Modelling the accruals process and assessing unexpected accruals*

Appendix 2: Derivation of Abnormal Accruals Model
If the income of a firm can be shifted between periods, then they can be represented as
t
T
u, t
t, ts
T
u, ts th, t
EC
u, t
s1 h1
CNI CNI m CNI m CNI
where m t1, t2
is a parameter that represents the proportion of underlying income in future periods
embedded in or shifted to period t‟s reported income. The first and second subscripts denote the
period in which the income is recognized and from which the income is borrowed, respectively.
As the maximum that a firm can borrow from the future is what is available to lend, m jt , is
smaller than 1. Zero, negative, and positive mtt , 1 signifies neutral, conservative, and aggressive
accounting distortions in period t respectively.
Adding and deducting the two items
s1 s1
T
T
th , t u, t
t, tsu, t1
m CNI
and m CNI
yields the following:
h1
s1
T T T T
t u, t t, ts u, ts th , t u, t t, ts u, t1 t, ts u, t1
CNI CNI m CNI m CNI mCNImCNI s1 h1 h1 h1
Relating
T T
t, ts u, t1 t, ts u, t1
m CNI m CNI
CNI
u, t i
to
CNI
i1
k
using time-varying growth rates 1 g
ut , 1
equation yields the following
where
T
t u, t th, t u, t1 u, t
CNI CNI m CNI CNI
h1
re-arranging the
T T T s1
t, ts th , t u, t1 t, ts k u, t1
m m CNI m 1 g 1 CNI (26)
k1
h1 h1 s1 k1
CNI m CNI CNI dm CNI gm CNI
u, t t u, t1 u, t t u, t1 t u, t1
T
t t, t h
m m
T T
t t, tsth, t
, dm m m
s1
T s1
t t, ts k
gm m 1g1 s1 k1
s1 h1
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