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Accounting in three dimensions: a case for momentum revisited

Eric Melse Strategy Center, Nyenrode Business Universiteit, Breukelen, The Netherlands

Abstract

Purpose – This paper aims to extend an earlier analysis of the profitability of an individual firm operating in the professional services industry from the perspective of the triple-entry framework of the momentum accounting theory of Yuji Ijiri.

Design/methodology/approach – The paper presents a “common-size-format” model of balance-sheet momentum, an approach typical of financial statements’ mathematical analysis.

Findings – Common-size-format momentum ratios offer an alternative measurement of (the change of) business performance. They model stabilizing phenomena that might develop very differently from ratios like return on total assets or return on equity and thus provide important informational signals to the analyst of financial statements. The common-size-format ratio of net wealth momentum herein discussed is proposed as a supplemental measurement for business performance analysis.

Originality/value – The paper discusses a new method for performance measurement and risk analysis.

Keywords Accounting, Accounting theory, Performance measures, Risk analysis

Paper type Research paper

Introduction Melse (2004a) explored what meaningful new information the momentum accounting theory of Yuji Ijiri can disclose in addition to the regularly used performance measures: profit before income tax (PBIT), profit after tax (PAT), return on equity (ROE) and return on total assets (ROTA). His conclusion was that financial accounting ratios should not be calculated from data that are temporally different. Preferably, ratios should either be calculated from data pertaining to a given time-period, say a year, quarter or month, or from data measured at a particular time point. The triple-entry framework of the momentum accounting theory of Yuji Ijiri extends the two dimensions of the financial accounting system with a third dimension to account for the forces that drive the momentum, or rate of change, of the creation of new wealth. Accounts can be identified in this framework by their temporal property which makes it rather easy to calculate unitless and timeless ratios. This paper discusses the same example firm as presented by Melse (2004a) but with the time series extended by four more years. The stability of the profitability of this individual firm is investigated further and how it recovers after a brief period of serious decline in performance during 2002-2003. A new accounting measure for financial statement analysis is proposed: the common-size format of momentum and force ratios. In particular, net wealth momentum is here investigated as a supplemental method for performance measurement and risk analysis.

The current issue and full text archive of this journal is available at

www.emeraldinsight.com/1526-5943.htm

The author is grateful for the constructive comments of the anonymous reviewer. Participants of the European Accounting Association’s 2008 Conference are also gratefully acknowledged for their comments on an earlier version of the paper. Financial assistance was provided by the Nyenrode Research Group (NRG).

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The Journal of Risk Finance Vol. 9 No. 4, 2008 pp. 334-350 q Emerald Group Publishing Limited 1526-5943 DOI 10.1108/15265940810895007

Accounting for disclosure, risk analysis or decision making? Financial statements supposedly depict the current condition of a company completely and accurately (McEnroe and Martens, 2004; Haskins and Sack, 2006). Aside unwittingly made mistakes, technical flaws or fraud, accounting information is by definition “historic” and therefore “reliable” because financial statements are compiled from facts, past facts (ex post facto)[1]. At times we may find in the notes to the financial statements information about the expectations management has for the future (Hutton et al., 2003). Obviously past results cannot offer any guarantee for results in the future, such notes are indications only for better or worse. The framework of triple-entry momentum accounting, or TEMA in short, is seen here as an initiative to innovate financial accounting so that management or the auditor are better facilitated to disclose trends that have future bearings. The objective of the TEMA framework is to add a dynamic perspective to the financial accounting system for the purpose of additional disclosure, analysis and decision making. The TEMA framework explicitly requires attention for the causal links in the business model and administers business economic facts outside the scope of traditional bookkeeping, for example with revenue accounting (Glover and Ijiri, 2002). This is an ambitious effort that, certainly in the eyes of the critics of triple-entry accounting strains the boundary between financial and management accounting (Fraser, 1994; Salvary, 1985; Vaassen, 2002, p. 33; Wagensveld, 1995).

Management by momentum – fasten your seatbelt! Yuji Ijiri proposes a so-called triple-entry framework with three dimensions to account for the income capacity of a firm (Ijiri, 1982, 1984, 1986, 1987, 1988, 1989, 1993). The essential idea is to account for the income capacity of a firm in terms of levels instead of differences. Ijiri seeks to account for the level of growth instead of net wealth as such at any particular point in time. He calls this the momentum at which rate net wealth is accrued. By comparison with car driving, he wants to measure the speed at which the car travels instead of only measuring the distance traveled so far (Ijiri, 1988, p. 160). His car driving metaphor can be extended and deepened to further explain the measurements of the triple-entry framework as well as its managerial use. The two principal meters in any dashboard are the odometer that measures the mileage driven during the cars’ life time and the speedometer. Most if not all dashboards also have an odometer that counts the mileage driven per day and cycles its measurement from 0 to 999 miles or kilometers. While the odometers count the state of the cars mileage, the speedometer reports the rate of change of the car – its speed. The importance of the difference between these two meters becomes very clear when we match them against the balance sheet and the income statement for their explanation of wealth magnitude, composition and its change:

. Odometer continuous – balance sheet, wealth magnitude and composition as of “now.”

. Odometer period – income statement, wealth change explained by its “how.”

. Speedometer – the change of wealth change explained by its “why.”

The fundamental notion we have to grasp is that it is impossible to read from any financial statement the rate of change by which new wealth is created, or the change of any financial variable for that matter[2]. We should compare the user of financial statements with a driver in a car with his or her attention focused solely on the

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revolving number wheels of the odometers. Indeed, it is possible to see wealth increase and conclude that the company is in business, but without any other reference against which we can perceive speed, it is impossible to tell by which speed wealth is increasing[3]. In other words, the financial accounting dashboard is lacking speedometers: a pretty uncomfortable position to be in[4].

However, we cannot stretch the metaphor too far. Neither financial analysts nor investors are the “drivers” of the company, therefore, should we be bothered with the missing speedometer on the financial dashboard? Ijiri feels that we should expect from management that they are able to “see” at which speed their business is “moving.” How else can they intervene when momentum is dissipating? The foundational notion Ijiri puts forward is that the double-entry accounting framework does not exclude the possibility to include “speed” measurements. He thinks it is feasible to extend the double-entry bookkeeping framework with a third dimension so that we can account for the “rate of change” of a firm’s business. He wants to apply the same methodological and procedural rigor to the administration of facts pertaining to the future as is expected from the administration of transactions past (Blommaert, 1994).

Dimensions of the accounting measurement The accounting dimensions are temporally determined sources of information and concern the substance of information and not its form (Wagensveld, 1995, p. 3; Melse, 2004c). Figure 1 shows the purpose of each dimension as wealth measurements in time. Through the accounts it should be possible at any point in time to explain the composition of wealth (1D), i.e. how it was acquired (liabilities and equity) and used (assets). Next, it should be possible to determine for a given period between points if an increase of wealth was realized (2D). To this 2D system of accounts, Ijiri adds the ability to account for the capacity to acquire new wealth in the future (3D) by means of

Figure 1. The arrow of time in the framework of triple-entry and momentum accounting

Change 2D

PERIOD 2D

Net Wealth Increases

Past

Net Wealth Unchanged

Capacity 3D

CHANGE RATE 3D

Future

Net Wealth Decrease

Expensing Forces

Net Wealth Increase

Earning Forces

C om

position 1D P

O IN

T IN

T IM

E 1D

Present

Realisation t−1

Net Wealth Decreases

Estimation t+1

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administration of cost and income forces. A framework of three dimensions is proposed by Ijiri (1986):

(1) Wealth – the first dimension for the administration of the magnitude of wealth and wealth composition, with accounting variables that are set apart as net wealth (equity) and liabilities (sources of capital), or as assets (uses of capital). Accounts of this dimension are on the balance sheet.

(2) Momentum – the second dimension for the administration of the change in magnitude of wealth (the first dimension), with accounting variables that are set apart as cost (outflows) and income (inflows). Accounts of this dimension are on momentum statements that includes the income statement.

(3) Force – the third dimension for the administration of the change of capacity to acquire new wealth (the second dimension), with accounting variables that are set apart to administer internal and external forces. Accounts of this dimension are on force statements that also include impulse and action.

Melse (2004a) discusses these dimensions of momentum accounting theory with more detail. Figure 2 shows the relations between the three accounting dimensions in Ijiri’s framework for triple-entry and momentum accounting, TEMA in short. Ijiri introduces a new set of financial variables he calls momentum accounts that are in the same vertical column of the framework as income. Although they are also period related, they have a different temporal position because they explain the rate of (new) income and their values aggregate dynamically into income in the same manner as income aggregates into wealth. Suppose a firm realizes net income at a rate of $12 per month, its “level” of income momentum. Assuming nothing else changes, income realized after one year should be: $144 (Ijiri, 1987, p. 27). At that time, income is reported as $144 while income momentum is reported as $12/month. The information added to the

Figure 2. A framework for

triple-entry and momentum accounting

IMPULSE

FORCE

ACTION

MOMENTUM

INCOMEWEALTH

Momentum Statement

Wealth Statement

Force Statement

CreditDebit Trebit

Force Accounting Single-Entry Bookkeeping in Dollars/Month2

Momentum Accounting Double-Entry Bookkeeping in Dollars/Month

Wealth Accounting Triple-Entry Bookkeeping in Dollars

A Derivative Relationship An Integral Relationship

Source: Ijiri (1986)

A Difference Relationship

−

ΣΣ

−

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income statement is that we now know the rate by which new income is expected to be created, namely $12 per month. Assuming that this is the firm’s first year of business, recalling the car driving metaphor discussed before, the odometer is now at $144 and the speedometer is at $12.

Financial-ratio analysis Robert Half International Inc., a US based firm, pioneered specialized staffing services in 1948 and today is recognized as an industry leader. There is no reason to use this company’s financial statement data other than for the purpose of illustrating how ratios disclose information for analysis outside and within the TEMA framework of Yuji Ijiri as an extension of Melse (2004a). No proprietary financial statements data is used.

Figure 3 shows both ROTA and ROE time series of Table I, like in Melse (2004a), but now extended with four more years[5]. We derive the ratio ROTA from the division of the return of PBIT by total assets. Likewise, we get ROE by division of PAT by shareholder equity. During the period from 1989 to 1992, each ratio shows a sharp decline reaching a low point in 1991 and 1992, but gradually increases again to reach high points in 1998 and – after a small drop in 1999 – in 2000. The next two years again show a dramatic decrease to arrive at almost reaching 0 percent in 2002 and 2003. The last three years show a just as dramatic increase to reach in 2006, about the same level as in the period 1997-2000. Comparing Figure 3 with Figure 4, which shows the sales margin during these years, it is obvious that the sales margin displays a trend similar to both ratios, notably ROE. Indeed, as reported in Table II, the Pearson correlation coefficient indicates a positive and rather strong association between these three accounting ratios. As Melse (2004a) showed, the point of interest here is the observation that ROTA, ROE, and sales margin are exchangeable ratios as far as the trend in time is concerned also during the last four years (2003-2006). They tell us the same “business story,” we see similar “ups and downs.”

Walsh (1996, p. 72) sees ROTA as the most important benchmark against which the performance of business operations can be measured. But, like any other ratio, as a single figure it is not much more then a target to aim for. It is of more interest to explain

Figure 3. Robert Half, ROTA and ROE 0

P er

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ROTA ROE

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why such a ratio moves up or down when it does. However, using the ratios discussed above has a disadvantage. Westwick (1981) points at the need to investigate the cause of the “ups and downs” of a ratio and for this purpose wants to be able to disaggregate from the “total” to the “parts.” For example, we can calculate the return not only on total assets but also on the disaggregated current and fixed assets. A brief digression on the calculation of ROTA as operating performance ratio to support our explanation:

Year Wealth (point)

Net wealth (point)

Sales (period)

PBIT (period)

PAT (period)

ROTA (ratio)

(percent)

ROE (ratio)

(percent)

Sales margin (ratio)

(percent)

1987 155.69 48.13 105.69 13.54 7.25 10.51 14.91 12.81 1988 194.87 61.70 182.05 20.11 12.03 12.91 24.99 11.04 1989 184.41 68.68 234.50 23.62 13.47 12.12 21.83 10.07 1990 188.37 77.29 248.56 14.93 8.87 8.10 12.91 6.01 1991 178.95 84.42 209.46 8.02 4.06 4.26 5.25 3.83 1992 181.76 90.97 220.18 7.91 4.38 4.42 5.19 3.59 1993 204.60 133.60 306.17 21.56 11.72 11.86 12.89 7.04 1994 227.76 177.00 446.33 45.21 26.12 22.10 19.55 10.13 1995 301.14 227.93 628.53 69.09 40.30 30.33 22.77 10.99 1996 416.01 308.45 898.64 103.65 61.10 34.42 26.81 11.53 1997 561.37 418.80 1,302.88 158.83 93.70 38.18 30.38 12.19 1998 703.72 522.47 1,793.04 221.18 131.58 39.40 31.42 12.34 1999 777.19 576.10 2,081.32 234.70 141.44 33.35 27.07 11.28 2000 971.03 718.54 2,699.32 301.63 186.10 38.81 32.30 11.17 2001 994.16 805.70 2,452.85 196.28 121.11 20.21 16.85 8.00 2002 935.67 744.97 1,904.95 3.50 2.17 0.35 0.27 0.18 2003 979.90 788.66 1,974.99 11.72 6.39 1.25 0.86 0.59 2004 1,198.66 911.87 2,675.70 234.67 140.60 23.95 17.83 8.77 2005 1,318.69 970.87 3,338.44 392.17 237.87 32.72 26.09 11.75 2006 1,459.02 1,042.67 4,013.55 466.20 283.18 35.35 29.17 11.62

Note: Data scaling factor: millions US$ Source: Compustat/Thomson

Table I. Robert Half, time series

Figure 4. Robert Half, sales margin0

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We get the following ratios: . sales margin ¼ PBIT/sales; and . turn over ¼ sales/total assets.

ROTA can be calculated by the product of sales margin times turn over. Because sales are the denominator of sales margin as well as the numerator of turn over, it is cancelled out in the alternatively ROTA calculation of: PBIT/total assets.

Now, following the above method of calculation, Table III gives the return on fixed assets and on current assets for Robert Half in the first two columns of Panel A. Figure 5 shows ROTA and the time series of its two disaggregated ratios. Observe how the ratio return on fixed assets reaches a much higher value in 2006 compared to the period 1995-2000, or ROTA at that point (1.54). This is somewhat peculiar when we compare this to the ROTA (0.35). Although these disaggregated ratios are correct, can we trust them? In the fourth column of Panel A of Table III, with the title check, the disaggregated return ratios are subtracted from the ROTA. Clearly, in each year, there is a difference between the sum of the “parts,” the disaggregated return ratios, and

Variables Association

ROTA vs ROE r ¼ 0.918 *

ROTA vs sales margin r ¼ 0.797 *

ROE vs sales margin r ¼ 0.916 *

Note: *Significant at 1 percent level

Table II. Robert Half, association between return ratios and sales margin

A: sales/assets B: assets/sales Year Fixed Current Total Check Fixed Current Total Check

1987 0.21 0.21 0.11 20.3153 4.76 4.75 9.51 0.0000 1988 0.20 0.36 0.13 20.4294 4.93 2.81 7.74 0.0000 1989 0.18 0.37 0.12 20.4307 5.57 2.69 8.25 0.0000 1990 0.10 0.36 0.08 20.3795 9.54 2.81 12.35 0.0000 1991 0.05 0.21 0.04 20.2228 18.77 4.71 23.48 0.0000 1992 0.05 0.25 0.04 20.2610 18.66 3.97 22.63 0.0000 1993 0.14 0.67 0.12 20.6924 6.93 1.50 8.43 0.0000 1994 0.29 0.95 0.22 21.0192 3.48 1.05 4.53 0.0000 1995 0.43 1.02 0.30 21.1488 2.32 0.98 3.30 0.0000 1996 0.62 0.78 0.34 21.0501 1.62 1.29 2.91 0.0000 1997 0.80 0.73 0.38 21.1487 1.25 1.37 2.62 0.0000 1998 0.97 0.66 0.39 21.2410 1.03 1.51 2.54 0.0000 1999 0.86 0.55 0.33 21.0705 1.16 1.83 3.00 0.0000 2000 1.05 0.61 0.39 21.2790 0.95 1.63 2.58 0.0000 2001 0.66 0.29 0.20 20.7457 1.53 3.42 4.95 0.0000 2002 0.01 0.01 0.00 20.0129 88.12 196.17 284.29 0.0000 2003 0.04 0.02 0.01 20.0457 24.97 54.90 79.87 0.0000 2004 0.83 0.34 0.24 20.9307 1.20 2.98 4.18 0.0000 2005 1.39 0.43 0.33 21.4898 0.72 2.34 3.06 0.0000 2006 1.54 0.46 0.35 21.6498 0.65 2.18 2.83 0.0000

Table III. Robert Half. Panel A: return on assets; Panel B: inverse calculation

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their “total,”, i.e. ROTA (Figure 5). In other words, disaggregated return ratios calculated as “sales over assets” do not add up! As an alternative, Westwick (1981) recommends to inverse the fraction terms as “assets over sales.” Table III, Panel B, reports these time series and clearly, for each year, the inversed disaggregated ratios now do add up to their “total:ROTA”.

However, solving one problem introduces another: the return ratios themselves are now a bit more difficult to understand intuitively. They also tend to become very large when PBIT is very small, like in 2002 and 2003, respectively, 284.29 and 79.87. Therefore, for our analysis, the disaggregated return ratios are first multiplied by 100 and then scaled by their natural logarithm to create Figure 6 with the y-axis inversed (because now, like in Figure 5, when the line “drops” this is “less good”). The disaggregated analysis of return on assets by inverse calculation reveals in a more balanced manner the shift in weight over time from fixed to current assets. Figure 6, for example, shows, from 1997 onwards to 2006, the increasing contribution of the return on current assets to ROTA. Owing to a poor PBIT, this is particularly difficult to grasp

Figure 5. Robert Half, return

on assets0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

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Fixed Assets Current Assets Total Assets

Figure 6. Robert Half, return on

assets by inverse calculation (ratios £ 100

and scaled by logN)

100

1,000

10,000

1,00,000

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Fixed Assets Current Assets Total Assets

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for the years 2002 and 2003 using the regular return ratios in Figure 5. Hence, we propose the inverse calculation of disaggregated ratios and subsequent graphing with a natural logarithm-based scale like in Figure 6.

Unitless and timeless accounting ratios Of some concern is that accounting ratios are not necessarily timeless as was concluded before in Melse (2004a). To get ROTA or ROE, we divide period measurements, respectively, PBIT and PAT, by point measurements, respectively, total assets and shareholders’ equity (net wealth)[6]. Or, seen from a temporal perspective, we divide data related to period (p) measurements by data from point (t) measurements (p?t). In Ijiri’s TEMA framework, this implies that the accounting ratio is calculated as a momentum measurement (income) divided by a wealth measurement; PBIT divided by total assets in the example of ROTA.

Ratios become unitless when they relate quantities of the same dimension. Within the TEMA framework this is clearly not the case for ROTA or ROE. Although the accounting data are in some way related to the same medium of exchange in use – , i.e. monetary values – it is their time property we are uncomfortable with. ROTA and ROE are ratios that express “return by point,” a state at date, which is something different then a rate of change or “return by period.” A ratio like the sales margin is unitless and timeless because it relates two period measurements through the division of PBIT by sales (p?p). In economic accounting terminology, only when we divide stock accounts by stock accounts, or flow accounts by flow accounts, will we get unitless ratios.

To obtain unitless and timeless ratios, in the TEMA framework (Figure 2), we have to divide accounting variables of the same temporal “dimension” wealth, momentum or force. In other words, unitless ratios are calculated intra-dimensionally, i.e. between accounting variables with the same temporal dimension. In this approach, an accounting ratio is a quantity that denotes the proportional amount or magnitude of one period accounting variable relative to another period accounting variable (p?p), or of one point relative to another point (t?t). Following this temporal decision rule, we can calculate ratios between items, like the current ratio, current assets by current liabilities (two wealth accounts), but not divide a balance sheet account by sales (i.e. divide a wealth measurement by a momentum measurement). For example, the well known working capital to sales ratio that tries to capture a dynamic perspective of short-term liquidity conflicts with this temporal decision rule (Walsh, 1996, p. 118)[7]. This is not to say that such ratios should not be used. The observation here is that such ratios are calculated extra-dimensionally, and therefore are not timeless, which possibly leads to less clear interpretations. This is a motivation to investigate what intra-dimensional ratios might have to offer over and above extra-dimensional ratios.

Common-size-format momentum ratios In Ijiri’s TEMA framework, momentum accounts are rates per period that measure the change of a wealth account. Once we divide one such momentum account by another we get a true ratio that can be expressed as a pure number or as a percentage. For momentum, such a ratio expresses the proportion of change per period relative to another change per period. Melse (2004a) presented the momentum ratio of net wealth composition. In the same manner, a momentum ratio of disaggregated balance sheet

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accounts can be calculated. When the momentum of balance sheet accounts is divided by total wealth momentum we get common size ratios, or percentages, i.e. a change fraction of the whole change. However, this requires that the sign of raw data negative momentum is first inversed to be included in the denominator before the fraction is calculated[8]. Assuming two disaggregated parts, the following equation gives the required logic:

For A=BjA=ðifðA , 0 then 2 A else AÞ þ ifðB , 0 then 2 B else BÞÞ:

This equation renders unitless and timeless force or momentum ratios that can be compared with any other such ratio. Table IV gives the common size momentum ratios for total liabilities and net wealth and Table V for current and fixed assets. Likewise, for force accounts, such ratios convey the proportion of the rate of change per period squared relative to the whole change of momentum per period squared. Thus, we can compare momentum or force between periods of a single firm or between companies for panel analysis of markets or sectors. A whole new set of ratios is thus available in the TEMA framework to investigate business dynamics and possible relationships between the accounting variables from which they are derived.

Ratio analysis should provide an insight into the financial health of a firm by looking into its liquidity, solvability, profitability, activity, and capital and market structure. We limit ourselves here to the comparison of the sales margin and net wealth momentum of Robert Half. One way to look at sales margin is too see it as a momentum ratio because the accounting data involved is income-related period measurements (p).

A: raw data B: common size

Year

Wealth momentum

(period)

Net wealth momentum

(period)

Liabilities momentum

(period)

Net wealth momentum

(ratio)

Liabilities momentum

(ratio) Check (sum)

1987 26.89 20.50 27.38 20.02 0.98 1.0000 1988 39.18 13.57 25.61 0.35 0.65 1.0000 1989 210.46 6.97 217.43 0.29 20.71 1.0000 1990 3.95 8.62 24.66 0.65 20.35 1.0000 1991 29.42 7.13 216.55 0.30 20.70 1.0000 1992 2.81 6.55 23.74 0.64 20.36 1.0000 1993 22.84 42.63 219.79 0.68 20.32 1.0000 1994 23.16 43.39 220.23 0.68 20.32 1.0000 1995 73.38 50.94 22.44 0.69 0.31 1.0000 1996 114.87 80.52 34.36 0.70 0.30 1.0000 1997 145.36 110.36 35.00 0.76 0.24 1.0000 1998 142.35 103.67 38.68 0.73 0.27 1.0000 1999 73.47 53.63 19.84 0.73 0.27 1.0000 2000 193.84 142.44 51.41 0.73 0.27 1.0000 2001 23.13 87.16 264.02 0.58 20.42 1.0000 2002 258.49 260.73 2.24 20.96 0.04 1.0000 2003 44.23 43.69 0.54 0.99 0.01 1.0000 2004 218.75 123.21 95.55 0.56 0.44 1.0000 2005 120.03 59.00 61.03 0.49 0.51 1.0000 2006 140.34 71.80 68.54 0.51 0.49 1.0000

Note: Data scaling factor: millions US$

Table IV. Robert Half. Panel A: net

wealth and liabilities momentum; Panel B:

common size momentum ratios

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PBIT divided by sales; the numerator and the denominator have the time dimension momentum in Ijiri’s TEMA framework. Both are realized during the period in between the two moments when financial statements are drawn up; in our case a year. Consequently, it is more fitting to compare PBIT with net wealth momentum because both are period measurements (p). Additionally, sales margin can be compared with the net wealth momentum ratio, each being a period ratio (p?p). Before we discuss this in more detail, we first turn our attention to PBIT and net wealth momentum as individual momentum variables.

Analysis of net wealth momentum and its common-size-format ratio The common-size-format ratio of net wealth momentum is a fraction or percentage of total wealth momentum. It is calculated for each period by the change of net wealth (total shareholders’ equity) relative to the change of total wealth of which it is a part. When we compare the graph of net wealth momentum raw data in Figure 7 with its common-size-format ratio in Figure 8, it is worthy to note that the net wealth momentum movement raw data and its common-size-format ratio are similar in 2002 and 2003. However, before 2002 and after 2003, the trend of raw data and the common-size-format ratio is very different. Notably, the common-size-format ratio is characterized by a steady rate of change during the periods 1992-2001 and 2004-2006. On average the ratio is, respectively, 0.63 and 0.52. This implies that although net wealth momentum itself might fluctuate (Figure 7), relative to the fluctuation of all

A: raw data B: common size

Year

Wealth momentum

(period)

Current assets

momentum (period)

Fixed assets

momentum (period)

Current assets

momentum (ratio)

Fixed assets

momentum (ratio)

Check (sum)

1987 26.89 27.81 34.70 20.18 0.82 1.0000 1988 39.18 6.94 32.24 0.18 0.82 1.0000 1989 210.46 221.44 10.98 20.66 0.34 1.0000 1990 3.95 24.18 8.13 20.34 0.66 1.0000 1991 29.42 26.40 23.02 20.68 20.32 21.0000 1992 2.81 0.91 1.90 0.32 0.68 1.0000 1993 22.84 15.13 7.71 0.66 0.34 1.0000 1994 23.16 20.24 2.93 0.87 0.13 1.0000 1995 73.38 65.95 7.43 0.90 0.10 1.0000 1996 114.87 84.10 30.77 0.73 0.27 1.0000 1997 145.36 116.26 29.10 0.80 0.20 1.0000 1998 142.35 96.40 45.95 0.68 0.32 1.0000 1999 73.47 60.13 13.34 0.82 0.18 1.0000 2000 193.84 181.07 12.77 0.93 0.07 1.0000 2001 23.13 14.40 8.74 0.62 0.38 1.0000 2002 258.49 242.83 215.66 20.73 20.27 21.0000 2003 44.23 55.45 211.21 0.83 20.17 1.0000 2004 218.75 217.70 1.06 1.00 0.00 1.0000 2005 120.03 100.59 19.44 0.84 0.16 1.0000 2006 140.34 95.45 44.89 0.68 0.32 1.0000

Note: Data scaling factor: millions US$

Table V. Robert Half. Panel A: current and fixed assets momentum; Panel B: common size momentum ratios

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accounts it can still be stable (Figure 8). It is this steady rate of change, this momentum that Ijiri considers to be of great importance in the appraisal of corporate performance. As far as the creation of net wealth is concerned, Robert Half is shown here to be a reliable performer from 1992 onwards. Only during 2002 and 2003 the stability is lost. Indeed, in those years the staffing industry experienced a major downturn in the USA and in Europe (Fleming, 2002), from which it quickly recovered (Krampf, 2004).

The common-size-format ratio of net wealth momentum can also be seen as a coefficient. The Robert Half time series provides some evidence that there is a relation between the growth rate of total wealth and net wealth, and that it holds firm at the same level over several years (Figure 8). In this, we should not only see an accounting logic – we can expect that net income is accrued into net wealth – but we should also read this as an economic phenomenon. That the amount of new wealth gained and added to the balance sheet is about the same for a certain number of years might not be

Figure 7. Robert Half, net wealth

momentum, raw data–75

–50

–25

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Figure 8. Robert Half, net wealth

momentum, common size ratio−1.0

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too big a surprise. But, that this firm, after experiencing large shocks during 2002 and 2003 in its business model, drives back (so quickly) to a stable level of momentum is striking. However, the difference between the new and the previous level of momentum, on average 0.11 lower, might be somewhat of a disappointment for analysts and shareholders alike.

That the business model of Robert Half changed after 2003, compared to the period 1993-2001, can also be seen from the stacked bar graph in Figure 9 of the common-size-format ratios reported as percentages of net wealth momentum and total liabilities momentum. In Figure 9, each whole stacked bar represents the momentum of total wealth (of course that is always 100 percent). The lower half of each bar graphs total liabilities momentum, except for 2002, while the upper half graphs net wealth momentum. When a momentum is negative, i.e. when the balance sheet account decreases, the bar is drawn below the 0 percent line which indicates “no change.” Thus, from Figure 9 it is clear that during the period 1989-1994 Robert Half successively reduced its debt whereas net wealth showed considerable growth. From 1995 to 2000, Robert Half kept increasing total assets, financing this with about 25 percent of debt. In 2001, the pattern shifts considerably with a substantial decrease of debt. Therefore, it is not without good reason that, during the market downturn, Fleming’s (2002) comment was: “Robert Half does have a firm financial foundation, with $303 million in cash, no debt and [a] healthy cash flow.” At the time, “Robert Half announced that it would buy back as many as ten million of its own shares” (Id.), which we see reflected partly in the negative net wealth momentum of 2002 as well as in the negative current assets momentum (Table V)[9]. But, the recovery from this downturn is just as remarkable. In 2003 net wealth momentum is about the same as total wealth momentum, respectively, $43.69 and 44.23 million (Table IV). These changes on the balance sheet of Robert Half are a good illustration of the use of the net wealth account as a buffer of funds at the disposal of management to face bad times.

Discussion and conclusions A great advantage of the TEMA framework is that it allows for the temporal as well as the categorical analysis of accounting measurements. To this purpose, in this paper

Figure 9. Robert Half, net wealth and total liabilities momentum, common size percentages

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ROTA was analyzed both as an aggregated and disaggregated performance measurement. We proposed to use an inverse method of ratio calculation for disaggregated ratio analysis. This will allow the comparison of disaggregated accounting variables relative to their aggregated totals in the TEMA framework. Preferably, we should not compare time period data with time step data.

Further to Melse (2004a), the extended example of Robert Half demonstrated that with the TEMA framework new information can be disclosed that is relevant for performance analysis. It is possibly more meaningful to limit the use of ratios to only intra-dimensional relations within the TEMA framework for the benefit of temporal correctness and improved interpretability of the data. Consequently, we should use the TEMA framework to search for more informative ratios. In our case, we were able to tell apart years that have a comparable common-size-format ratio of net wealth momentum but a very different trend of ROTA. This adds new insight to how we should appreciate the structural aspects of the profitability of a firm. This new method sheds more light at a desirable stability of the firm’s business model. Vice versa, observing years that have a comparable ROTA but a different common-size-format ratio of net wealth momentum might deepen the analysis of balance sheet dynamics, something of interest to shareholders and analysts alike.

Improving the ability to analyze trends within financial data can benefit all users of financial statements. It will be worthwhile to broaden this research to larger population now that it has been shown that common-size-format momentum ratios offer meaningful insight in the example of Robert Half Inc. By way of additional case examinations we expect to be able to confirm the findings of this paper. An extension is to further research the possible association between TEMA variables of a firm and the market performance of its stock as an alternative to models with balance sheet or income variables or their ratios (Barniv and Myring, 2006; Biddle et al., 1997; Bird et al., 2001; Collins et al., 1997; Damant, 2001). A second line of investigation would be to compare the forecast success rate of TEMA models with that of alternative valuation models or analysts’ earnings forecasts (Richardson and Tinaikar, 2004). A third line of investigation could be to investigate if Spectramap factor decomposition of TEMA variables can be employed in econometric models for investment portfolio management (Melse, 2004b). Beside the identification of firms that exhibit mean-like behavior, locating companies that occupy contrasting positions in the decomposed data space of TEMA variables might be useful to balance investment portfolios (Haensley, 2003).

We conclude with the contention that implementing momentum accounting might be beneficial for strategic accounting purposes as well as for the ex post analysis of financial statements (Bell et al., 1997; Barniv and Myring, 2006; Haskins and Sack, 2006). Possibly, this will prompt a renewed interest in the practical use of the TEMA framework and Ijiri’s momentum accounting theory as a means to improve performance measurement and risk analysis.

Notes

1. Misrepresentation of facts in financial statements is a subject that in this study is not discussed further but nonetheless it is an important and problematic issue. However, we think that momentum accounting increases transparancy and, as a result, is expected to reduce the risk of misrepresentation of facts (Blommaert, 1994, p. 230).

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2. That is, the rate of change per time unit smaller than the time period in between two financial statements. As will become clear when the research methodology is discussed in the next paper, we can count the rate of change per year or quarter with the currently available financial statements of firms.

3. Or decreasing; whereas the mileage of a car cannot be reduced (something which is illegal to do) wealth can decrease during the lifetime of the firm when capital is retired or dividend is paid out. See Melse (2004b) for another example of TEMA balance sheet analysis.

4. To be honest, the items on the cash flow statement can be viewed as “speedometers” when we set the rate of change equal to one year or one quarter. However, Ijiri’s vision is to provide much more detailed information with a much shorter time rate of change.

5. Source of non-proprietary data used: Compustat provided by Thomson One Banker Analytics.

6. It is a matter of taste to choose the point of measurement. One can opt for the period’s closing balance sheet or the opening balance sheet (that is done in this study). A third alternative is to average the opening and closing balance sheet to get, in a manner of speaking, a point in the middle of the period. However, none of this method mitigates the problem of temporal inconsistency of the ratio.

7. A shortcoming of the current ratio is that point measurements are static data. It is possible to “window dress” the accounts so that the ratio “looks good” on that day. Possibly, period measurements and their derived common-size-format momentum ratios make this more difficult to do.

8. Consequently, the denominator of this division can be larger then the aggregate of the disaggregated momentum or force accounts.

9. Common shares outstanding were reduced from 174.929 in 2001 to 170.909 in 2002.

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