SAJEMS NS Vol 4 (2001) No 2 286 A Financial Model to Determine the Distortions in Economic Value Added (EVA) Caused by Inflation JUde Villiers Department of Business Management, University of Stellenbosch ABSTRACT This paper presents an algebraic model to study the extent to which inflation distorts Economic Value Added (EVA). The model consists of a theoretical finn in steady state, consisting entirely of projects with the same known internal rate of return. The EVA this finn reports is then calculated, and compared to the true economic profit calculated from the known return of the fInn. The model shows that both conventional EVA and EVA based on the current value of assets are distorted by inflation. The distortion in the latter is more systematic, and this could fonn the basis of an adjusted EVA calculation to provide an estimate actual profitability. 1 .INTRODUCTION Economic value added (EVA) is a new name for an old concept, economic profit. Economic profit is the revenue generated by a finn after the cost of the capital it employs has been taken into account. Stewart (1991) called this economic value added (and abbreviated it to EVA, a tenn subsequently registered as a trademark by the finn Stem Stewart & Co). Stewart fonnalised the calculation of EV A and advocated its wide use in financial decision making. He recommends that managers should aim to maximise EV A instead of maximising profits, and that EVA should be used for "setting goals, evaluating perfonnance, detennining bonuses, communicating with investors, and for capital budgeting and valuations of all sorts" (Stewart 1991: 4). EV A is based on accounting profit. It is well known that the accounting return a firm reports is often a poor proxy for its true return. This discrepancy between accounting and true return is exacerbated by inflation. EV A will be distorted by inflation too. De ViIliers (1997) studied this distortion and found that inflation distorts EV A to such an extent that it cannot be used under inflation to estimate R ep ro du ce d by S ab in et G at ew ay u nd er li ce nc e gr an te d by th e P ub lis he r (d at ed 2 00 9) . 287 SAlEMS NS Vol 4 (2001) No 2 actual profitability. De VilJiers (1997: 289-91) provided a numerical example to show the distortions. The present paper provides the more general algebraic model to derive the relationships between the true return of a firm and the EVA it reports. The basis of the model is the construction of a theoretical firm in steady state, made up entirely of projects with the same known internal rate of return. The return of the firm is known, since it is equal to the internal rate of return of the projects that comprise the firm. The EVA that this firm will report under various circumstances can then be calculated. This is compared to the true economic profit to determine the distortion in reported EVA. The true economic profit is known because the true return of the firm is known. This technique (constructing theoretical firms of known return and calculating the accounting figures the firms will report under various circumstances) was first used by Harcourt (1965) to study the relationship between accounting return and true return. It has since become a standard method used in many studies [see De Villiers (1997) for an overview]. The model to study the distortion in EV A under inflation is presented below in four sections. After the Introduction, the second section specifies the cash flows of the projects comprising the theoretical firm. This includes calculating the annual trading surplus that will give a project a particular internal rate of return. The third section then determines the EVA reported by the theoretical firm. To do this, it calculates the net operating profit after tax that the theoretical firm reports, and the book value of the assets of this firm. These are then used to calculate the EV A that the firm reports, and to compare this to the known true economic profit. The fourth section focuses on EVA based on the current value of assets. It determines the current value of assets and then uses this in the EVA calculation, again comparing to the known true economic profit to determine distortions. The fifth section concludes the paper. The model presented below comprises a theoretical firm consisting of a number of projects. The variables that are used to describe the firm and its projects refer to activity during a year or balance at the end of a year, as applicable. S, for example, refers to sales during a year, and C refers to creditors at the end of a year. It is necessary to distinguish between variables relating to individual projects and variables relating to the firm, and single or double subscripts are used to do this. Double subscripts indicate a project variable; the first subscript relating to the year of the project and the second to the year the project was initiated. S2.3, for example, is the project sales during the second year of a project started in R ep ro du ce d by S ab in et G at ew ay u nd er li ce nc e gr an te d by th e P ub lis he r (d at ed 2 00 9) . SAJEMS NS Vol 4 (2001) No 2 288 year 3, and C4 ,1 the project creditors at the end of the fourth year of a project started in year 1. A single subscript refers to a variable relating to the firm as a whole, Thus, S5 is the total sales by the firm in year 5, and C 1 is the sum of the creditors of the firm at the end of year 1, The variables themselves will be defined as they are introduced. 2 PROJECT CASH FLOWS Each individual project consists of an initial investment in current, depreciable and non-depreciable assets. The project runs for d years in which the annual turnover, expenses, and cost of goods sold stay constant in real terms. In these subsequent years no investment is made in depreciable or non-depreciable assets. Current assets employed increase in nominal terms in line with the nominal increase in turnover, and this requires an annual investment in current assets. At the end of the project the depreciable assets are taken to have zero scrap value. Current assets and non-depreciable assets have wound-up values equal to the initial investment in real terms, In any year n of the project initiated in year k, the annual cash flow (Fn,k) consists of the cash received minus the cash paid out during that year. The cash received consists of payments for goods sold, and is equal to the annual sales (Sn,k) minus sales on credit not yet paid for (debtors added during the year, D ~,k ) plus the payments received from the sales on credit during the previous years (debtors that paid during the year, D :,k ). The cash payments in any year n consists of payments to purchase inventory, cash expenses incurred during the year (Xn,k)' depreciable assets acquired during the year (DA :,k ), non-depreciable assets acquired during the year (NA :,k ), and tax payments made during the year (Tn.k). The payments to purchase inventory are equal to the amount of inventory acquired (I:,.), minus the purchases on credit not yet paid (creditors added during the year, C:.k ) plus payments for inventory previously purchased (creditors paid during the year, C:. k ). The total annual cash flow in any year n of the project initiated in any year k can therefore be expressed as: F.,. =(5 •.• D:k +D:k)-(I:.k Cn~k +C:'k)-Xn,k -DA:k -NA;k -Tn.k (1) The firm is assumed to pay income tax on its accounting profits at a rate of t. Taxable income is calculated according to historical cost conventions, and the R ep ro du ce d by S ab in et G at ew ay u nd er li ce nc e gr an te d by th e P ub lis he r (d at ed 2 00 9) . 289 SAJEMS NS Vol 4 (2001) No 2 tax is assumed to be payable immediately. The model assumes that no capital gains tax applies. In any year n of the project started in year k, the taxable income of the ftrm equals annual sales (S •. t) minus the deductible expenses. Tax deductible expenses consist of the cash expenses (X •. k ), the inventory processed (l:.k ), and the depreciation of depreciable assets (DA~,k)' The tax is payable at a rate t, and therefore: Tn .• = t(Sn,. - X.,. - I:'. DA:.) (2) During any year n of the project the amount of debtors at the end of the year is equal to the debtors at the beginning of the year plus the debtors added during the year minus debtors that paid during the year, so that: D •.• ::;: D._1.k + D:k - D:'k Similarly for creditors and inventory: C ==C +C A -C P n,k If-l~k lI,k lI.k In,k = I._I,. + I:k - I:'. (3) The model assumes that the project is initiated in year 0 and operates for d years until it is terminated in year d. We shall ftrst analyse the cash flows in year 0 of the project, then analyse the cash flows in any of the subsequent years of the project (except the last year), and ftnally analyse the cash flows in the last year of the project. 2.1 First Year of the Project In year 0 of the project (the year in which the project is initiated) no sales take place, no cash expenses are incurred, and no inventory is processed. Therefore: SO,k ::;: XO,k == It.. 0 No debtors, creditors or inventory exist before the project is initiated, and therefore: D_I,k = C_1,k = I_I,k = 0 If these are substituted into equation (3), and the resulting relationships rearranged and substituted into equations (2) and (1), then the cash flow in year o is: Fe,. = -CAe.. DA;'. - NA;'. (4) where CAo; (the current assets at the end of year 0) consist of the debtors plus inventory minus creditors at the end of year O. R ep ro du ce d by S ab in et G at ew ay u nd er li ce nc e gr an te d by th e P ub lis he r (d at ed 2 00 9) . SAJEMS NS Vo14 (2001) No 2 290 2.2 Subsequent Years of the Project We now proceed to analyse the cash flows in the subsequent years of the project (except the last year, which will follow later), In these subsequent years no investment is made in depreciable or non-depreciable assets. For any year j of the project (where O