In the past decade, economists have be-gun to realize that inflation, even when fully anticipated, constitutes a great deal more than a tax on money balances. The primary reason for inflation's wider impact is the existence of a tax system designed with stable prices in mind. This paper offers a brief summary of the effects of inflation on the tax treatment of the firm, focusing on four important decisions the firm makes: the scale of investment; the method of finance; the durability of assets used in production; and the holding period of these assets. There are a number of interesting and related issues which cannot be covered in a paper of this length. As I will be considering inflation that is both uniform and fully anticipated, questions concerning the behavior of the firm in response to uncertainty about inflation, or to a concommitant change in relative prices, will not arise.

Alan J. Auerbach

English

Research Papers in Economics

NBER WORKING PAPER SERIES
INFLATION AND THE TAX TREATMENT
OF FIRM BEHAVIOR
Alan J. Auerbach
Working Paper No. 547
NATIONAL BUREAU OF ECONOMIC RESEARCH
1050 t4assachusetts Avenue
Cambridge MA 02138
September 1980
The research reported here is part of the NBER's research program
in Taxation and project in Capital Formation. Any opinions
expressed are those of the author and not those of the National
Bureau of Economic Research.NBER Working Paper #547
September, 1980
Inflation and the Tax Treatment of Firm Behavior
ABSTRACT
Because the tax system in the U.S. is not price-level indexed, the tax
treatment of the corporation depends on the inflation rate. These effects of
inflation are particularly complicated because corporate and personal income
are taxed independently, and there are different ways of transferring income
from the corporation to the individual.
This paper analyzes the influence of inflation on the corporation's choice
of asset durability, asset holding period, debt-equity ratio and investment
scale, under a simplified version of the current U.S. tax law.
Alan J. Auerbach
National Bureau of Economic Research
1050 Massachusetts Avenue
Cambridge, Massachusetts
(617) 868-3927In the past decade, economists have begun to realize that inflation, even
when fully anticipated, constitutes a great deal more than a tax on money
balances. The primary reason for inflation's wider impact is the existence
of a tax system designed with stable prices in mind. This paper offers a br~ef
summary of the effects of inflation on the tax treatment of the firm, focusing
on four important decisions the firm makes: the scale of investment, the
method of finance, the durability of assets used in production, and the holding
period of these assets.
There are a number of interesting and related issues which cannot be
covered in a paper of this length. As we will be considering inflation that
is bqth uniform and fully anticipated, 'questions conCerning the behavior of the
firm in response to uncertainty about inflation, or to a concommitant change
in relative prices, will not arise.
I. The Model
We consider a simple model of a corporation which uses a single type of
capital good in producing one type of output.
The firm seeks to maximize the wealth of its shareholders, who discount
after-tax cash flows at rate e and are subject to personal taxes on dividends at
rate 8, and capital gains, at an accrual-equivalent rate c. The firm pays
taxes at rate T on corporate profits, which are calculated by deducting interest
payments and depreciation allowances from gross cash flows. The nominal
interest rate is i, and b is the fraction of capital structure that the firm
chooses to devote to debt.
All capital goods are assumed to have service patterns which decline
exponentially; the rate of decay, 0, is indicative of how durable the asset- 2 -
is. The price, relative to that of output sold concurrently, of a unit of
capital of type a yielding a certain standard level of capital services is
q(a). All prices inflate at rate rr. As the purpose of this paper is to focus
on the specific impact of inflation, we shall consider the simple case in which
depreciation allowances accorded assets would reflect actual economic deprecia-
tion in the absence of inflation, but are based on historic cost. This implies
that the nominal depreciation allowance received by an asset of age t and type
-at o is oe times its original purchase price. We also omit the investment tax
credit in the interest of simplicity.
Firms not only choose the durability of the assets used, but the length
of time, T, that they are held before being sold and replaced. Upon such
resale, firms are taxed at rate Y<T on the difference between sale price and
basis (the nominal value of remaining depreciation deductions).
As shown in the appendix, the firm's optimal behavior may be viewed as a
two-stage process. In the first stage, it chooses the decay rate, 0, the
holding period T, and the debt-value ratio, b, to minimize the "user cost
ll
of capital, which is the shadow rental price of capital goods. In the second
stage, the firm invests until the marginal product of capital goods equals this
minimized cost. For given values of o~ T and b, the user cost is
(1)
where
q(o)(p+a) -rrT e-(P+o)T
c = - [(l-TZ) + (Y-TZ) (l-e ) ( -(P+o)T)]
(l-T) l~e
(2) p bi(l-T) (1-8)+(1-b)e
b(1-8)+(1-b) (l-c) - rr
may be interpreted as the real after-tax cost of funds to the firm and(3) z =
- 3 -
tax deductions and inflation; when b=O, p
is the present value of depreciation allowances accruing to an initial invest-
ment of one dollar which is never resold (discounted at the nominal discount
rate p+TI because allowances are in nominal terms). To get an intuitive sense
of what p represents, note that when b=l, p=i(l-T)-rr, the interest rate net of
e =---rr.
l-c
Equation (1) differs from the standard formula for user cost because it
explicitly accounts for the tax treatment of the disposal of assets by resale.
It reduces to the basic formula when T = 00.
II. The Effects of Inflation
A. Asset Holding Period
In a more general model than that considered here, firms might find it
optimal to sell and replace assets of a certain vintage, rather than use them
until fully exhausted, even in a world without taxes. In the current model,
all assets are identical in productive characteristics, so such behavior could
have no real consequences.
However, the introduction of taxes may cause assets identical in produc-
tive characteristics to differ in another sense. If depreciation allowances
are accelerated, an asset declines in value faster than would be dictated by
its decline in productivity alone. This is because it is now really two
"assets": one that produces capital services, and one that "produces"
depreciation deductions, the second declining in value more rapidly than the
first. However, if the asset is sold, under current u.s. law the depreciation
allowances that remain are not transferred. Rather, the sale price is used- 4 -
as a new basis for depreciation deductions. Thus, if the depreciation schedule
is accelerated, the asset transfer will increase the value of remaining deduc-
tions and generate an increase in the value of the asset. This is countered
by the fact that the seller must pay a tax at rate y on the difference between
sale price and basis (the nominal value of remaining depreciation allowances).
The rate y simply equals L for equipment, but for structures is
actually a weighted average of the ordinary corporate rate and
the lower corporate capital gains rate; the ordinary rate is applied only to
the amount by which the asset's basis falls short of ,that which would have
obtained had straight-line tax depreciation been used. (This practiCe is
technically referred to as the "recapture" of "excess" depreciation, though
such a designation is rather inappropriate.) Imagining a firm selling the
asset to itself, we can see that it must weigh the increased value of depre-
ciation allowances against the tax liability incurred on transfer.
When there is economic depreciation of assets, as we have assumed in our
analysis, such a distortion disappears; basis and sale price would be identical
and turnover would have no real impact on the firm. However, inflation once
again introduces the same divergence caused by accelerated depreciation.
Historic cost depreciation implies that turnover provides a step-up in basis,
generating both an increase in the value of future depreciation deductions and
an immediate tax liability.
This effect is represented by the second term in brackets in the cost of
capital expression in equation (1). This term increases or decreases with T
according to whether the turnover tax y is less than or greater than the present
value of tax deductions. Since, for structures, Y is approximately equal to
L, currently .46, for small values of T, and approximately equal to the cor-
porate capital gains rate, currently .28, for T large (because the fraction of
sale price less basis "recaptured" declines over time), the optimal holding- 5 -
period T, with positive inflation, will be zero, infinite, or somewhere in
> < between according to whether z - 1, z - .28/.46 or 1 > z > .28/.46. The first
condition is never met, and the second requires that 0 < (p~)x(.28/.l8). For a
nominal discount rate of .10, this critical value of 0 is .156, much higher than the
rate of depreciation for any general category of structures. Since y=T for equip·-
ment, an optimal holding period less than infinity never obtains. Thus, for
most assets, inflation will encourage holding assets, despite their inflation-
eroded depreciation allowances, rather than replacing them.
B. Debt-Equity Ratio
As the Modigliani-Miller Theorem shows, the choice of debt-equity ratio is
of no consequence in a taxless world under a variety of circumstances, and debt
dominates equity with a corporate tax but no personal taxes. However, in reality,
holders of debt and equity pay taxes, too, and because of the favorable tax
treatment of capital gains, the personal tax rate on debt income is higher for
any given individual than the tax on equity income. Thus, the choice between
debt and equity depends on the relative magnitudes of the corporate tax rate, T,
the capital gains rate, c, and the personal tax rate, 6. As discussed in an
earlier paper (author, 1979b), the debt-equity choice is knife-edged if all inves-
tors possess the same tax rates, even in the presence of short sale constraints
on individuals. However, with progressive taxes, an interior solution is possi-
ble in which firms are indifferent between debt and equity and individuals are
specialized in clienteles.
To examine the effect of inflation on the debt-equity decision, we rewrite
equation (2) by replacing i and e with the real, after-tax returns to holders of
equity and debt, eN = e-n, and iN = i(1-6')-n, where 6' is the personal tax rate
of those who hold debt, and not necessarily equal to 6. Equation (2) becomes:
(4) -1 1-6 1-6
P = [b(1-6)+(1-b)(1-c)] {[biN(l-T) (1-6,)+(1-b)eN ]+TI[b(1_6,)(6'-T)+(1-b)c]}- 6 -
For given underlying real rates of return eN and iN' inflation influences
the real cost of funds p in three ways, depicted in the term multiplying TI in (4).
First, corporations can deduct at rate T the inflation premium component of the
nominal interest rate; second, bondholders must pay tax at rate e' on the same amount.
Thus, for iN given, debt becomes cheaper to the firm as inflation increases if
T>e', and more expensive if T<e'. Although T is directly observable, e' is not,
because individual tax rates differ; estimates of e' vary considerably. From a
comparison of returns on tax-exempt and taxable long-term debt, Roger Gordon and
Burton Ma1kie1 estimate e' to have been approximately 22.5 percent in 1978. Using
flow of funds data to identify holders of debt and calculate e' directly, Martin
Feldstein and Lawrence Summers arrive at a value of 42 percent for 1977. It is
thus unclear to what extent inflation reduces the effective tax rate on debt, if
at all, though it seems likely that no appreciable additional tax burden is
introduced.
The final influence of inflation on p is through the taxation of nominal
rather than real capital gains. Here, there is no question about the direction
of the effect; for eN given, equity becomes more expensive. Estimates of c, like
those of e', are not very accurate, though c may very well be under 10 percent,
as suggested by Martin Bailey. (Remember that c is the accrual-equivalent of
the tax rate on realizations.) Thus, for given values of eN and iN' the likely
effect of inflation is to make debt a cheaper source of finance, and equity more
expensive, encouraging greater use of the former. Of course, the general equil-
ibrium effect of inflation on b is more complicated, for it must also depend on
the behavior of eN and iN.
C. Choice of Asset Life
Assuming the choice of asset durability to be among values of 0 in the
"normal" range where the optimal holding period T is infinite, the cost of capital- 7 -
for given band 0 may be written more simply as
(5) c = q~~~;~+O) (l-Tz) = q(o) [1~T + 0 + ~:~]
Expression (5) shows that the user cost per dollar of capital consists of three
terms: the gross of tax real firm discount rate, the rate of asset decay, and the
rate of decline due to inflation in the value of the nominally denominated "asset"
representing the present value of the stream of depreciation allowances.
Perhaps a commonly-held belief is that this "inflation tax" on depreciation
allowances weighs more heavily on longer-lived assets which have to wait longer
to collect their depreciation allowances. This view is incorrect (author, 1979a).
For any given value of P, the required internal rate 'of return before taxes on an
asset of type 0 is
(6) \!(0) = c(o) _ 0 =
q(o)
(P+T'ITz) I (1-T)
It is evident that while inflation raises t~is rate for all values of 0, the rate
of change increases monotonically with 0; the size of the inflation tax declines
with asset durability.
It is important to realize that just as the increase in the tax burden on
equity relative to debt does not necessarily imply that inflation will lead to
increased leverage in a full general equilibrium model, the heavier rate of tax
on short-lived assets needn't imply that a smaller value of 0 will result from
inflation. The ultimate answer depends on the behavior of the real after-tax
return p. If p is fixed, there are two offsetting effects which determine the
optimal o. The relatively higher tax rate on shor~-lived assets will favor the
choice of a small value of o. However, the general increase in all tax rates,
with the resulting higher before-tax rate of return, favors the choice of short-
lived assets with large values of o. As has been pointed out by Richard Kopcke,
the total effect on the choice of 0 is ambiguous, as can be seen from considering- 8 -
the effect of ~ on the cost of capital. On the other hand, if p decreases with
the increase in inflation, as Patric Hendershott has suggested, this second effect
favoring short-lived investment is lessened.
D. Investment Scale
The scale of investment depends on the cost of capital. If we hold constant
the underlying rates of return to investors, eN and iN' and the other decision
variables of the firm, b, 0 and T, then the likely effect of inflation, as discussed
by Feldstein and Summers, will be an increase in user cost and a drag on invest-
ment. The effect on p will be ambiguous but small relative to the increase in
the inflation tax on depreciation allowances. For example, for representative
values of the relevant parameters (8=.4, 8'=.3,T=.46, c=.l, T=oo, b=.3, 0=.1,
p=.04 and ~=.06) an increase in the rate of inflation of /::;.~ raises p by .036/::;'~"
while T~Z increases by .16l/::;.~.
However two important qualifications are necessary. First, if the real
after-tax rates of return eN and iN fall as a result of inflation, as some theory
and evidence suggests, p will increase less (or decrease more) and so will user
cost, than has been proposed. Moreover, to the extent that firms can alter their
debt-equity ratio and choice of asset durability, this must also diminish the
increase in user cost. The answer to how inflation affects the scale of investment
thus depends in part on a number of empirical magnitudes about which more informa-
tion should be acquired.- 9 -
Appendix - The Firm's Optimizing Behavior
We assume the firm produces output with the concave production function
F(K), where K is the capital stock on hand. The firm seeks to maximize the
wealth of its owners as represented by the present value of net cash flows, dis-
counted at the equity rate e. As demonstrated in an earlier paper (author, 1979b),
this is equivalent to choosing b to minimize P (as presented in equation (2) in
the text), and then maximizing the present value, calculated with discount rate
P+TI, of flows to the firm before interest payments and debt issues. Letting It
be the physical investment in capital at time t, this present value is:
(AI) v
where x is the present value of depreciation allowances times T plus turnover
tax payments per dollar of investment. If each asset is turned over every T
years, the present value of depreciation deductions it receives per initial
dollar is
(A2) J
T -(P+TI)t~ -otd + -PTJ2T ~(P+TI)(t-T)~ -otd + o e ue t e T e ue t .~.
l_e-(P+TI+o)T
= z (l_e-(P+O)T )
which exceeds z because of the step-up in basis every T years. The present value
of turnover tax payments is
-(p+o)T
(A3) [ -pT -oT(l -TIT) + -2pT -2oT(1 -TIT) + ] ( e ) (l_e-TIT) y e.e -e e e -e ••. = y _ (p+o)T
l-e
Combining (A2) and (A3) yields
(A4) X = (~ )(1- -TIT) (e-(p+o)T )
TZ + TZ Y e _( +o)T
l-e p- 10 -
Insertion of this value of x into (AI) and differentiating v with respect to I
t
yields the requirement that the marginal product of capital F' equals c, as
represented in equation (1) in the text. Differentiation of v with respect to
ac ac o and T yields the conditions that ~ and aT should equal zero.- 11 -
REFERENCES
Alan J. Auerbach, "Inflation and the Choice of Asset Life," J. Po1it. Econ.,
June 1979, 87, 621-638.
_______, "Wealth Maximization and the Cost of Capital," Quart.J. Econ,
August 1979, 93, 434-446.
Martin J. Bailey, "Capital Gains and Income Taxation," in A.C. Harberger and
M.J. Bailey, eds., The Taxation of Income from Capital, Washington
1969, 11-49.
Martin Feldstein and Lawrence Summers, "Inflation and the Taxation of Capital
Income in the Corporate Sector," Nat. Tax J., December 1979, 32, 445-470.
Roger H. Gordon and Burton G. Ma1kie1, "Taxation and Corporation Finance,"
Princeton U. Financial Research Center Memorandum no. 31, Princeton 1980.
Patrie H. Hendershott, "The Decline in Aggregate Share Values: Inflation,
Taxation, Risk and Profitability," paper presented at NBER Conference on
Taxation, November 1979.
Richard W. Kopcke, "Inflation, Corporate Income Taxation, and the Demand for
Capital Assets," J. Po1it. Econ., forthcoming.

Capital Gains and Income Taxation,&quot;

Inflation and the Choice of Asset Life,&quot;

Inflation and the Taxation of Capital Income in the Corporate Sector,&quot; Nat. Tax

Maximization and the Cost of Capital,&quot;

Taxation and Corporation Finance,&quot; Princeton U. Financial Research Center Memorandum no. 31,

The Decline in Aggregate Share Values: Inflation, Taxation, Risk and Profitability,&quot; paper presented at NBER Conference on Taxation,

Inflation and the Tax Treatment of Firm Behavior

Inflation and the Tax Treatment of Firm Behavior

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