Modelling the accruals process and assessing unexpected accruals*

accrued (initiated deferred) proportion of income and the growth in past (forward) income. It can
be seen as an adjustment term for accruals that take more than one period to reverse. They are
zero when (a) there is no growth in past and future income, or (b) no portion of income is
deferred or prepaid in the past and the future, or (c) when T is equal to one, where T is the
number of periods it takes the accruals to reverse.
As in the implications from (5), expression (24) indicates that normal accruals comprise of
accrued and deferred components, with each of them respectively consisting of three parts. The
first part of the accrued (deferred) component of normal accruals captures the interaction
between short-term growth in income and proportions of accrued (deferred) component in
current income. If any of the two factors is zero, then the first part of the accrued (deferred)
component of normal accruals will be zero. The second part is attributed to the relaxation of
credit (payable) policy. With the same level of income, firms can end up with higher magnitudes
of accrued (deferred) components of accruals if a greater proportion of accrued revenue and/or
expenses is recognized. The final part serves as an adjustment term for accruals which take more
than one period to reverse.
Finally, the above expression can be generalized to different categories of accruals. Let AC be a
particular category of accruals, and EC is the income from the associated clean-surplus relation
in Table 1. In our previous derivation AC represents TACC and EC will represent CNI. Likewise,
if AC represents ∆NOA, then EC will represent OI. One can show that for a given AC,
where
a
EC
T ut ,
t ti ut ,
i1
EC
da
ga
,
d
AC a EC EC da ga EC
u, t t u, t u, t1 t t u, t1
T ut ,
t ti ut ,
i1
EC
d EC EC dd gd EC
EC
ECEC ,
dd
T u, t u, ti t ti t
u, t u, ti i1
EC EC
EC
1
T u, ti i1
t t 1
u, tik i1 EC k1 1
gEC
t u, t1 u, t t t u, t1
ECEC ,
T u, ti u, t
t t ti u, ti u, t
i1
EC EC
u, ti 1
EC
1 1
i1 EC
k1
T i
t t
k
, gd u, t i g
EC
, , 1
k u t k u t k
g EC EC
1
EC
(25)
47