i,j,t = auxiliary indexes
g 0
= initial level of capital investments
g t
= capital investments in year t
k = growth rate of the capital investments
T = length of the simulation period
n = length of the observation period (number of years under
observation for the profitability estimation)
A = amplitude of the cycle
C = length of the cycle
f
= technical phase adjustment for the cycle
s
= the standard deviation of the random fluctuation in the
capital expenditures
z = random variable following the (0,1)-normal distribution
S = capital investment shock coefficient
t
= the year of the capital investment shock (
t
=
¥
for no shock in the simulation)
d
=
Kronecker's delta,
dtt
= 1 when t = t, and 0
otherwise
f ti
= absolute contribution (cash-inflow) in year t from
capital investment i years back
bi
= relative contribution from capital investment i years
back
N = life-span of a capital investment project (the same for
all capital investments)
f t = cash inflow in year t
r = true internal rate of the simulated firm
= estimate of the internal rate of return
q = shape parameter for negative binomial distribution
m = location parameter for negative binomial distribution
Pj
= negative binomial distribution
s = scaling factor
pt
= accounting profit in year t
dt
= depreciation in year t
vt
= book value of the firm at the end of year t
wt = market value of the firm at the end of year t
= cash recovery rate in year t
Vt
= gross assets at the end of year t
Dt
= accumulated depreciation
= estimate of the gross assets at the end of year t
= estimate of the accumulated depreciation
E(N) = Estimate of the life-span of the capital investments
= annuity factor for N years at a rate of k
F = capital investment ratio
= estimate of the (constant) capital investment ratio
= OLS estimate of the firm's growth from f(t)
= accountant's rate of return in year t
= average of the accountant's rate of return over a period