increasing
investment in mature firms, may in fact
have the opposite impact on new firms.
When the tax is cut to zero, the initial
capital stock as a fraction of its level at
maturity declines, becoming from 15.5
to 21.9 percent of the corresponding
mature capital level. This is a relative
decline of 4.5 percent (13.5 percent at
c = 0.14) when β = 0.1, and of 16.6
percent (32.9 percent at c = 0.14) when
β = 0.5. In every case, investment in
mature firms increases by a greater
absolute amount, and by a greater
relative percent, than investment in new
firms.26 The capital gains tax cut would
shift investment toward mature firms,
not new ventures.
Table 2 simulates the case of a separating equilibrium, in which new firms are
created by “small businessmen,” who
face a higher effective capital gains tax
rate than the “diversifiers” who own
mature firms.27 At, for example, β =
0.167, the small businessman creates the
firm with 20.6 units of capital, allowing
it to grow through retained earning for
the next 32 years, until K = 76.2. The
diversifiers would then presumably
purchase a controlling interest in the
firm, taking it through internal growth to
its mature size of K = 100.
Perhaps, more significantly, at the larger
values of β, the capital gains tax cut
actually reduces the total investment in
TABLE 1
ALL EQUITY MODEL
Capital Gains Tax c = 0.14
Capital Gains Tax c = 0.07
β
K0
KT
K0 /KT
T
0.10
0.17
0.25
0.33
0.50
15.5
20.6
23.1
23.5
21.6
63.5
76.2
83.4
87.3
91.3
0.244
0.271
0.277
0.270
0.231
50
32
21
15
9
Capital Gains Tax c = 0
K0
KT
K0 /KT
T
K0 '
K T’
K0'/KT’
T’
22.1
23.9
23.9
22.8
18.6
100.0
100.0
100.0
100.0
100.0
0.221
0.239
0.239
0.228
0.186
62
39
26
18
10
31.7
28.0
25.1
22.4
16.9
150.3
127.7
117.7
113.0
108.5
0.211
0.219
0.213
0.199
0.155
77
47
30
21
11
TABLE 2
SEPARATING EQUILIBRIUM
Capital Gains Tax c = 0.14/0.07
Capital Gains Tax c = 0
β
K0
KT
K0 /KT
T
K0'
KT’
K0' /KT ’
T’
0.10
0.17
0.25
0.33
0.50
15.5
20.6
23.1
23.5
21.6
100.0
100.0
100.0
100.0
100.0
0.155
0.206
0.231
0.235
0.216
62
39
26
18
10
31.7
28.0
25.1
22.4
16.9
150.3
127.7
117.7
113.0
108.5
0.211
0.219
0.213
0.199
0.155
77
47
30
21
11
666
National Tax Journal
Vol 51 no. 4 (December 1998) pp. 653-73
CAPITAL GAINS TAXATION AND NEW FIRM INVESTMENT
As Table 2 shows, in this separating
equilibrium story, it is possible for the
capital gains tax cut to increase the
relative amount of capital in new firms
—but only for small values of β. At
β = 0.167, for example, the tax cut
increases the small businessman’s initial
investment to K = 28, a 36 percent
increase, but expands the size of the
diversifier-owned mature firm only 28
percent, to 127.7. However, at the three
higher levels of β, the tax cut reduces
the relative size of the initial capital
stock in this separating equilibrium
model, and at the two highest levels of
β, the tax cut reduces the absolute size
of the initial capital stock as well. The
best that proponents of this separating
equilibrium story can claim is that the
capital gains tax cut might disproportionately benefit new firm investment,
and, even then, they could not guaran-
tee that new firm investment would
increase at all.
Table 3 reports the results of simulations
in which firms are both equity and debt
financed. Three sets of agency parameter values were used. Values for γ,
which determined the optimal debt/
capital ratio in the absence of taxation,
range from 0.003 to 0.25 and 0.30; the
first value is used to verify that the
model with very small amounts of debt
gives approximately the same results as
the all-equity model, while the latter
two values more reasonably approximate actual debt/capital ratios. Values
for ν, which determines the size of the
firm’s agency costs, range from 0.1 to
1.0. The larger ν is, the greater the cost
of deviating from the debt/capital ratio
γ. In the first set of simulations, when ν
equals 1, these debt/capital ratios stay
TABLE 3
ENDOGENOUS DEBT
γ = 0.003, ν = 1
Capital Gains Tax c = 0.07
Capital Gains Tax c = 0
β
K0
KT
K0 /KT
λ0
λT
T
K0'
KT’
K0'/KT’
λ 0'
0.10
70.1
0.25
0.33
0.50
22.1
24.6
25.2
24.7
21.9
100.0
100.0
100.0
100.0
100.0
0.221
0.246
0.252
0.248
0.219
0.027
0.040
0.060
0.086
0.165
0.006
0.006
0.006
0.006
0.006
62
39
25
17
9
31.7
28.8
26.5
24.4
20.2
150.1
127.6
117.6
113.0
108.5
0.211
0.226
0.225
0.216
0.186
0.022
0.036
0.058
0.086
0.179
λT’
0.001
0.001
0.001
0.001
0.001
T’
77
46
29
20
10
γ = 0.20, ν = 0.3
Capital Gains Tax c = 0.07
Capital Gains Tax c = 0
β
K0
KT
K0 /KT
λ0
λT
T
K0'
KT’
K0'/KT’
λ 0'
0.10
0.17
0.25
0.33
0.50
23.1
27.0
29.3
30.9
35.2
100.0
100.0
100.0
100.0
100.0
0.231
0.270
0.293
0.309
0.352
0.300
0.354
0.435
0.533
0.795
0.210
0.210
0.210
0.210
0.210
54
33
21
15
8
29.4
29.5
29.6
30.2
34.3
138.5
121.6
113.9
110.3
106.7
0.212
0.243
0.260
0.273
0.322
0.283
0.342
0.432
0.545
0.844
λT’
0.193
0.193
0.193
0.193
0.193
T’
67
39
25
17
10
γ = 0.30, ν = 0.1
Capital Gains Tax c = 0.07
Capital Gains Tax c = 0
β
K0
KT
K0 /KT
λ0
λT
T
K0'
KT’
K0'/KT’
λ 0'
0.10
0.17
0.25
0.33
0.50
32.3
42.0
52.6
61.5
76.8
100.0
100.0
100.0
100.0
100.0
0.323
0.420
0.526
0.615
0.768
0.620
0.767
0.921
1.052
1.302
0.330
0.330
0.330
0.330
0.330
49
31
22
17
12
37.8
43.6
52.7
61.6
77.8
132.8
118.6
112.0
108.9
105.8
0.284
0.367
0.471
0.566
0.735
0.565
0.733
0.911
1.060
1.330
667
λT’
0.279
0.279
0.279
0.279
0.279
T’
62
38
26
20
13
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Vol 51 no. 4 (December 1998) pp. 653-73
NATIONAL TAX JOURNAL VOL. LI NO. 4
within a relatively narrow range, while
the last set of simulations, when ν
equals 0.1, allows firm financial policies
to vary considerably more.28
have impacted both interest rates and
exchange rates, in both cases, partially
offsetting the impact of the tax cut. The
numbers nevertheless support my
central thesis here: that any increased
corporate investment resulting from the
capital gains tax cut will occur primarily
in mature firms, with only a small or
perhaps negative impact on new
startups.
The introduction of debt into the
simulation increases the amount of
investment in new firms relative to
mature firms (K0/KT and K0'/KT’), reduces
the capital growth the tax cut induces in
mature firms (KT’ relative to KT), and
reduces the length of time to maturity
(T ).29 All three effects are small for
γ = 0.003 and increase as γ increases.
Summary
This paper has examined the impact of a
capital gains tax cut on new and
established firms, assuming that new
firms differed from their older counterparts because of the dividend trap. For
all parameter values, the tax cut
increased the mature firms’ desired
capital stock, holding interest rates
constant.
More significantly, as in Table 1, in every
simulation reported in Table 3, the
capital gains tax cut reduces investment
in new firms relative to mature firms (K0 /
KT > K0'/KT’) and, in four cases, reduces
the absolute level of investment in new
firms (K0 > K0'). Hence, the endogenous
financing model delivers the same
message found in the all-equity model:
in a trapped equity model, a capital
gains tax cut would relatively favor
established firms, not new startups.
In nearly every case, however, the tax
cut was more beneficial to mature firms
than to new startups. And indeed, in
many of the cases portrayed, the tax cut
actually resulted in a reduction in new
firm investment. Hence, this paper
contradicts the widely held view that a
capital gains tax cut would be a welltargeted approach for encouraging new
firm capital formation.
The previous simulations were run prior
to the 1997 reduction in the top capital
gains tax rate to 20 percent. Table 4
simulates the impact of that tax cut on
new and established firms, for several of
the previously examined sets of parameter values. Caution should be used in
reading too much into these numbers:
the simulations assume other things
remained constant, whereas the
predicted increase in domestic corporate
demand for investment would likely
Obviously, this paper does not preclude
the possibility that the capital gains tax
cut is nonetheless a desirable policy
change. Clearly, its impacts on the cost
of capital and on firm financial policy
are desirable. But there are a variety of
TABLE 4
REDUCTION IN THE CAPITAL GAINS TAX RATE TO 20 PERCENT
Capital Gains Tax c = 0.07
Capital Gains Tax c = 0.05
β
γ
ν
K0
KT
λ0
λT
T
K0 '
K T’
λ0'
λT ’
T’
%dK0
%dKT
0.17
0.17
0.25
0.25
0.33
0.2
0.3
0.2
0.3
0.2
0.3
0.1
0.3
0.1
0.3
27.0
42.0
29.3
52.6
30.9
100.0
100.0
100.0
100.0
100.0
0.35
0.77
0.44
0.92
0.53
0.21
0.33
0.21
0.33
0.21
39
26
39
26
18
27.7
42.4
29.4
52.6
30.7
105.9
105.0
103.9
103.3
102.9
0.35
0.76
0.43
0.92
0.54
0.20
0.31
0.20
0.31
0.20
47
30
47
30
21
2.5
0.9
0.2
0.0
–0.9
5.9
5.1
3.9
3.3
2.9
668
National Tax Journal
Vol 51 no. 4 (December 1998) pp. 653-73
CAPITAL GAINS TAXATION AND NEW FIRM INVESTMENT
other tax instruments, such as a cut in
the corporate tax rate, the various forms
of tax integration, or a corporate cash
flow tax, that can achieve similar
impacts. Which tax policy provides these
benefits with the fewest negative side
effects is still an open question. This
paper however does cast serious doubt
on the capital gains tax cut’s alleged
advantage over these other policy
options, and will make it more difficult
for its proponents to argue that it
confers a policy advantage that these
other policy options fail to provide.
9
ENDNOTES
10
1
2
3
4
5
6
7
8
Typical of this view is Hauser (1995), who asserts
that “because the [capital gains] tax restricts
capital formation, its burden falls on new business
startups.”
Auerbach (1989) presents such an argument.
This asset market equilibrium only examines the
choice investors face between different saving
instruments; the choice between saving and
consumption is not considered. Therefore, the
asset values that result from this analysis should be
interpreted as values relative to other investment
instruments, such as bonds.
This presentation, for simplicity, treats the
investment options as risk free. Poterba and
Summers (1983) include a relatively simple analysis
of risk in their asset market equilibrium, requiring
that the risk-adjusted return to investors be the
same across all assets. Their results are virtually
identical to those presented here. A more
complete asset market equilibrium would take into
account the covariances between the return
distributions of the various assets. Such a model is
beyond the scope of this paper.
The capital gain earned by existing shareholders
will equal the increase in firm. value net of the
value of new shares issued, (Vt – VNt).
Capital gains are modeled here as being taxed on
accrual. In reality, capital gains are taxed on a
realization basis, and some are never taxed.
However, since some fraction of all gains is
continually being realized and taxed, it is
conventional to consider our capital gains tax on
realizations as approximately equivalent to an
accrual capital gains tax with a substantially lower
tax rate.
See, for example, Sinn (1987) for the mathematical
details.
It can be easily shown that the value of a firm
paying a constant dividend stream and making no
11
12
13
14
15
16
669
share repurchases will be invariant to the ordinary
income tax rate. Intuitively, such a firm’s shares
have a payoff structure identical to an infinitely
lived bond; its value relative to such a bond
therefore will be constant. If the dividend stream
increases over time, the ordinary income tax will
increase the current share value of a firm that will
never repurchase shares; if a constant dividend
firm also repurchases shares, the tax will reduce its
current share value.
Of course, since capital gains are taxed on
realization rather than accrual, for many investors,
there will be no loss in tax deferment. For at least
some investors, however, those who need to
liquidate some of their share holdings, the capital
gains tax creates tax liabilities at the time of sale
that reflect future dividend payments. This impact
is similar to that which a lower rate accrual capital
gains tax would generate and is modeled
accordingly.
An earlier version of this paper incorporated the
rate of inflation into the model as well. To simplify
the exposition, the inflation variable has been
dropped; the simulations in the fifth section,
however, are based upon the model with inflation.
Copies of this section with the inflation variable
are available from the author on request.
See Harris and Raviv (1991) for a survey of the
literature on agency costs. That literature suggests
that increasing the debt/equity ratio will increase
the conflicts of interest between equityholders and
debtholders, including but not limited to
bankruptcy costs, while reducing the conflicts
between management and equityholders. The
resulting optimal debt/equity ratio, even in the
absence of taxation, will be an interior solution.
Kanniainen and Södersten (1994) similarly adopted
a monitoring cost function m(B,K) in their model.
They assume that mK > 0, mB < 0, and mBB > 0,
implying a convex cost function.
See Zodrow (1991) for a discussion of the
“Traditional” and “New” views of dividend
taxation. Sinn (1991b,c) has argued that, even
with share repurchases, many of the features of
the New View continue to hold; Bernheim’s (1991)
analysis of dividends as signals supports this
argument. However, the important New View
feature for this paper, that the initial level of
investment in new firms should differ substantially
from that of mature firms, would disappear if there
were no binding constraint on repurchases at the
margin.
Neither dividends nor share repurchases will occur
when (1 – θ)/(1 – c) > q > 1.
ΨK measures the change in agency cost due to a
change in capital, holding debt constant.
Therefore, since additional capital must be equity
financed, ΨK reflects the marginal agency cost of
equity.
See note 12.
National Tax Journal
Vol 51 no. 4 (December 1998) pp. 653-73
NATIONAL TAX JOURNAL VOL. LI NO. 4
17
18
As Gravelle and Kotlikoff (1989) point out, unless
there are significant economies of large scale
production to exploit, firms are unlikely to form as
corporations in the first place. Similarly, Dixit and
Pindyck (1994) show that, in the presence of risk,
no firms will invest at all for sufficiently small β.
This can be derived from the Cobb–Douglas
function form as follows: Let
R[Q(K,L)] =
[
A
(1 – β)(1 – α)
α
.[αW ] K
]
24
1–α
25
(1–α)(1–β ) α
L .
26
Since the real wage rate will be assumed constant,
including it in the revenue function is innocuous.
Setting the marginal revenue product of labor
equal to the wage rate, and solving for L, gives
L=
[
A
(1 – α)(1 – β )
][α ]
W
α
K (1–β )
27
19
20
21
which, when substituted into the revenue function
and simplifying, gives equation 19.
Mello and Parsons (1992) measured the agency
cost of debt alone, using a contingent claims
model of a firm that faces a randomly fluctuating
market price. Their agency cost function is either
approximately linear (at a low commodity price,
where very little debt is optimal) or almost exactly
quadratic (at a higher commodity price, where a
substantial amount of debt is optimal). My
assumed functional form is consistent with the
latter case. See also note 12.
More generally, the model can allow some share
repurchases, but the total earnings so dispersed
are constrained to some suboptimal level. The
difference between the Traditional and New Views
is not whether dividends are issues and shares
repurchased, since in the United States both clearly
occur. The difference is which form of distribution
is available to the firm at the margin.
From equations 3 and 20, the derivative
ρ
d
ν 2
– λ
dc (1 – u) 2
(
22
23
)
=
28
29
ρ (1 – λ)
anonymous referee for bringing his work to my
attention.
Because capital gains are not taxed until realized,
and because gains held until death are untaxed
altogether, the effective (accrual equivalent) capital
gains tax rate is well below the statutory tax rate
on realizations. Bailey (1969) estimated that when
the statutory rate is 25 percent, the effective tax
rate will be between 5 and 9 percent, depending
on the rate of real gain accruals. Ballard et al.
(1985) use the one-fourth statutory rate as a
reasonable approximation.
Figure 1 depicts the evolution of firm capital from
birth to maturity, for β = 0.25.
At c = 0.07 and β = 0.0617, investment in new
and mature firms retains the same ratio, of 19
percent, before and after the tax cut; for smaller
values of β, the ratio will rise when capital gains
taxes are cut. Such low values of β imply demand
elasticities greater than –16 and lengths to
maturity of 92 years or longer, neither of which
seems to reasonably reflect reality.
Presumably, the small businessmen gain part of the
deferral advantage of capital gains taxation, since
they only pay the tax on realization, but not all of
the advantage, since they are unable to hold a
significant fraction of their gains until death. I am
indebted to an anonymous referee, who suggested
this scenario to me.
Indeed, when ν equals 0.1, the simulated debt/
capital ratio for new firms exceeds one for the
larger values of β. Although these results suggest
that such a low value for ν is unreasonable, they
are reported nonetheless, because they help verify
the robustness of the model’s firm investment
results, even into this untenable range of
parameter values.
As in the all-equity simulations, the values for the
revenue function parameter A were chosen so
mature firms, before the tax cut, would have 100
units of capital.
REFERENCES
(1 – u)(1 – c)
Auerbach, Alan J. “Wealth Maximization and
the Cost of Capital.” Quarterly Journal of
Economics 93 No. 3 (August, 1979): 433–46.
is positive, so dK/dc must be negative.
The figure uses the baseline all-equity parameter
values discussed in the next section, with β equal
to 0.25, and an initial effective capital gains tax
rate of 0.07. It corresponds with the simulation
results reported in the third row of Table 1.
Weichenrieder (1995), focusing on issues of
dividend taxation rather than capital gains,
simulated a trapped equity model similar to the
one presented here. His numerical results are
broadly consistent with mine. I am indebted to an
Auerbach, Alan J. “Capital Gains Taxation and
Tax Reform.” National Tax Journal 42 No. 3
(September, 1989): 391–401.
Bailey, Martin J. “Capital Gains and Income
Taxation.” In The Taxation of Income from
Capital, edited by A. C. Harberger and M. J.
Bailey. Washington, D.C.: The Brookings
Institute, 1969.
670
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Vol 51 no. 4 (December 1998) pp. 653-73
CAPITAL GAINS TAXATION AND NEW FIRM INVESTMENT
Ballard, Charles L., Don Fullerton, John B.
Shoven, and John Whalley.
A General
Equilibrium Model for Tax Policy Evaluation.
Chicago: National Bureau of Economic Research,
1985.
Sinn, Hans-Werner. Capital Income Taxation
and Resource Allocation. Amsterdam: NorthHolland, 1987.
Sinn, Hans-Werner. “The Vanishing Harberger
Triangle.” Journal of Public Economics 45 No. 3
(August, 1991a): 271–300.
Bernheim, B. Douglas.
“Tax Policy and the
Dividend Puzzle.” Rand Journal of Economics 22
No. 4 (Winter, 1991): 455–76.
Sinn, Hans-Werner. “Taxation and the Cost of
Capital: the ‘Old’ View, the ‘New’ View, and
Another View.” In Tax Policy and the Economy
5, edited by David Bradford. Cambridge, MA:
National Bureau of Economic Research, 1991b.
Bradford, David F.
“The Incidence and
Allocation Effects of a Tax on Corporate
Distributions.” Journal of Public Economics 15
No. 1 (February, 1981): 1–22.
Sinn, Hans-Werner. “Share Repurchases, the
‘New’ View, and the Cost of Capital.” Economics Letters 36 No. 2 (June, 1991c): 187–90.
Dixit, Avinash K., and Robert S. Pindyck.
Investment Under Uncertainty. Princeton:
Princeton University Press, 1994.
Stapleton, R. C. “Taxes, the Cost of Capital, and
the Theory of Investment.” Economic Journal 82
(December, 1972): 1273–92.
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“The Incidence and Efficiency Costs of Corporate
Taxation when Corporate and Noncorporate
Firms Produce the Same Good.” Journal of
Political Economy 97 No. 4 (August, 1989): 749–
80.
Weichenrieder, Alfons J.
Besteuerung und
Direktinvestition (Taxation and Foreign Direct
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APPENDIX
Hayashi, Fumio. “Corporate Finance Side of
the Q Theory of Investment.” Journal of Public
Economics 27 No. 3 (August, 1985): 261–80.
For notational convenience, define
Hulten, Charles R., and Frank C. Wycoff.
“The Measurement of Economic Depreciation.”
In Depreciation, Inflation, and the Taxation of
Income from Capital, edited by Charles R.
Hulten. Washington, D.C.: The Brookings
Institute, 1981.
A1
∆ = δ(1 – u).
In the all-equity model, equation 32 can be used to
solve the canonical equation 29 for qt:
Kanniainen, Vesa, and Jan Södersten.
“Costs
of Monitoring and Corporate Taxation.” Journal
of Public Economics 55 No. 2 (October, 1994):
307–21.
A2
King, Mervyn A. “Taxation and the Cost of
Capital.” Review of Economic Studies 41 No. 1
(January, 1974): 21–35.
qt =
Mello, Antonio S., and John E. Parsons.
“Measuring the Agency Cost of Debt.” Journal
of Finance 47 No. 5 (December, 1992): 1887–
1904.
1–β
( ) [
(1 – β) ∆
1 – θ (∆+ρ)(t–T)
e
1–c
(∆ + ρ)eβ∆(t–T) – (β∆ + ρ)
]
β
.
At t = 0, qt equals one, so equation A2 implies
Poterba, James M., and Lawrence H.
Summers. “Dividend Taxes, Corporate
Investment, and ‘Q’.” Journal of Public
Economics 22 No. 2 (November, 1983): 135–67.
A3
Pye, Gordon. “Preferential Tax Treatment of
Capital Gains, Optimal Dividend Policy, and
Capital Budgeting.” Quarterly Journal of
Economics 86 No. 2 (May, 1972): 226–42.
β
(1–β)(∆+ρ)T =
e
671
( ) [
β
1 – θ (1–β)
1–c
(1 – β) ∆
(∆ + ρ)e –β∆T – (β∆ + ρ)
]
.
National Tax Journal
Vol 51 no. 4 (December 1998) pp. 653-73
NATIONAL TAX JOURNAL VOL. LI NO. 4
Also, at t = 0, equation 32 gives the initial capital stock
equation A7 becomes
A4
A9
K0β =
{ [ ( ) ]}
β ∆ + ρ β∆T
A(1 – u)
1–
e
(1 – β)∆
∆+ρ
R
β
( )
–
( ) {
1–θ
1–c
1–β
(∆ + ρ) – (1 – β)∆ R
(β∆ + ρ)
}
(β∆+ρ)
(1–β)∆
=1
which can be rearranged as
an implicit function F(R,c). Its partial derivatives are
A5
A10
–A(1 – u)[β∆ + ρ]
(∆ + ρ)e –β∆T =
β
[(1 – β)∆K 0 – A(1 – u)]
(∆ + ρ)(1 – R)
∂ In F
=
∂R
R[(∆ + ρ) – (1 – β)∆R]
or
which must be positive, since R < 1;
A6
β
( )(∆+ρ)T =
e 1–β
{
(∆ + ρ)[( 1– β)∆K0β – A(1 – u)]
–A(1 – u)[β∆ + ρ]
}
A11
∆+ρ
(1–β)∆
.
∂ In F
∂ρ
Substituting equation A5 into the denominator of A3,
and equation A6 for the left-hand side of A3, gives
=
1
(1 – β)∆
–
A7
β
0
K =
A(1 – u)
1–θ
1–c
β
1–β
( )
[ ] ( )
{
∆+ρ
A(1 – u)[β ∆ + ρ]
(∆ + ρ)[A(1 – u) – (1 – β)∆K0β ]
{[
In 1 +
(1 – β)∆(1 – R)
(1 – β)∆(1 – R)
β∆ + ρ
]
}
∆ + ρ – (1 – β)∆R
and
A12
(β∆+ρ)
}
(1–β)∆
.
∂ In F ρ∂ In F
β
=
–
.
∂c
(1 – c)∂ρ (1 – β)(1 – c)
Using equation 30, both the A(1 – u) terms can be
replaced by (∆ + ρ) K Tβ. Defining R as
Now, equation A11 will have the same sign as the term
in brackets, which can be rewritten as
{ln (1 + m1) – m0}; both m0 and m1 are positive. However,
since (1 + m1) = 1/(1 – m0), that bracketed term is equal
to –{m0 + ln (1 – m0)}. Replacing the logarithm with its
Maclaurin expansion, and simplifying, gives
A8
R = [K0/KT]β,
A13
672
National Tax Journal
Vol 51 no. 4 (December 1998) pp. 653-73
CAPITAL GAINS TAXATION AND NEW FIRM INVESTMENT
This is consistent with equation 33, which showed a
similar result for expanding firms.
A13
∂ In F
∂ρ
=
1
(1 – β)∆
{
m02
2
+
m03
3
+
m04
4
In contrast, the sign of equation A12 is not
unambiguous: for sufficiently small (β/(1 – β)), it is
positive; otherwise, it is negative. Hence, only for
relatively small β (e.g., constant returns to scale
production function, with extremely elastic firm
demand curves) will dR/dc be negative, with a
reduction in the capital gains tax, holding the interest
rate constant, increasing the initial optimal capital
stock relative to its level at maturity.
}
+ ...
which is clearly positive. Hence, by the implicit
function theorem, dR/dρ must be negative, and a
reduction in the discount rate will increase the initial
optimal capital stock relative to its level at maturity.
673