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where
FI
and
FE
denote financial income and financial expenses, which are classified
as non-operating expenses in Japan.
7
Let
DTD
denote the current balance of tax deductible temporary differences which
result from deferred tax assets and loss carry-forward balances. Accordingly, net
income of the firm,
NI
, and retained earnings,
RE
, are defined as a function of
EBT
and
DTD
as shown in equations (6), (7), and (8).
When the realization of the random variable,
EBT
, is negative, i.e., firm
j
has a
deficit in year
t
, firm
j
does not pay taxes and
DTD
increases as in (6) by the amount
of additional tax loss carry-forward allowances which are valid for the next seven
fiscal years to be expensed against future income.
8
In this case the net income of firm
j
is negative and is equal to
EBT
. By further assuming that firm
j
does not pay any
dividends to its shareholders when her/his net income is negative, we get the
following relations when
EBT
<0.
9
DTD
=
DTD
−
EBT
,
NI
=
EBT
,
RE
=
NI
(6)
j
,
t
j
,
t
−
1
j
,
t
j
,
t
j
,
t
j
,
t
j
,
t
On the other hand, when realization of
EBT
is positive but less than or equal to
DTD
,
firm
j
does not pay taxes and at the same time, the asset balance of deductible
temporary differences is exactly reduced by the amount of
EBT,
*
DTD
=
DTD
−
EBT
,
NI
=
(
−
τ
)
⋅
EBT
,
RE
=
NI
⋅
κ
,
(7)
j
,
t
j
,
t
−
1
j
,
t
j
,
t
c
j
,
t
j
,
t
j
,
t
τ
*
c
where
is the effective corporate tax rate and
κ
is a retention ratio of the firm which
we assume to be constant over time.
Finally, when
EBT
is greater than
DTD
j
,
t
-1
as shown in (8), it becomes a normal
case in which firms pay full corporate tax rates. Then it coincides with the statutory
corporate tax rate when any other investment tax credit cannot be applied to this firm.
*
DTD
=
0
,
NI
=
(
−
τ
)
⋅
EBT
,
RE
=
NI
⋅
κ
(8)
j
,
t
j
,
t
j
j
,
t
j
,
t
j
,
t
Given such a way of computing the evolvement of retained earnings and the balance
of tax deductible temporary differences from realizations of net income before-tax for
each period, we are ready to proceed to discount future net income after-tax in the
next sub-section based on our production functions and evolvement accounting
variables.
3.2
Firm Valuation Equation
We compute fundamental value of firms using the Edwards-Bell-Ohlson formula
(Ohlson, 1995) and plug in inputs from simulated future income series readjusted on an
after-tax basis. The fundamental value is defined in equation (9) where
B
t
is the
7
In this formulation, we abstract from extraordinary gains and expenses for expository
simplicity, but it is included for net income before tax items.
8
This becomes multiple integral equations over many periods
ex ante
to derive firm valuation,
and we resort to a simulation method in this paper.
9
This assumption is only for expository simplicity here, and in the simulation current dividend
payout ratio is used as an input parameter.
