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SECOND THOUGHTS ON THE ANALYTICAL PROPERTIES OF EARNED ECONOMIC INCOME
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29-08-95 08:02:32
British Accounting Review (1995) 27, 229–239
SECOND THOUGHTS ON THE ANALYTICAL PROPERTIES OF EARNED ECONOMIC INCOME K. V. PEASNELL Lancaster University The present paper amends the two propositions in Peasnell (1995) concerning the fitness of J. R. Grinyer’s ‘earned economic income’ (EEI) model for its declared purpose of evaluating managerial performance in the light of comments in Grinyer (1995). Proposition I now includes the requirement that the profitability index is the same for each depreciable asset in the multi-asset firm in order for EEI to yield the same answers as the net present value (NPV) of the firm itself. Proposition II is now adjusted to reflect the possibility that errors in forecasted benefits can be large in magnitude. The new version distinguishes between random forecast errors and ‘earnings management’. The original result concerning the conditions when EEI will be more or less reliable than re-computed NPV holds as far as random forecast errors are concerned. In the case of management manipulations, the results depend on whether the investment is believed by management to be worthwhile and on whether the forecast biases are sufficient to turn a poor performance into a good one. The paper concludes with a brief reply to certain key points raised by Grinyer concerning my earlier analysis. 1995 Academic Press Limited
John Grinyer’s (1995) response to my examination of the analytical properties of his earned economic income (EEI) model (Peasnell, 1995) has served to clarify a number of important issues. My reply consists of two parts. The two propositions in my article dealing with issues of aggregation and reliability of the EEI model are first amended in the light of Grinyer’s comments. This is followed by brief comments on various points raised by Grinyer concerning my article. THE PROPOSITIONS The most important of my findings concerning the fitness of EEI for its declared purpose as a one-period measure of managerial performance are Thanks are due to the anonymous referee for helpful comments on an earlier version of the paper. Correspondence should be addressed to: K. V. Peasnell, International Centre for Research in Accounting, Management School, Lancaster University, Lancaster LA1 4YX, UK. Received 1 March 1995; revised 15 June 1995; accepted 27 June 1995 0890–8389/95/030229+11 $12.00
1995 Academic Press Limited
230
. .
summed up in two propositions. Proposition I addresses the issues which arise on moving from a single-asset setting to the more realistic one where the firm possesses a number of distinct depreciable assets. I combine below Grinyer’s insights with mine to form a revised version of this proposition. Proposition II deals with the issue of EEI’s sensitivity to the manipulation of forecasts of future benefits compared to that of Net Present Value (NPV). I provide a modified version of this proposition, showing EEI in a slightly more favourable light. EEI provides a method of allocating the historical cost of a depreciable asset to periods in a way designed to ensure that the resultant income measure has the same sign as the NPV of future benefits. Problems arise when the firm owns more than one asset. Grinyer’s approach to the aggregation problem is to allocate depreciation expense to periods by reference to cost savings made possible by reason of ownership, thereby avoiding the need to apportion the firm’s revenues to its constituent assets. Proposition I states that constancy through time of the ratio of aggregate cost savings to revenue is a necessary and sufficient condition for the aggregation problem to disappear. This is incorrect. My analysis shows that constancy of the ratio is certainly a necessary condition. I also show that the requirement is sufficient when the firm comprises identical assets. Grinyer provides the useful additional insight that the profitability index, Z=PV0/C0, must be equal across all projects as well. Z is bound to be the same for identical assets, of course; but Grinyer provides a numerical example which reveals that this identical assets assumption can be relaxed—as long as Z is the same across assets and aggregate cost savings equal the revenue (or cash flows) of the firm as a whole. I demonstrate below that the necessary and sufficient conditions for EEI depreciation computed on an asset-byasset basis to equal the amount obtainable on a global firm basis are even more stringent than those set out in Proposition I in my paper, but less so than those suggested in Grinyer’s numerical example. Suppose a firm holds a portfolio of m depreciable assets each with n years useful life, which together produce revenue of Xt in period t (t=1, . . . , n), yielding a value for the firm of n
] X (1+i)
PV0=
−t
t
.
(1)
t=1
The cost of acquiring the portfolio is the sum of the outlays on the m individual assets: m
]C
C 0=
k=1
.
k0
(2)
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EEI depreciation based on global cash flows is simply the product of the inverse of the firm’s overall profitability index and its revenue: Dt=
AB
1 Xt (t=1, . . . , n). Z
(3)
The benefits used to compute EEI depreciation on an individual asset basis are the cost savings achieved by purchase of the asset in question, Xkt (k= 1, . . . , m; t=1, . . . , n), the present value of which is n
] X (1+i)
PVk0=
−t
kt
(k=1, . . . , m).
(4)
t=1
Depreciation is computed with a single-asset version of (3), Dkt=(1/Zk)Xkt, using the profitability index for each asset, Zk=PVk0/Ck0. Summed across assets, this gives a charge for the year of m
]
m
]
Dkt=
k=1
k=1
AB
1 Xkt (t=1, . . . , n). Zk
(5)
Finally, note the relationship between cost savings and revenue can be expressed in completely general terms as follows: m
] X =c X kt
t
t
(t=1, . . . , n).
(6)
k=1
These definitions and assumptions are enough to be able to conclude that Proposition I should read as follows: Proposition I (amended): In the multi-asset firm, EEI will yield a non-arbitrary measure of performance consistent with the NPV rule if and only if (i) the ratio of cost savings to revenue is constant across all periods (ct=c, !t) and (ii) the profitability index is the same for each depreciable asset (Zk=p, !k). Proof: see Appendix for details. Φ
Proposition II states that EEI will provide a more reliable measure than will updated NPV if and only if the project is believed by management to have a positive NPV. This assertion is based on a comparison of the elasticities of EEIt and NPV0 to a change in forecast benefits s periods hence, Xt+s. This involves computing the ratio of (i) the proportionate change in magnitude in the performance measure in question (EEIt or NPV0, as the case may be) to (ii) an infinitesimally small proportionate change in Xt+s.
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It is conventional practice in economic analysis to measure elasticities by reference to infinitesimal changes. However, accounting measurements are made on a discrete basis in practice. Grinyer is therefore surely right to question its appropriateness here. Indeed, I show below that a term which disappears when changes are infinitesimal is potentially important in a discrete setting. Let DXt+s denote a variation in the forecast of Xt+s, made at time t. The change in NPV0 induced by changing Xt+s by DXt+s is DXt+s(1+i)−(t+s). The discrete elasticity of NPV0 with respect to Xt+s is therefore
A BA
B
DNPV0/NPV0 PV0 Xt+s(1+i)−(t+s) = . DXt+s/Xt+s NPV0 PV0
nts=
(7)
This is identical to the elasticity obtained with infinitesimals; see equation (44) in Peasnell (1995, p. 25). The discrete elasticity of EEIt with respect to Xt+s can be derived as follows. The effect on EEIt of DXt+s stems from its impact on the charge for depreciation: DEEIt=−DDt. Using (3), we can show straightforwardly that DEEIt=−XtC0
A
B
1 1 − , PV0+DPV0 PV0
or equivalently, DEEIt=
A BA
B
XtC0 DXt+s(1+i)−(t+s) . PV0 PV0+DXt+s(1+i)−(t+s)
The discrete elasticity of EEIt with respect to Xt+s, denoted here as Xts, is therefore
A BA
B
DEEIt/EEIt C0 Xt+s(1+i)−(t+s) = . DXt+s/Xt+s NPV0 PV0+DXt+s(1+i)−(t+s)
Xts=
(8)
The connection between the two elasticities can be seen to be of the form
A
Xts=
BA B
PV0 C0 nts. PV0+DXt+s(1+i)−(t+s) PV0
(9)
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The effects of moving from an infinitesimal to a discrete-change setting can be determined by taking limits. Note that the denominator on the righthand side of either (8) or (9) contains a term, DXt+s(1+i)−(t+s), which was not present in my earlier paper. When DXt+s→0, this term disappears, yielding Xts=(C0/PV0)nts=xts, which is the elasticity computed with infinitesimal changes. Unlike with infinitesimals, it is not sufficient in a discrete-change setting to know whether the project has a positive NPV. Information concerning both the sign and the magnitude of the forecast error is also needed to determine whether EEI is more reliable than NPV. The answer depends on the nature and source of forecast errors. Where management’s expectations of future benefits are symmetrically distributed and EEI and NPV are derived from unbiased estimates of these forecast values, the relationship between |Xts| and |nts| depends on the sign of management’s unbiased estimate of NPV. Errors arising from ‘earnings management’ will tend to exhibit systematic patterns related to the sign and magnitude of unbiased NPV, which in turn affects the reliability of EEI relative to NPV. The results can be summed up as follows: Proposition 2 (amended): (i) EEI is more likely to provide a measure of managerial performance less (more) sensitive to random forecast errors than will one based on updated NPV itself if and only if the project is believed by management to have a positive (negative) NPV. (ii) When underlying performance is poor (EEI and NPV both negative), reported EEI will be less sensitive to earnings management than reported NPV if and only if the biases in forecasts are sufficient to change the sign of the performance measures. (iii) When underlying performance is good (positive EEI and NPV), EEI provides opportunities for income smoothing, but the resultant forecasting biases affect EEI less than NPV. Proof: see Appendix for details. Φ
GRINYER’S CONTRIBUTIONS TO THE LITERATURE Is EEI a flawed concept? Grinyer clearly accepts that Proposition I poses obstacles to the acceptance of EEI. Indeed, he provides a numerical example of his own, involving the special case where c=1 and, hence, p=Z, which illustrates the difficulties very clearly. Grinyer’s solution rests on the notion that any surplus of net cash inflows of the firm as a whole over the benefits attributable to the ownership of tangible assets must stem from intangible assets and goodwill. This has led him to divide the EEI income statement into two parts. One part shows operating results by charging cost savings on assets and services against cash inflow, and this he describes as ‘gross returns to investment in goodwill’. The other measures ‘returns to investment in assets’ by charging interest-adjusted historical cost against cost savings attributable to ownership of current and fixed tangible assets. Cost savings will ordinarily be the replacement cost outlays avoided by reason of ownership of the assets in question.
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EEI measured in this way can be thought of as a residual income version of what Edwards & Bell (1961) label ‘realized profit’, with current operating performance calculated by reference to current replacement costs. Previously, Grinyer computed costs of production in an asymmetrical fashion, with the consumption of current assets shown at interest-adjusted historical cost and the depreciation of fixed assets at replacement cost. He has taken up my suggestion (Peasnell, 1995, p. 28) that this inconsistency be eliminated: both are now on a current cost basis. The issue which remains is whether it would be better to go the whole hog and compute total performance in the manner advocated by Edwards & Bell (1961) and Edwards, Kay & Mayer (1987), by measuring returns to investment in terms of realizable (net-of-interest) changes in current costs over the period. Grinyer has moved a long way towards the current cost approach. But it must be assumed he would balk at this final step, since it would entail the abandonment of the realization principle by which he sets such store, and with it any role for the EEI depreciation calculus. The problem which has exercised Grinyer is that of finding a method of allocating costs to periods in a manner which would preserve the primacy of realization and matching without introducing arbitrariness. His costsavings concept is an interesting—albeit controversial (Skinner, 1993; see also Grinyer, 1993)—contribution to the literature in this regard. A useful area for further research would be to consider its application to other matching-based approaches to the measurement of depreciation. The most obvious competitor to EEI is the internal-rate method, whereby cost is allocated to periods in a manner which results in the book return on assets being equal to the internal rate of return obtained by equating costs with benefits. Grinyer’s cost savings could equally well be used as the measure of benefits in the internal-rate method as it is in the EEI one. Grinyer adopts a far more stringent view of revenue recognition than is usual in practice. He takes me to task in this regard for substituting interestadjusted net revenue figures for cash receipts in my generalization of the EEI model. His concern is that this change could result in the cash flow series being replaced by figures having ‘no economic significance at all’. This is clearly a possibility. All I had in mind, however, was putting (interest-adjusted) sales and purchases in place of cash receipts and payments. This change relaxes what seems to me to be an unnecessary constraint Grinyer imposes on the EEI model, one both at odds with practice and likely to diminish the usefulness of the concept as a performance measure. At the technical level, nothing in my mathematical analysis is affected by incorporating revenue accruals into the model. What Grinyer’s comments have made me appreciate is that my development of EEI has greater theoretical and practical significance than I originally thought. It increases the scope of EEI, to the extent that even socalled economic income (which recognizes all gain in the first period) can be treated as a special case. Not only does this allow us to obtain a firmer grasp of the mathematics of EEI, it also provides more practical scope for the
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measurement of income under uncertainty. The move from a certain world to an uncertain one is not an all-or-nothing affair. While realization may continue to serve as the accountant’s working hypothesis as far as most income recognition decisions are concerned, there are many exceptions, the use of the production basis in mining for precious metals, the percentage-of-completion method for long-term contracts, and the marking-to-market of actively traded securities being obvious examples. Uncertainty raises all sorts of problems for accountants. One is the issue of reliability of accounting measurements. Grinyer’s main objection to my treatment of this in Proposition II is in the use I make of NPV as a yardstick for judging EEI. This still seems to me to be a self-evident standard to use to evaluate the sensitivity of EEI to measurement errors, given that the stated purpose is to devise a measure that yields signals consistent with NPV. Indeed, a notable feature of his system is that it is possible to unscramble NPV from EEI disclosures, because NPV0=(EEIt/Dt)C0. An obvious alternative would therefore be to measure performance in terms of NPV, as Rappaport (1986, ch. 8) proposes. Proposition II reveals that the price paid for EEI’s conceptual linkage with NPV is that it exhibits much of the latter’s subjectivity. The revised version of this proposition brings out more clearly than before the situations in which EEI will, and those in which it will not, be more robust than NPV. Whether EEI depreciation is better than conventional historical cost is another question. Another problem which has to be faced in adapting EEI from a certainty setting to an uncertain one is the choice of an appropriate interest rate. Peasnell (1995) is entirely silent on the matter. Grinyer advocates using the risk-free rate, on the ground that to do otherwise would introduce unrealized gains into the financial statements. I adopt the same position in Peasnell (1993) with regard to the capitalization of interest in models where the opportunity cost of equity is not recognized. Nevertheless, it should be pointed out that this rationale sits oddly with EEI or any other model of residual income, since interest enters only as an item of cost. As Anthony (1975) clearly recognizes, in this situation the use of a risk-adjusted rate lowers rather than raises residual income and as such does not accelerate the recognition of gain. And it has the additional advantage of keeping financial reports on the same footing as expectations. Grinyer skates lightly over the connections I draw between EEI and residual income (RI). He is right in one regard: whether interest cost charged against revenues appears in the conventional RI manner, as a separate lineitem in the income statement, or is submerged in depreciation and cost of sales, as with EEI, makes no difference to the bottom-line income number. My reason for focusing on the relationship between EEI and RI is that the former is a new concept, whereas the latter has been around a long time and is currently receiving much attention from accounting researchers (Feltham & Ohlson, 1995; O’Hanlon, 1995; Ohlson, 1995). Moreover, the relationship between EEI and RI appears not to be well understood. For
236
. .
example, Anthony (1983, p. 260, n. 30) explicitly considers the EEI approach of continuing to capitalize interest on depreciating assets and rejects it as not being in conformity with his framework, without apparently realizing that the two approaches can be constrained to give the same bottom line. Moreover, the quotation I give in Peasnell (1995, p. 15) of the principles Anthony advances for the recognition of depreciation would seem to accord exactly with those underpinning the EEI depreciation calculus. Close examination of the properties of EEI yields fresh insights into the relationship between RI and capitalization of interest. EEI requires the adding of interest to all account balances brought forward from the previous period. It therefore follows that the amount of interest capitalized must exactly equal the interest expense figure charged in arriving at RI. In contrast, where the RI concept is grafted on to a current value model, interest capitalization is generally unnecessary, the time-maturity effect being captured in changes in the market values of the assets (Peasnell, 1993). Unrealized holding gains therefore have to be included in income if doublecounting of costs is to be avoided (Archer & Peasnell, 1984). More work clearly needs to be done to develop our understanding of the way the treatment of interest interacts with other aspects of accounting measurement. An attractive feature of John Grinyer’s work on EEI is that it is what Mattessich (1995) calls ‘conditional-normative’ in character: he eschews the traditional normative approach of championing a particular accounting model against all comers in favour of a more limited programme: EEI is proffered as a solution to a particular problem (measurement of managerial performance against an explicit standard). A competitor to EEI in this regard is Kay’s (1993) ‘added value’ concept, which is a current cost-based version of residual income. It could be, of course, that Grinyer has misstated the problem: the elimination of the imperfections of accounting measures might be too costly to remedy; the difficulties such imperfections give rise to are perhaps better resolved by the use of supplementary nonfinancial performance indicators or by the design of incentive-compatible managerial employment contracts. My contribution has been the less radical one of drawing connections with prior work in the literature and to identify key theoretical properties. More research is clearly needed.
APPENDIX Proof of new proposition I Clearly, if (5) yields the same charge for depreciation in every period as (3), there is no aggregation problem in the EEI model. The joint sufficiency and necessity of conditions (i) and (ii) in the proposition for this result to hold can be shown as follows.
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Sufficiency Suppose both conditions (i) (ct=c, !t) and (ii) (Zk=p, !k) are met. Condition (ii) of the proposition implies Zk can be factored out of (5):
A B]
m
m
1 Dkt= p k=1
]
Xkt.
(A.1)
k=1
Substituting (6) into (A.1) and using condition (i) of the proposition yields m
AB c
]D = p kt
k=1
Xt.
(A.2)
Recalling that discounted EEI depreciation charges must add up to original cost (Peasnell, 1995, eq. (12)) and substituting for (1), we obtain from (A.2) n
AB
m
c
] (1+i) ] D = p −t
t=1
kt
k=1
PV0=C0.
(A.3)
It follows immediately from (A.3) that p=cZ, and so (5) must generate the same depreciation charge as (3). Conditions (i) and (ii) are therefore sufficient. Necessity Proof is by contradiction. Assume (3) and (5) yield the same amount of depreciation in every period, as required by the proposition: m
] k=1
A B AB
1 1 Xkt= Xt. Zk Z
(A.4)
Further, suppose the cost savings of all the m assets are constant in amount through time: Xk1=Xk2=. . .=Xkn=Xk, !k, whereas revenue fluctuates to some degree (i.e. Xp≠Xq, for some p≠qv{t=1, . . . , n}). This is sufficient to ensure that condition (i) does not hold. Using (4), the cost savings of the k-th asset can be valued as a perpetuity: PVk0=an,iXk with an,i= [1−(1+i)−n]/i. Substituting this for PVk0 in Zk on the left-hand side of (A.4), cancelling terms and using (2) yields m
A B 1
]D = a kt
k=1
C0.
(A.5)
n,i
Depreciation is therefore the same in every period. On the other hand,
. .
238
depreciation computed at the global level, obtained by rearranging the righthand side of (A.4) as Dt=
A B
Xt C0, PV0
(A.6)
is not constant, since Xt varies through time by hypothesis. Since (A.5) and (A.6) yield different answers in some periods, (A.4) is contradicted, as required. Next, assume condition (i) is met, but (ii) is not. More precisely, suppose Z1=p+d with Zk=p for the remaining k=2, . . . , m assets. The left-hand side of (A.4) can now be expanded as m
] k=1
AB C
D
m
AB
1 1 1 1 − X1t+ Xkt= Xkt. Zk p+d p p k=1
]
(A.7)
However, we have already shown in the proof of sufficiency that the second term on the right-hand side of (A.7) is equal to the right-hand side of (A.4). Since the first term on the right-hand side of (A.7) is non-zero, (A.4) involves a contradiction. Conditions (i) and (ii) are therefore both necessary and sufficient to ensure that depreciation by reference to the cost savings of individual assets will give the same figure for depreciation as would result from treating the firm as a single asset. Φ Proof of new proposition II The necessary and sufficient condition for EEI to be more reliable than revised NPV can be seen from (9) to be |Xts|<|nts| iff DXt+s>−NPV0(1+i)t+s.
(A.8)
To prove part (i) of the proposition, reliability has to be defined in terms of the uncertainties surrounding management’s best estimates of future benefits. These errors are assumed to be drawn from a symmetrical distribution. Since errors of the same amount but different sign are therefore equally probable, part (i) follows directly from (A.8), which ranks Xts and xts according to whether it is likely that realized-NPV has the opposite sign to expected-NPV because Prob(|Xts|<|nts||NPV0>0)>Prob(|Xts|>|nts||NPV0>0). In the case of forecast errors induced by managerial manipulation, reliability has to be defined by comparing the resultant biased forecasts with
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management’s best estimates. Proof of part (ii) of the proposition follows the same lines as that for part (i) and is not repeated here. However, to prove part (iii), it is necessary to consider what rational behaviour would dictate, recognizing that NPV0<0⇔EEIt<0. When NPV0>0, management has little incentive to manipulate NPV, but it might be tempted to ‘smooth’ the pattern of reported EEI over time. Inflating the forecast for period t+s (thereby allocating more of C0 to period t+s) in order to boost EEIt will simply increase the margin by which EEI is more reliable than NPV. Deflating the forecast of Xt+s in order to build a cushion for future periods will reduce this margin but still leave EEI the more reliable of the two measures: it would not be rational smoothing behaviour to violate the bound on DXt+s given in (A.8) since beyond this point re-computed NPV0 (and hence reported EEIt) turns negative. Φ R Anthony, R.N. (1983). Tell It Like It Was: A Conceptual Framework for Financial Accounting, Homewood, Illinois, Irwin. Archer, G.S.H. & Peasnell, K.V. (1984). ‘Debt finance and capital maintenance in current cost accounting’, Abacus, December, pp. 111–124. Edwards, E.O. & Bell, P.W. (1961). The Theory and Measurement of Business Income, Berkeley and Los Angeles, University of California Press. Edwards, J., Kay, J. & Mayer, C. (1987). The Economic Analysis of Accounting Profitability, Oxford, Oxford University Press. Feltham, G. & Ohlson, J. (1995). ‘Valuation and clean surplus accounting for operational and financial activities’, Contemporary Accounting Research, forthcoming. Grinyer, J.R. (1993). ‘The concept and computation of earned economic income: a reply’, Journal of Business Finance and Accounting, September, pp. 747–753. Grinyer, J.R. (1995). ‘Earned economic income—a flawed concept?’, British Accounting Review, September, pp. 211–228. Kay, J. (1993). Foundations of Corporate Success: How Business Strategies Add Value, Oxford, Oxford University Press. Mattessich, R. (1995). ‘Conditional-normative accounting methodology: incorporating value judgments and means–ends relations of an applied science’, Accounting, Organizations, and Society, May, pp. 259–284. O’Hanlon, J. (1995). ‘Return/earnings regressions and residual income: empirical evidence’, Journal of Business Finance and Accounting, January, pp. 53–66. Ohlson, J. (1995). ‘Earnings, book value, and dividends in security valuation’, Contemporary Accounting Research, forthcoming. Peasnell, K.V. (1993). ‘Capitalisation of interest’, British Accounting Review, March, pp. 17–42. Peasnell, K.V. (1995). ‘Analytical properties of earned economic income’, British Accounting Review, March, pp. 5–33. Rappaport, A. (1986). Creating Shareholder Value: The New Standard for Business Performance, New York, The Free Press. Skinner, R.C. (1993). ‘The concept and computation of earned economic income’, Journal of Business Finance and Accounting, September, pp. 737–745.
29-08-95 08:02:32
British Accounting Review (1995) 27, 229–239
SECOND THOUGHTS ON THE ANALYTICAL PROPERTIES OF EARNED ECONOMIC INCOME K. V. PEASNELL Lancaster University The present paper amends the two propositions in Peasnell (1995) concerning the fitness of J. R. Grinyer’s ‘earned economic income’ (EEI) model for its declared purpose of evaluating managerial performance in the light of comments in Grinyer (1995). Proposition I now includes the requirement that the profitability index is the same for each depreciable asset in the multi-asset firm in order for EEI to yield the same answers as the net present value (NPV) of the firm itself. Proposition II is now adjusted to reflect the possibility that errors in forecasted benefits can be large in magnitude. The new version distinguishes between random forecast errors and ‘earnings management’. The original result concerning the conditions when EEI will be more or less reliable than re-computed NPV holds as far as random forecast errors are concerned. In the case of management manipulations, the results depend on whether the investment is believed by management to be worthwhile and on whether the forecast biases are sufficient to turn a poor performance into a good one. The paper concludes with a brief reply to certain key points raised by Grinyer concerning my earlier analysis. 1995 Academic Press Limited
John Grinyer’s (1995) response to my examination of the analytical properties of his earned economic income (EEI) model (Peasnell, 1995) has served to clarify a number of important issues. My reply consists of two parts. The two propositions in my article dealing with issues of aggregation and reliability of the EEI model are first amended in the light of Grinyer’s comments. This is followed by brief comments on various points raised by Grinyer concerning my article. THE PROPOSITIONS The most important of my findings concerning the fitness of EEI for its declared purpose as a one-period measure of managerial performance are Thanks are due to the anonymous referee for helpful comments on an earlier version of the paper. Correspondence should be addressed to: K. V. Peasnell, International Centre for Research in Accounting, Management School, Lancaster University, Lancaster LA1 4YX, UK. Received 1 March 1995; revised 15 June 1995; accepted 27 June 1995 0890–8389/95/030229+11 $12.00
1995 Academic Press Limited
230
. .
summed up in two propositions. Proposition I addresses the issues which arise on moving from a single-asset setting to the more realistic one where the firm possesses a number of distinct depreciable assets. I combine below Grinyer’s insights with mine to form a revised version of this proposition. Proposition II deals with the issue of EEI’s sensitivity to the manipulation of forecasts of future benefits compared to that of Net Present Value (NPV). I provide a modified version of this proposition, showing EEI in a slightly more favourable light. EEI provides a method of allocating the historical cost of a depreciable asset to periods in a way designed to ensure that the resultant income measure has the same sign as the NPV of future benefits. Problems arise when the firm owns more than one asset. Grinyer’s approach to the aggregation problem is to allocate depreciation expense to periods by reference to cost savings made possible by reason of ownership, thereby avoiding the need to apportion the firm’s revenues to its constituent assets. Proposition I states that constancy through time of the ratio of aggregate cost savings to revenue is a necessary and sufficient condition for the aggregation problem to disappear. This is incorrect. My analysis shows that constancy of the ratio is certainly a necessary condition. I also show that the requirement is sufficient when the firm comprises identical assets. Grinyer provides the useful additional insight that the profitability index, Z=PV0/C0, must be equal across all projects as well. Z is bound to be the same for identical assets, of course; but Grinyer provides a numerical example which reveals that this identical assets assumption can be relaxed—as long as Z is the same across assets and aggregate cost savings equal the revenue (or cash flows) of the firm as a whole. I demonstrate below that the necessary and sufficient conditions for EEI depreciation computed on an asset-byasset basis to equal the amount obtainable on a global firm basis are even more stringent than those set out in Proposition I in my paper, but less so than those suggested in Grinyer’s numerical example. Suppose a firm holds a portfolio of m depreciable assets each with n years useful life, which together produce revenue of Xt in period t (t=1, . . . , n), yielding a value for the firm of n
] X (1+i)
PV0=
−t
t
.
(1)
t=1
The cost of acquiring the portfolio is the sum of the outlays on the m individual assets: m
]C
C 0=
k=1
.
k0
(2)
—
231
EEI depreciation based on global cash flows is simply the product of the inverse of the firm’s overall profitability index and its revenue: Dt=
AB
1 Xt (t=1, . . . , n). Z
(3)
The benefits used to compute EEI depreciation on an individual asset basis are the cost savings achieved by purchase of the asset in question, Xkt (k= 1, . . . , m; t=1, . . . , n), the present value of which is n
] X (1+i)
PVk0=
−t
kt
(k=1, . . . , m).
(4)
t=1
Depreciation is computed with a single-asset version of (3), Dkt=(1/Zk)Xkt, using the profitability index for each asset, Zk=PVk0/Ck0. Summed across assets, this gives a charge for the year of m
]
m
]
Dkt=
k=1
k=1
AB
1 Xkt (t=1, . . . , n). Zk
(5)
Finally, note the relationship between cost savings and revenue can be expressed in completely general terms as follows: m
] X =c X kt
t
t
(t=1, . . . , n).
(6)
k=1
These definitions and assumptions are enough to be able to conclude that Proposition I should read as follows: Proposition I (amended): In the multi-asset firm, EEI will yield a non-arbitrary measure of performance consistent with the NPV rule if and only if (i) the ratio of cost savings to revenue is constant across all periods (ct=c, !t) and (ii) the profitability index is the same for each depreciable asset (Zk=p, !k). Proof: see Appendix for details. Φ
Proposition II states that EEI will provide a more reliable measure than will updated NPV if and only if the project is believed by management to have a positive NPV. This assertion is based on a comparison of the elasticities of EEIt and NPV0 to a change in forecast benefits s periods hence, Xt+s. This involves computing the ratio of (i) the proportionate change in magnitude in the performance measure in question (EEIt or NPV0, as the case may be) to (ii) an infinitesimally small proportionate change in Xt+s.
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It is conventional practice in economic analysis to measure elasticities by reference to infinitesimal changes. However, accounting measurements are made on a discrete basis in practice. Grinyer is therefore surely right to question its appropriateness here. Indeed, I show below that a term which disappears when changes are infinitesimal is potentially important in a discrete setting. Let DXt+s denote a variation in the forecast of Xt+s, made at time t. The change in NPV0 induced by changing Xt+s by DXt+s is DXt+s(1+i)−(t+s). The discrete elasticity of NPV0 with respect to Xt+s is therefore
A BA
B
DNPV0/NPV0 PV0 Xt+s(1+i)−(t+s) = . DXt+s/Xt+s NPV0 PV0
nts=
(7)
This is identical to the elasticity obtained with infinitesimals; see equation (44) in Peasnell (1995, p. 25). The discrete elasticity of EEIt with respect to Xt+s can be derived as follows. The effect on EEIt of DXt+s stems from its impact on the charge for depreciation: DEEIt=−DDt. Using (3), we can show straightforwardly that DEEIt=−XtC0
A
B
1 1 − , PV0+DPV0 PV0
or equivalently, DEEIt=
A BA
B
XtC0 DXt+s(1+i)−(t+s) . PV0 PV0+DXt+s(1+i)−(t+s)
The discrete elasticity of EEIt with respect to Xt+s, denoted here as Xts, is therefore
A BA
B
DEEIt/EEIt C0 Xt+s(1+i)−(t+s) = . DXt+s/Xt+s NPV0 PV0+DXt+s(1+i)−(t+s)
Xts=
(8)
The connection between the two elasticities can be seen to be of the form
A
Xts=
BA B
PV0 C0 nts. PV0+DXt+s(1+i)−(t+s) PV0
(9)
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The effects of moving from an infinitesimal to a discrete-change setting can be determined by taking limits. Note that the denominator on the righthand side of either (8) or (9) contains a term, DXt+s(1+i)−(t+s), which was not present in my earlier paper. When DXt+s→0, this term disappears, yielding Xts=(C0/PV0)nts=xts, which is the elasticity computed with infinitesimal changes. Unlike with infinitesimals, it is not sufficient in a discrete-change setting to know whether the project has a positive NPV. Information concerning both the sign and the magnitude of the forecast error is also needed to determine whether EEI is more reliable than NPV. The answer depends on the nature and source of forecast errors. Where management’s expectations of future benefits are symmetrically distributed and EEI and NPV are derived from unbiased estimates of these forecast values, the relationship between |Xts| and |nts| depends on the sign of management’s unbiased estimate of NPV. Errors arising from ‘earnings management’ will tend to exhibit systematic patterns related to the sign and magnitude of unbiased NPV, which in turn affects the reliability of EEI relative to NPV. The results can be summed up as follows: Proposition 2 (amended): (i) EEI is more likely to provide a measure of managerial performance less (more) sensitive to random forecast errors than will one based on updated NPV itself if and only if the project is believed by management to have a positive (negative) NPV. (ii) When underlying performance is poor (EEI and NPV both negative), reported EEI will be less sensitive to earnings management than reported NPV if and only if the biases in forecasts are sufficient to change the sign of the performance measures. (iii) When underlying performance is good (positive EEI and NPV), EEI provides opportunities for income smoothing, but the resultant forecasting biases affect EEI less than NPV. Proof: see Appendix for details. Φ
GRINYER’S CONTRIBUTIONS TO THE LITERATURE Is EEI a flawed concept? Grinyer clearly accepts that Proposition I poses obstacles to the acceptance of EEI. Indeed, he provides a numerical example of his own, involving the special case where c=1 and, hence, p=Z, which illustrates the difficulties very clearly. Grinyer’s solution rests on the notion that any surplus of net cash inflows of the firm as a whole over the benefits attributable to the ownership of tangible assets must stem from intangible assets and goodwill. This has led him to divide the EEI income statement into two parts. One part shows operating results by charging cost savings on assets and services against cash inflow, and this he describes as ‘gross returns to investment in goodwill’. The other measures ‘returns to investment in assets’ by charging interest-adjusted historical cost against cost savings attributable to ownership of current and fixed tangible assets. Cost savings will ordinarily be the replacement cost outlays avoided by reason of ownership of the assets in question.
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EEI measured in this way can be thought of as a residual income version of what Edwards & Bell (1961) label ‘realized profit’, with current operating performance calculated by reference to current replacement costs. Previously, Grinyer computed costs of production in an asymmetrical fashion, with the consumption of current assets shown at interest-adjusted historical cost and the depreciation of fixed assets at replacement cost. He has taken up my suggestion (Peasnell, 1995, p. 28) that this inconsistency be eliminated: both are now on a current cost basis. The issue which remains is whether it would be better to go the whole hog and compute total performance in the manner advocated by Edwards & Bell (1961) and Edwards, Kay & Mayer (1987), by measuring returns to investment in terms of realizable (net-of-interest) changes in current costs over the period. Grinyer has moved a long way towards the current cost approach. But it must be assumed he would balk at this final step, since it would entail the abandonment of the realization principle by which he sets such store, and with it any role for the EEI depreciation calculus. The problem which has exercised Grinyer is that of finding a method of allocating costs to periods in a manner which would preserve the primacy of realization and matching without introducing arbitrariness. His costsavings concept is an interesting—albeit controversial (Skinner, 1993; see also Grinyer, 1993)—contribution to the literature in this regard. A useful area for further research would be to consider its application to other matching-based approaches to the measurement of depreciation. The most obvious competitor to EEI is the internal-rate method, whereby cost is allocated to periods in a manner which results in the book return on assets being equal to the internal rate of return obtained by equating costs with benefits. Grinyer’s cost savings could equally well be used as the measure of benefits in the internal-rate method as it is in the EEI one. Grinyer adopts a far more stringent view of revenue recognition than is usual in practice. He takes me to task in this regard for substituting interestadjusted net revenue figures for cash receipts in my generalization of the EEI model. His concern is that this change could result in the cash flow series being replaced by figures having ‘no economic significance at all’. This is clearly a possibility. All I had in mind, however, was putting (interest-adjusted) sales and purchases in place of cash receipts and payments. This change relaxes what seems to me to be an unnecessary constraint Grinyer imposes on the EEI model, one both at odds with practice and likely to diminish the usefulness of the concept as a performance measure. At the technical level, nothing in my mathematical analysis is affected by incorporating revenue accruals into the model. What Grinyer’s comments have made me appreciate is that my development of EEI has greater theoretical and practical significance than I originally thought. It increases the scope of EEI, to the extent that even socalled economic income (which recognizes all gain in the first period) can be treated as a special case. Not only does this allow us to obtain a firmer grasp of the mathematics of EEI, it also provides more practical scope for the
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measurement of income under uncertainty. The move from a certain world to an uncertain one is not an all-or-nothing affair. While realization may continue to serve as the accountant’s working hypothesis as far as most income recognition decisions are concerned, there are many exceptions, the use of the production basis in mining for precious metals, the percentage-of-completion method for long-term contracts, and the marking-to-market of actively traded securities being obvious examples. Uncertainty raises all sorts of problems for accountants. One is the issue of reliability of accounting measurements. Grinyer’s main objection to my treatment of this in Proposition II is in the use I make of NPV as a yardstick for judging EEI. This still seems to me to be a self-evident standard to use to evaluate the sensitivity of EEI to measurement errors, given that the stated purpose is to devise a measure that yields signals consistent with NPV. Indeed, a notable feature of his system is that it is possible to unscramble NPV from EEI disclosures, because NPV0=(EEIt/Dt)C0. An obvious alternative would therefore be to measure performance in terms of NPV, as Rappaport (1986, ch. 8) proposes. Proposition II reveals that the price paid for EEI’s conceptual linkage with NPV is that it exhibits much of the latter’s subjectivity. The revised version of this proposition brings out more clearly than before the situations in which EEI will, and those in which it will not, be more robust than NPV. Whether EEI depreciation is better than conventional historical cost is another question. Another problem which has to be faced in adapting EEI from a certainty setting to an uncertain one is the choice of an appropriate interest rate. Peasnell (1995) is entirely silent on the matter. Grinyer advocates using the risk-free rate, on the ground that to do otherwise would introduce unrealized gains into the financial statements. I adopt the same position in Peasnell (1993) with regard to the capitalization of interest in models where the opportunity cost of equity is not recognized. Nevertheless, it should be pointed out that this rationale sits oddly with EEI or any other model of residual income, since interest enters only as an item of cost. As Anthony (1975) clearly recognizes, in this situation the use of a risk-adjusted rate lowers rather than raises residual income and as such does not accelerate the recognition of gain. And it has the additional advantage of keeping financial reports on the same footing as expectations. Grinyer skates lightly over the connections I draw between EEI and residual income (RI). He is right in one regard: whether interest cost charged against revenues appears in the conventional RI manner, as a separate lineitem in the income statement, or is submerged in depreciation and cost of sales, as with EEI, makes no difference to the bottom-line income number. My reason for focusing on the relationship between EEI and RI is that the former is a new concept, whereas the latter has been around a long time and is currently receiving much attention from accounting researchers (Feltham & Ohlson, 1995; O’Hanlon, 1995; Ohlson, 1995). Moreover, the relationship between EEI and RI appears not to be well understood. For
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example, Anthony (1983, p. 260, n. 30) explicitly considers the EEI approach of continuing to capitalize interest on depreciating assets and rejects it as not being in conformity with his framework, without apparently realizing that the two approaches can be constrained to give the same bottom line. Moreover, the quotation I give in Peasnell (1995, p. 15) of the principles Anthony advances for the recognition of depreciation would seem to accord exactly with those underpinning the EEI depreciation calculus. Close examination of the properties of EEI yields fresh insights into the relationship between RI and capitalization of interest. EEI requires the adding of interest to all account balances brought forward from the previous period. It therefore follows that the amount of interest capitalized must exactly equal the interest expense figure charged in arriving at RI. In contrast, where the RI concept is grafted on to a current value model, interest capitalization is generally unnecessary, the time-maturity effect being captured in changes in the market values of the assets (Peasnell, 1993). Unrealized holding gains therefore have to be included in income if doublecounting of costs is to be avoided (Archer & Peasnell, 1984). More work clearly needs to be done to develop our understanding of the way the treatment of interest interacts with other aspects of accounting measurement. An attractive feature of John Grinyer’s work on EEI is that it is what Mattessich (1995) calls ‘conditional-normative’ in character: he eschews the traditional normative approach of championing a particular accounting model against all comers in favour of a more limited programme: EEI is proffered as a solution to a particular problem (measurement of managerial performance against an explicit standard). A competitor to EEI in this regard is Kay’s (1993) ‘added value’ concept, which is a current cost-based version of residual income. It could be, of course, that Grinyer has misstated the problem: the elimination of the imperfections of accounting measures might be too costly to remedy; the difficulties such imperfections give rise to are perhaps better resolved by the use of supplementary nonfinancial performance indicators or by the design of incentive-compatible managerial employment contracts. My contribution has been the less radical one of drawing connections with prior work in the literature and to identify key theoretical properties. More research is clearly needed.
APPENDIX Proof of new proposition I Clearly, if (5) yields the same charge for depreciation in every period as (3), there is no aggregation problem in the EEI model. The joint sufficiency and necessity of conditions (i) and (ii) in the proposition for this result to hold can be shown as follows.
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Sufficiency Suppose both conditions (i) (ct=c, !t) and (ii) (Zk=p, !k) are met. Condition (ii) of the proposition implies Zk can be factored out of (5):
A B]
m
m
1 Dkt= p k=1
]
Xkt.
(A.1)
k=1
Substituting (6) into (A.1) and using condition (i) of the proposition yields m
AB c
]D = p kt
k=1
Xt.
(A.2)
Recalling that discounted EEI depreciation charges must add up to original cost (Peasnell, 1995, eq. (12)) and substituting for (1), we obtain from (A.2) n
AB
m
c
] (1+i) ] D = p −t
t=1
kt
k=1
PV0=C0.
(A.3)
It follows immediately from (A.3) that p=cZ, and so (5) must generate the same depreciation charge as (3). Conditions (i) and (ii) are therefore sufficient. Necessity Proof is by contradiction. Assume (3) and (5) yield the same amount of depreciation in every period, as required by the proposition: m
] k=1
A B AB
1 1 Xkt= Xt. Zk Z
(A.4)
Further, suppose the cost savings of all the m assets are constant in amount through time: Xk1=Xk2=. . .=Xkn=Xk, !k, whereas revenue fluctuates to some degree (i.e. Xp≠Xq, for some p≠qv{t=1, . . . , n}). This is sufficient to ensure that condition (i) does not hold. Using (4), the cost savings of the k-th asset can be valued as a perpetuity: PVk0=an,iXk with an,i= [1−(1+i)−n]/i. Substituting this for PVk0 in Zk on the left-hand side of (A.4), cancelling terms and using (2) yields m
A B 1
]D = a kt
k=1
C0.
(A.5)
n,i
Depreciation is therefore the same in every period. On the other hand,
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depreciation computed at the global level, obtained by rearranging the righthand side of (A.4) as Dt=
A B
Xt C0, PV0
(A.6)
is not constant, since Xt varies through time by hypothesis. Since (A.5) and (A.6) yield different answers in some periods, (A.4) is contradicted, as required. Next, assume condition (i) is met, but (ii) is not. More precisely, suppose Z1=p+d with Zk=p for the remaining k=2, . . . , m assets. The left-hand side of (A.4) can now be expanded as m
] k=1
AB C
D
m
AB
1 1 1 1 − X1t+ Xkt= Xkt. Zk p+d p p k=1
]
(A.7)
However, we have already shown in the proof of sufficiency that the second term on the right-hand side of (A.7) is equal to the right-hand side of (A.4). Since the first term on the right-hand side of (A.7) is non-zero, (A.4) involves a contradiction. Conditions (i) and (ii) are therefore both necessary and sufficient to ensure that depreciation by reference to the cost savings of individual assets will give the same figure for depreciation as would result from treating the firm as a single asset. Φ Proof of new proposition II The necessary and sufficient condition for EEI to be more reliable than revised NPV can be seen from (9) to be |Xts|<|nts| iff DXt+s>−NPV0(1+i)t+s.
(A.8)
To prove part (i) of the proposition, reliability has to be defined in terms of the uncertainties surrounding management’s best estimates of future benefits. These errors are assumed to be drawn from a symmetrical distribution. Since errors of the same amount but different sign are therefore equally probable, part (i) follows directly from (A.8), which ranks Xts and xts according to whether it is likely that realized-NPV has the opposite sign to expected-NPV because Prob(|Xts|<|nts||NPV0>0)>Prob(|Xts|>|nts||NPV0>0). In the case of forecast errors induced by managerial manipulation, reliability has to be defined by comparing the resultant biased forecasts with
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management’s best estimates. Proof of part (ii) of the proposition follows the same lines as that for part (i) and is not repeated here. However, to prove part (iii), it is necessary to consider what rational behaviour would dictate, recognizing that NPV0<0⇔EEIt<0. When NPV0>0, management has little incentive to manipulate NPV, but it might be tempted to ‘smooth’ the pattern of reported EEI over time. Inflating the forecast for period t+s (thereby allocating more of C0 to period t+s) in order to boost EEIt will simply increase the margin by which EEI is more reliable than NPV. Deflating the forecast of Xt+s in order to build a cushion for future periods will reduce this margin but still leave EEI the more reliable of the two measures: it would not be rational smoothing behaviour to violate the bound on DXt+s given in (A.8) since beyond this point re-computed NPV0 (and hence reported EEIt) turns negative. Φ R Anthony, R.N. (1983). Tell It Like It Was: A Conceptual Framework for Financial Accounting, Homewood, Illinois, Irwin. Archer, G.S.H. & Peasnell, K.V. (1984). ‘Debt finance and capital maintenance in current cost accounting’, Abacus, December, pp. 111–124. Edwards, E.O. & Bell, P.W. (1961). The Theory and Measurement of Business Income, Berkeley and Los Angeles, University of California Press. Edwards, J., Kay, J. & Mayer, C. (1987). The Economic Analysis of Accounting Profitability, Oxford, Oxford University Press. Feltham, G. & Ohlson, J. (1995). ‘Valuation and clean surplus accounting for operational and financial activities’, Contemporary Accounting Research, forthcoming. Grinyer, J.R. (1993). ‘The concept and computation of earned economic income: a reply’, Journal of Business Finance and Accounting, September, pp. 747–753. Grinyer, J.R. (1995). ‘Earned economic income—a flawed concept?’, British Accounting Review, September, pp. 211–228. Kay, J. (1993). Foundations of Corporate Success: How Business Strategies Add Value, Oxford, Oxford University Press. Mattessich, R. (1995). ‘Conditional-normative accounting methodology: incorporating value judgments and means–ends relations of an applied science’, Accounting, Organizations, and Society, May, pp. 259–284. O’Hanlon, J. (1995). ‘Return/earnings regressions and residual income: empirical evidence’, Journal of Business Finance and Accounting, January, pp. 53–66. Ohlson, J. (1995). ‘Earnings, book value, and dividends in security valuation’, Contemporary Accounting Research, forthcoming. Peasnell, K.V. (1993). ‘Capitalisation of interest’, British Accounting Review, March, pp. 17–42. Peasnell, K.V. (1995). ‘Analytical properties of earned economic income’, British Accounting Review, March, pp. 5–33. Rappaport, A. (1986). Creating Shareholder Value: The New Standard for Business Performance, New York, The Free Press. Skinner, R.C. (1993). ‘The concept and computation of earned economic income’, Journal of Business Finance and Accounting, September, pp. 737–745.