A mystifying problem in value-based management is that residual income does not measure value creation in the period considered, so that either some adjustments are made to residual income itself or compensation plans are devised so as to tie residual income to value creation, in order to align managers’ behaviors to shareholders’ objectives (Ehrbar, 1998; Stewart, 1991; O’Hanlon and Peasnell, 2000; Young and O’Byrne, 2001; Martin et al., 2003). Grinyer (1985, 1987) proposes an index labelledEarned Economic Income, which has the nice property of being aligned with the Net Present Value. However, beside the fact that “the relationship between EEI and RI appears not to be well understood” (Peasnell, 1995, p. 235), his metric is equal in sign to the NPV only if the project’s cash flows are all of the same sign (Martin et al., 2003, Peasnell, 1995, Grinyer, 1995). This section shows that converting Fern´andez’s (2002) Created Shareholder Value into the corresponding lost-capital metric, one obtains a metric that is perfectly aligned with the Net Present Value, irrespective of the sign of the cash flows (i.e. even if some cash flows are opposite in sign).
The Created Shareholder Value (CSV) belongs to the class of standard residual income models. It is computed by pickingat=ECF,wt(x)=Etfor everyt≥1 andi=ke. Reminding the initial conditionw0(x):=a0, the residual income in this model is
CSVt= a0(xt−ke) if t= 1 Et−1(xt−ke) if t >1 (31)
wherext=(Et+at−at−1)/at−1ift=1 (see Fern´andez, 2002, p. 281), xt=keotherwise (this implies CSVt=0 for allt>1 if expectations are met). In order to convert the standard CSV into its lost-capital companion,
the capital chargekeEt−1 must be replaced bykeEt−1so that residual income becomes lost-capital CSVt= a0(xt−ke) if t= 1 ke(Et−1−Et−1) if t >1. (32)
As for thet=1, we have CSV1=a0 E1+a1−a0 a0 −ke = E1+a1 1 +ke −a0(1 +ke) = NPV(1 +ke).
As for t>1, note that the difference (Et−1−Et−1) is exactly the keynesian user cost of eq. (15) in an eq-
uity approach, because Et=P n k=t+1ak(1 +ke)−(k−t) and Et=P n k=t+1ak(1 +ke)−(k−t)+En(1 +ke)−(n−t). Therefore, Et−1−Et−1=En(1 +ke)−(n−t+1). ButEn=a0(1 +ke)n−Pn
k=1ak(1 +ke)n−k=−NPV(1 +ke)n,so that one may write Et−1−Et−1= NPV(1 +ke)t−1
whence
CSVt=ke(Et−1−Et−1) =keNPV(1 +ke)t−1.
As a result, the lost-capital companion of CSV is always aligned in sign with the NPV. Indeed, it measures the increase of Net Present Value period by period:
ke(Et−1−Et−1) = NPV(1 +ke)t−NPV(1 +ke)t−1= ∆ NPV.
Referring to the example of section 7, Table 11 supplies the value of CSV in the two paradigms.17
9
Conclusions
This paper presents a new paradigm of residual income aimed at appraising projects (firms) as well as measuring periodic performance. Originally introduced with the name with the name of Systemic Value Added (Magni, 2000a, 2000b, 2001, 2003), the new paradigm translates the notion of opportunity cost differently from the classical paradigm. The new paradigm takes account of the capital foregone by the investor as well as the foregone return rate. In other words, if the investor invested in the alternative asset he would have, at the beginning of each period, a different capital than the actual one. This capital, which is definitely lost if project is undertaken, would generate income at the opportunity cost of capital. Hence, the paradigm is here relabeled “lost-capital paradigm”. This paper presents five different but equivalent ways of conceptualizing the lost-capital paradigm: (i) the project’s (firm’s) cash-flow stream may be replicated by
17If an entity approach is taken, rather than a proprietary approach, the the lost-capital companion of CSV becomes Drukar-
investing funds at the cost of capital: the lost-capital RI is given by the difference between the alternative incomes; (ii) the dynamic system representing the investors’ wealth manifests a different increase if funds are invested funds at the cost of capital: the lost-capital RI is given by the difference between alternative wealth increases; (iii) alternative depreciation plans are considered: the lost-capital RI is obtained as difference between alternative depreciation charges; (iv) the keynesian notion of user cost (depreciation through use) is retrieved and the lost-capital RI is computed as the periodic variation of the (generalized) user cost (v) the standard RI may be ideally banked to earn a rate of return equal to the cost of capital: the lost-capital RI is calculated by summing the standard RI and the interest earned on the accumulated past standard RIs. The five arguments bear strong relations one another. In particular, user-cost is equal to the discounted value of the arbitrage payoff derived from the replicating portfolio (subsection 3.1) and equal to the accu- mulated past (standard) residual incomes (subsection 3.5). Also, the wealth increase argument is equivalent to the depreciation argument: in this case depreciation is computed on the entire net worth, taking account of the entire net worth derived from reinvestment of the cash flows at the cost of capital (see eq. (8)).
With the aid of the fifth argument, which relates the standard paradigm to the lost-capital paradigm, this paper shows that consistency with the NPV (MVA) is guaranteed in the lost-capital paradigm as well: however, the standard paradigm uses a discount-then-sum procedure, whereas the lost-capital paradigm uses a sum-then-discount mechanism; what differs is the distribution of the NPV across periods. While such a distribution is relevant for the standard paradigm to get the market value, it is not for the lost- capital paradigm: forecasting each (lost-capital) residual income and the corresponding period in which it is generated is unnecessary. Only the total sum of residual incomes is needed. Thus, the aggregation property of the lost-capital paradigm makes the residual income models particularly attractive as opposed to the discounted-cash-flow models and, in addition, offers an improvement with respect to the standard paradigm, given that the latter supplies the correct equity market value (and net terminal value) only if each and every residual income is forecasted for each and every year.
As for value-based management, the lost-capital paradigm tends to amplify results with respect to the standard paradigm, both in positive and negative sense. This and other features are worth investigating in order to ascertain which conditions make the new paradigm more incentive a tool for managers. Evidently, this also depends on the kind of compensation scheme used by the company to reward managers. For example, if the XY compensation plan is used (where bonus =x% RI+y% ∆ RI), the lost-capital paradigm is more incentive for positive-RI companies, because both RI and ∆ RI are greater in the lost-capital paradigm than in the standard one. A further element that deserves a detailed analysis is how residual incomes change when expectations change and/or are not met, with particular concern to relation with value creation.
A particular model that deserves a thorough investigation is the lost-capital companion of Fern´andez’s (2002) Created Shareholder Value. It is shown that the metric obtained from its conversion into the lost- capital paradigm is perfectly aligned in sign with the Net Present Value. In this particular case, residual income does measure value creation and this kind of metric could be fruitfully used for management com-
pensation.
The new paradigm may be an opportunity to search for new theoretical insights in management ac- counting and managerial finance as regards the relations among accounting values, market values, value creation. Also, it adds some irons in the fire of the value-based management debate. This, far from being a problem, should be seen as an opportunity for developing new measures and finding intriguing relations across metrics and across paradigms. It may be of some interest to find out whether the differences in the standard metrics are mirrored by the differences in the corresponding lost-capital metrics, or whether pros and cons of either measure change as the paradigm adopted is changed. It may be the case that the search for a satisfying compensation plan will lead to an index based on multiple metrics, possibly involving the use of both paradigms.
As a final consideration, it is evident that the aggregation property of the lost-capital paradigm establishes a powerful argument for management accounting to play a major role in project and firm valuation, as well as in capital budgeting decision problems. On one side, Ohlson’s breakthrough result says that, under suitable assumptions on the stochastic process of abnormal earnings and withnsufficiently large, thefuture market value is approximated by a function of earnings; on the other side, the lost-capital result says that, under no particular assumption on stochastic processes and whatever the value of n, thecurrent market value is
equal to a function of earnings. These two results are conducive to a reinstatement of fundamental analysis as an important tool for either valuation and capital budgeting purposes.
References
Arnold, G. 2005. Corporate Financial Management. Harlow, UK: Pearson Education.
Arnold, G. and M. Davies (Eds.) (2000). Value-based Management: Context and Application. Chichester, UK: John Wiley & Sons.
Arzac, E. R., L. R. Glosten 2005. A reconsideration of tax shield valuation, European Financial Manage- ment, 11(4), 453–461.
Bodenhorn, D.(1964). A Cash-flow concept of profit.Journal of Finance, 19(1), 16–31, March. Brealey, R. A., S. C. Myers 2000. Principles of Corporate Finance, Irwin McGraw-Hill.
Brief, R. P., R. A. Lawson 1990. The role of the accounting rate of return in financial statement analysis.
The Acc. Rev.Reprinted in R. Brief & K. V. Peasnell (Eds.),Cleans Surplus. A Link Between Accounting and Finance. New York: Garland, 1996.
Brief, R., K. V. Peasnell (Eds.) 1996. Clean Surplus: A Link Between Accounting and Finance. New York and London: Garland Publishing.
Coase, R. H. 1968. The nature of costs. In D. Solomons (ed.), Studies in Cost Analysis, London: Sweet & Maxwell, second edition.
Cooper, I. A., K. G. Nyborg 2006. The value of tax shields IS equal to the present value of tax shields,
Journal of Financial Economics, 81, 215–225.
Copeland, T., T. Koller, J. Murrin 2000. Valuation. Measuring and Managing the Value of Companies. New York: John Wiley & Sons.
Drukarczyk, J. and A. Schueler (2000). Approaches to value-based performance measurement. In G. Arnold & M. Davies (Eds.),Value-based Management: Context and Application. Chichester, UK: John Wiley & Sons
Edwards, E., P. Bell. 1961. The Theory and Measurement of Business Income.Berkeley University of Cali- fornia Press.
Edey, H.C. (1957). Business valuation, goodwill and the super-profit method. Accountancy, Jan- uary/February. Reprinted in W.T. Baxter and S. Davidson (1962) (Eds.),Studies in Accounting Theory. London: Sweet & Maxwell, pp. 201–217.
Ehrbar, A. 1998. Eva: The Real Key to Creating Value. New York: John Wiley & Sons.
Feltham, G. A., J. A. Ohlson 1995. Valuation and clean surplus accounting for operating and financial ac- tivities,Cont. Acc. Res.11, 689–731.
Fern´andez, P. 2002. Valuation Methods and Shareholder Value Creation.Elsevier Science, San Diego, CA. Fern´andez, P. 2005. Reply to “Comment on The value of Tax Shields is NOT equal to the present value of
tax shields”.Quart. Rev. of Ec. and Fin.45(1) 188–192.
Franks, J. R., S. D. Hodges 1984. The meaning of accounting numbers in target setting and performance measurement: implications for managers and regulators. In R. Brief and K. V. Peasnell (Eds.) (1996).
Clean Surplus: A Link Between Accounting and Finance. New York and London: Garland Publishing. Grinblatt, M., S. Titman 2002. Financial Management and Corporate Strategy, second edition. Boston,
MA: Irwin/McGraw-Hill.
Grinyer, J. R. 1985. Earned Economic Income – A theory of matching.Abacus, 21(2), 130–148.
Grinyer, J. R. 1987. A new approach to depreciation.Abacus,23(2), 43–54.
Grinyer, J. R. 1995. Analytical Properties of Earned Economic Income – a response and extension British Acc. Rev., 27,211–228.
Hansen, P. 1972 The Accounting Concept of Profit, second edition. Amsterdam: North-Holland. Kellison, S. G. 1991. The Theory of Interest, second edition. Homewood, IL: Irwin/McGraw-Hill.
Keynes, J. M. 1967. The General Theory of Employment Interest and Money. London: MacMillan. First published 1936.
Lee, T. 1985. Income and Value Measurement. Theory and Practice,third edition. Billing & Sons, Worcester, UK.
Lundholm, R., T. O’Keefe. 2001. Reconciling value estimates from the discounted cash flow model and the residual income model.Contemporary Acc. Res.18(2) 311–335, Summer.
Magni, C. A. 2000a. Tir, Roe e Van: convergenze formali e concettuali in un approccio sistemico [IRR, ROE and NPV: formal and conceptual convergences in a systemic approach].Finanza Marketing e Produzione, 18(4), 31–59, December. Available at SSRN:<http://ssrn.com/abstract=1104597>.
Magni, C. A. 2000b. Department of Political Economy, University of Modena and Reggio Emilia,
<http://merlino.unimo.it/web dep/materiali discussione/0318.pdf>.
Magni, C. A. 2000c. Decomposition of a certain cash flow stream: differential systemic value and net final value,Proceedings of XXIV AMASES Conference(Association for Mathematics Applied to Economic and Social Sciences), Padenghe, September 6-9. Available at SSRN:<http://ssrn.com/abstract=1029244>. Magni, C. A. 2001. Valore aggiunto sistemico: un’alternativa all’EVA quale indice di sovraprofitto periodale
[Systemic Value Added: an alternative to EVA as a residual income model].Budget, 25(1), 63–71. Available in bilingual version at SSRN:<http://ssrn.com/abstract=1103492>.
Magni, C. A. 2003. Decomposition of net final values: Systemic Value Added and residual income,Bulletin of Economic Research 55(2), 149–176.
Magni, C. A. 2004. Modelling excess profit,Economic Modelling, 21, 595–617.
Magni, C. A. 2005. On decomposing net final values: EVA, SVA and shadow project.Theory and Decision.
59, 51–95.
Magni, C. A. 2006. Zelig and the art of measuring excess profit,Frontiers in Finance and Economics, 3(1), 103–129, June.
Martin, J. D., J. W. Petty 2000. Value Based Management. Boston, MA: Harvard Business School Press Martin, J. D., J. W. Petty, S. Rich 2003. An Analysis of EVA and Other Measures of Firm Performance
Myers, S. C. 1974. Interactions of corporate financing and investment decisions - Implications for capital budgeting.J. of Fin.,29(1), 1–25, March.
O’Byrne. S. F., D. S. Young 2006. Incentives and investor expectations. J. of Appl. Corporate Fin. 18(2) 98–105, Spring.
O’Hanlon, J., K. V. Peasnell 2000. Residual income and EVA.Ec. and Fin. Computing, Summer, 53–95. O’Hanlon J., K. V. Peasnell 2002. Residual income and value creation: the ‘missing link’,Rev. of Acc. Stud-
ies,7(2/3), 229–245.
Ohlson, J. A. 1989. Accounting earnings, book values, and dividends: The theory of the clean surplus equa- tion in equity valuation. Unpublished paper, Columbia University. Reprinted in R. Brief & K. V. Peasnell (Eds.),Clean Surplus. A Link Between Accounting and Finance. New York: Garland, 1996.
Ohlson. J. A. 1995. Earnings, book values, and dividends in equity valuation. Contemp. Acc. Res. 11(2) 661–687, Spring.
Palepu, K. G., P. M. Healey, V. L. Bernard (2000). Business Analysis and Valuation Using Financial State- ments. Cincinnati: South-Western College Publishing.
Peasnell, K. V. 1981. On capital budgeting and income measurement.Abacus 17(1) 52–67.
Peasnell, K. V. 1982. Some formal connnections between economic values and yields and accounting num- bers.J. of Bus. Fin. Acc.9(3) 361–381.
Peasnell, K. V. 1995. Second thoughts on the analytical properties of earned economic income.British Acc. Rev.,27, 229–239.
Peccati, L. 1987. DCF e risultati di periodo. Proceedings of the XI AMASES Conference (Association for Mathematics Applied to Economic and Social Sciences), Torino-Aosta, Italy.
Peccati, L. 1990. Multiperiod analysis of a levered portfolio. Decisions in Economics and Finance, 12(1), 157–166. Reprinted in J. Spronk and B. Matarazzo (Eds.) (1992), Modelling for Financial Decisions. Berlin: Springer-Verlag.
Peccati, L. 1991. Valutazione analitica e sintetica di attivit`a finanziarie. Supplement toRivista milanese di economia, 39, Lug-Set, serie quaderni n.21. Milano: Laterza.
Penman, S. H. 1992. Return to fundamentals. J. of Acc. Audit. and Fin. Reprinted in R. Brief and K. V. Peasnell (Eds.) (1996). Clean Surplus: A Link Between Accounting and Finance. New York and London: Garland Publishing.
Preinreich, G. 1936. The fair value and yield of common stock. The Acc. Rev. Reprinted in R. Brief and K. V. Peasnell (Eds.) (1996). Clean Surplus: A Link Between Accounting and Finance. New York and London: Garland Publishing
Preinreich, G. 1938. Annual survey of economic theory: the theory of depreciation.Econometrica6(1), 219– 241, January.
Pressacco, F. and Stucchi, P. 1997. Su un’estensione bidimensionale del teorema di scomposizione di Pec- cati,Decisions in Economics and Finance, 20, 169-185.
Promislow, S. D. 2006. Fundamentals of Actuarial Mathematics. Chichester, UK: John Wiley & Sons. Rappaport, A. 1998. Creating Shareholder Value. New York: The Free Press.
Revsine, L., D. W. Collins, W. B. Johnson 2005. Financial Reporting and Analysis, third edition. Upper Saddle River, NJ: Pearson Prentice Hall.
Ruback, R. S. 2002. Capital Cash Flows: a simple approach to valuing cash flows. Fin. Manag., Summer, 85–103.
Scott, A. D. 1953. Note on user cost.Ec. J., 63, 368-384, June.
Solomons, D. 1965. Divisional Performance: Measurement and Control. Homewood, IL: Richard D. Irwin. Stewart, G. B. 1991. The Quest for Value: the EVAT M
Management Guide. HarperCollins Publishers Inc. Tham, J., I. V´elez-Pareja 2001. The correct discount rate for the tax shield: the N-period case, Working
paper, Available at SSRN:<http://ssrn.com/abstract=267962>.
V´elez-Pareja, I., J. Tham 2003. Do the RIM (Residual Income Model), EVA and DCF (Discounted Cash Flow) really match?.Working Paper n. 25,<http://ssrn.com/abstract=379740>.
Weingartner, H. M. 1966. The generalized rate of return. Journal of Financial and Quantitative Analysis
1(3), 1–29, September.
Werner, F. and Sotskov, Y.N. 2006. Mathematics of economics and business. New York: Routledge. Young, S. D., S. F. O’Byrne 2001. EVA and Value-Based Management. McGraw-Hill.
Table 1. The five arguments
cash-flow replicated
return from project
z }| { xwt−1(x) lost return z }| { iwt−1(i) wealth increases wealth increase z }| { Wt(x, i)−Wt−1(x, i)
lost wealth increase
z }| { Wt(i)−Wt−1(i) Lost-capital depreciation charges asset’s depreciation z }| { Dept(x) lost depreciation z }| { Dept(i) residual income user cost user cost int−1 z }| { [wt−1(i)−wt−1(x)] user cost int z }| { [wt(i)−wt(x)]. standard RI capitalized standard RI z }| { RISt foregotten return z }| { i t−1 X k=1 RISk(1 +i) t−1−k
Table 2. EVA and EBO variables in the two paradigms
x i wt(x) wt(i) =⇒ capital charge
⇓ ⇓ ⇓ ⇓ ⇓
Standard Paradigm
EVA RONA WACC Vbv =⇒ WACC·Vbv
EBO ROE ke Ebv =⇒ ke·Ebv
Lost-capital Paradigm
EVA RONA WACC Vbv V
=⇒ WACC·V
Table 3. Input data
Investment 13 800 Depreciation rate 20%
Gross Fixed Assets 12 000 Corporate tax rate 33%
WCR 1 800 Required return on assets 12%
Sales 10 000 Debt rate 7%
Cost of Sales 3 670 Required return on debt (kD) 7% Gen. & Admin. Expenses 1 600
Table 4. Balance Sheet, Income Statement, Cash Flows
time 0 1 2 3 4 5
BALANCE SHEET
Gross fixed assets 12 000 12 000 12 000 12 000 12 000 12 000
−cumulative depreciation 0 −2 400 −4 800 −7 200 −9 600 −12 000
Net fixed assets 12 000 9 600 7 200 4 800 2 400 0
WCR 1 800 1 800 1 800 1 800 1 800 0
NET ASSETS 13 800 11 400 9 000 6 600 4 200 0
Debt 4 000 4 000 4 000 4 000 4 000 0
Equity (book value) 9 800 7 400 5 000 2 600 200 0
NET WORTH & LIABILITIES 13 800 11 400 9 000 6 600 4 200 0
INCOME STATEMENT
Sales 10 000 10 000 10 000 10 000 10 000
Cost of sales 3 670 3 670 3 670 3 670 3 670
Gen. & Adm. expenses 1 600 1 600 1 600 1 600 1 600
Depreciation 2 400 2 400 2 400 2 400 2 400 EBIT 2 330 2 330 2 330 2 330 2 330 Interest 280 280 280 280 280 PBT 2 050 2 050 2 050 2 050 2 050 Taxes 677 677 677 677 677 PAT 1 374 1 374 1 374 1 374 1 374 +Depreciation 2 400 2 400 2 400 2 400 2 400 +∆ Debt 0 0 0 0 −4 000 −∆ WCR 0 0 0 0 1 800 ECF 3 774 3 774 3 774 3 774 1 574 FCF18 3 961 3 961 3 961 3 961 5 761 18FCF=ECF −∆D +kDD·(1−T).
Table 5. Valuation time 0 1 2 3 4 5 kU 12% 12% 12% 12% 12% VU=PV[FCF;kU] 15 300 13 175 10 795 8 129 5 144 0 DVTS=PV[T·kD·D;kD](a) 379 313 242 167 86 0 V=VU+DVTS 15 679 13 488 11 038 8 296 5 230 0 E=VU+DVTS−D 11 679 9 488 7 038 4 296 1 230 0