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Impulso = TABLE 1
The Conventional and Proposed Measurement Systems
= Área sob a curva Conventional Measurement Proposed Measurement
[Wealth W and Income ∆W] [Momentum Ẇ and Impulse ∆Ẇ]
O Impulso em Física tem como unidade de medida o Newton, N, que se (Balance Sheet) (Balance Sheet)
expressa por Kg m/s. Wealth Statement as of 1/1/87 Momentum Statement as of 1/1/87
Cash $150 Sales $125/mo
Importa ter presente na Física as denominadas “Conservation Laws”. As Receivables 300 Cost od Sales -85/mo
interacções podem provocar alterações nos objectos/partículas (“things”).
Todavia, alguns objectos/partículas (“things”) não são alterados pelas inte- Inventories 450 Operating Expenses -10/mo
racções. Diz-se, então, que eles são conservados (“conserved”). As partícu- Fixed Assets 900 Depreciation -5/mo
las de um sistema isolado (“isolated system”) interagem entre si – prova- TOTAL ASSETS $1,800 Interest Expenses -5/mo
velmente de forma intensa -, mas não com o ambiente externo. A Massa, o Payables -400 Income Taxes -8/mo
Momento e a Energia de um sistema isolado são conservados. As Leis da
Conservação (“Conservation Laws”) constituem a base para a solução de Loans -500 NET MOMENTA $12/mo
um novo e poderoso problema estratégico, designadamente, OWNERS’ EQUITY 900
Less: Owners’ Net Contribution 600
Valor Final (“Final Value”) = Valor Inicial (“Inicial Value”) NET WEALTH $300

(Change Sheet)
(Change Sheet)
A conservação do momento (“conservation fo momentum”) num sistema Income Statement for 1987 Impulse Statement for 1987
isolado é uma consequência da Terceira Lei de Newton (“Newton’s Third
Law”) Sales $1.800 New Product Introduction (4/1/87) $5/mo
Cost of Sales -1.200 Its Tax Effect (4/1/87) -2/mo
Operating Expenses -180 New Product Introduction (7/1/87) 10/mo
ANEXO 4 – UM EXEMPLO DE APLICAÇÃO DA “MOMENTUM ACCOUN- Depreciation -60 Operating Staff Addition (7/1/87) -10/mo
TING” À GESTÃO POR OBJECTIVOS COM BASE EM IMPULSOS Interest Expenses -60 Mfg Cost Cutting (10/1/87) 5/mo

Ninguém melhor que Ijiri pode explicar a sua “Momentum Accounting” Income taxes -120 Its Tax Effect (10/1/87) -2/mo
aplicada à Gestão por Objectivos numa empresa, inclusivamente com o NET INCOME $180 NET IMPULSES $6/mo
recurso a uma ilustração. Yuji Ijiri, no artigo intitulado “Momentum Accoun- (Change Sheet) (Change Sheet)
ting and Managerial Goals on Impulses”, publicado na Management Scien- Wealth Statement as of 12/31/87 Momentum Statement as of 12/31/87
ce, Feb 1988, Vol 34, Issue 2, pp 160-66, escreveu (sem tradução): Cash $200 Sales $175/mo
Receivables 360 Cost of Sales -115/mo

…………………….“ Inventories 600 Operating Expenses -20/mo
Fixed Assets 840 Depreciation -5/mo
1. Momentum Accounting TOTAL ASSETS $2.000 Interest Expenses -5/mo
Payables -420 Income Taxes -12/mo
Conventional accounting measures "wealth," positive (assets) or negative
(liabilities). It measures wealth not in isolation as in single-entry bookkee- Loans -500 NET MOMENTA $18/mo
ping but in relation to "income' so that every change in net wealth is explai- OWNERS’ EQUITY $1.080
ned or accounted for by revenue or expense items that are considered to be Less: Owners’ Net Contribution 600
responsible for the change. In this way, wealth W and income ∆W are linked NET WEALTH $480
together under a double-entry framework.
Momentum accounting measures various income momenta, or "momenta"
for short. Momenta are measured as a time rate of change in wea1th, na- In this table, wealth statement and momentum statement are shown as the
mely dW/dt or Ẇ. If wealth measurements are analogous to odometer balance sheet in the respective accounting system, and income statement and
readings, momentum measurements are analogous to speedometer rea- impulse statement are shown as the “change sheet” in the respective accounting
dings. Momentum differs from income in that income is a change in wealth system. The conventional balance sheet is slightly reorganized as wealth statement so that
between two points in time while momentum is a time rate of change in its relationship with other statements are made clearer. Note that in either system the
wealth at a given point in time. Two time points must be specified to define net balance amount at the end les the net balance amount at the beginning agrees
income while one time point is enough to specify momentum. Hence, just with the total in the change sheet (i.e., $480 - $300 = $ 180; $18/mo - $12/mo = $6/
like wealth, momenta can be "inventoried" at any given point in time and mo).
listed in a "balance sheet." WhiIe in conventional ,accounting wealth and income are measured in a monetary unit such as
Momentum accounting measures momenta Ẇ not in isolation as in single- dollars, momenta and impulses are measured in a time-rate of change in the
entry bookkeeping but in relation to "impulses" ∆Ẇ which account for chan- monetary measurement, such as dollars per month. Month is chosen here just as an
ges in net momenta. (The term was borrowed from Newtonian mechanics example; for some managerial uses a different time period such as quarter,
which relates impulse with momentum under the principle of impulse and week or even day may be preferable to month. The choice of the time period is
momentum.) Impulses describe reasons for momentum changes just as merely a matter of expression, just as stating an amount in cents , dollars,
income describes reasons for wealth changes. Hence, the same double- thousands of dollars or millions of dollars does not change the amount. The
entry framework can be applied to both wealth accounting and momentum choice has nothing to do with the frequency of measurements or journal
accounting, as shown in Table 1 which contrasts basic financial statements entries.
from the two systems using a simple example. The two system, wealth and momentum accounting, are not independent but are mathema-
tically related to each other by the derivative-integral relationship. In
particular, momenta integrated over time should equal income during the
period (although some reconciliations may be needed when there are