APPENDIX 1: List of Symbols

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
r^ = 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

CRR(t) = cash recovery rate in year t
Vt = gross assets at the end of year t
Dt = accumulated depreciation
V^(t) = estimate of the gross assets at the end of year t
D^(t) = estimate of the accumulated depreciation
E(N) = Estimate of the life-span of the capital investments

a(N,k) = annuity factor for N years at a rate of k
F = capital investment ratio
F^ = estimate of the (constant) capital investment ratio
k^ = OLS estimate of the firm's growth from f(t)

ARR(t) = accountant's rate of return in year t
E(ARR) = average of the accountant's rate of return over a period


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