The economic effects of EU-reforms in corporate income tax systems

( 1− φτ ) = (1 −φ)
λ + µ
(A.11)
δ f
λ = τ
(A.12)
R + δ
Y
K
f
( 1− τ ) = µ ( r + δ ) − d r − r − c ) − d τR
(A.13)
b (
b
b
b
b
where we used the property that λ and µ are constant on a steady state balanced growth path.
The first-order conditions in (A.11) – (A.13) together determine the optimal investment by
firms. In particular, by substituting (A.11) and (A.12) into (A.13), we get the following
expression for the optimal capital stock: 15
⎡ ⎡ + ⎤ ⎤
= 1 ⎢
* φR
δ f
YK r + δ −τ
⎢ ⎥(
r + δ ) ⎥
(A.14)
1−τ
⎢
⎣ ⎢⎣
R + δ f ⎥⎦
⎥
⎦
r
*
[ r + c − d R ] + (1 − d r
= d τ (A.15)
b b b b b b )
Expression (A.14) denotes the cost of capital, i.e. the marginal productivity of capital that is
required to make up for the cost of finance and depreciation. In the absence of a corporate
income tax, the cost of capital is equal to the financial cost of investment (i.e. the weighted
average of debt and equity) and economic depreciation. To understand the impact of corporate
taxation, we first consider the case of equity-financed investment (i.e. if the marginal debt share
is zero, d b = 0). In that case, (A.14) and (A.15) modify to:
τ ⎡ φR
+ δ f ⎤
YK = r + δ + ⎢1
− ⎥(
r + δ )
(A.16)
1−τ
⎢⎣
R + δ f ⎥⎦
We see that the cost of capital is equal to that in the absence of tax (r + δ), plus a tax term
between square brackets. The tax term is zero if φ = 1. In that case, there is immediate
expensing of investment, which transforms the corporate income tax into an R-based cash-flow
tax. This system is neutral to the cost of capital and, therefore, for investment. Also if the
normal return on equity-financed investment would be deductible from the corporate tax, the
corporate tax would be neutral to the cost of capital and investment. This neutrality property of
the ACE requires that the imputed return on equity equals the nominal discount rate used by the
firm.
If φ < 1, the term between square brackets on the right-hand side of (A.16) is always
positive. Hence, corporate taxes raise the cost of capital financed by equity. A higher cost of
15 We assume no adjustment costs in capital formation so the capital stock will immediately move to its new optimum
66