The revenue from the annual sales of product AS, minus the total annual cost or expense required to produce and sell the product ATE, excluding any annual provision for plant depreciation, is the annual cash income ACI:
ACI = AS – ATE
Net annual cash income ANCI is the annual cash income ACI, minus the annual amount of tax AIT:
ANCI = ACI - AIT (9-2)
Taxable income is (ACI - AD - AA), where AD is the annual writing down allowance and AA is the annual amount of any other allowances.
A distinction is made between the writing-down allowance permissible for the computation of tax due, the actual depreciation in value of an asset, and the book depreciation in value of that asset as shown in the company position statement. There is no necessary connection between these values unless specified by law, although the first two or all three are often assigned the same value in practice. Some governments give cash incentives to encourage companies to build plants in otherwise unattractive areas. Neither AD nor AA involves any expenditure of cash, since they are merely book transactions. The annual amount of tax AIT is given by
AIT = (ACI - AD - AA)t (9-3)
where t is the fractional tax rate. The value of t is determined by the appropriate tax authority and is subject to change. For most developed countries the value of t is about 0.35 or 35 percent. The annual amount of tax AIT included in Eq. (9-2) does not necessarily correspond to the annual cash income ACI in the same year. The tax payments in Eq. (9-2) should be those actually paid in that year. In the United States Un ited Kingdom
In modern methods of profitability assessment, cash flows are more meaningful than profits, which tend to be rather loosely defined. The net annual cash flow after tax is given by
ACF = ANCI - ATC (9-4)
where ATC is the annual expenditure of capital, which is not necessarily zero after the plant has been built. For example, working capital, plant additions, or modifications may be required in future years.
The total annual expense ATE required to produce and sell a product can be written as the sum of the annual general expense AGE and the annual manufacturing cost or expense AME:
ATE = AGE + AME (9-5)
Annual general expense AGE arises from the following items: administration, sales, shipping of product, advertising and marketing, technical service, research and development, and finance.
The terms gross annual profit AGP and net annual profit ANP are commonly used by accountants and misused by others. Normally, both AGP and ANP are calculated before tax is deducted. Gross annual profit AGP is given by
AGP = AS - AME - ABD (9-6)
where ABD is the balance-sheet annual depreciation charge, which is not necessarily the same as AD used in Eq. (9-3) for tax purposes. Net annual profit ANP is simply
ANP = AGP - AGE (9-7)
Equation (9-7) can also be written as
ANP = ACI - ABD (9-8)
Net annual profit after tax ANNP can be written as
ANNP = ANCI - ABD (9-9)
The relationships among the various annual costs given by Eqs. (9-1) through (9-9) are illustrated diagrammatically in Fig. 9-1. The top half of the diagram shows the tools of the accountant; the bottom half, those of the engineer. The net annual cash flow ACF, which excludes any provision for balance-sheet depreciation ABD, is used in two of the
more modern methods of profitability assessment: the net-present value (NPV) method and the discounted-cash-flow-rate-of-return (DCFRR) method. In both methods, depreciation is inherently taken care of by calculations which include capital recovery. Annual general expense AGE can be written as the sum of the fixed and variable general expenses:
AGE = AFGE + AVGE (9-10)
Similarly, annual manufacturing expense AME can be written as the sum of the fixed and variable manufacturing expenses:
AME = AFME + AVME (9-11)
A variable expense is considered to be one which is directly proportional to the rate of production RP or of sales RS as is most appropriate to the case under consideration. Unless the variation in finished product inventory is large when compared with the total production over the period in question, it is usually sufficiently accurate to consider RP and RS to be represented by the same-numerical-value R units of sale or production per year. A fixed expense is then considered to be one which is not directly proportional to R, such as overhead charges. Fixed expenses are not necessarily constant but may be subject to stepwise variation at different levels of production. Some authors consider such steps as included in a semi variable expense, which is less amenable to mathematical analysis than the above division of expenses.
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