KEITH SHWAYDER

A Critique of Economic Income as an Accounting Concept *

Economic income as defined in Hicks's influential book. Value and Capital,^ has achieved wide acceptance in accounting literature—especially since the publication of Alexander's monograph. Income Measurement in a Dynamic Economy.'^ Hansen, for example, enthusiastically endorses this concept: 'Profit as capital interest, . . . may be characterized as a theoretically complete concept, which is superior to other concepts of profit as a definition and as a guide point for an ideal practical procedure.'^ Solomons is equally sanguine: '. . . growth in present value . . . alone appears to be significant; and since it seems to carry out the function generally attributed to income, growth in present value must be what we had better understand income to mean. The concept of income to which we have been led corresponds, of course, to Hicks's definition of income.'* Goldberg questions this acceptance: '. . . the definition of income as given by J. R. Hicks . . . has been widely adopted both implicitly and explicitly, and often without question, in accounting and economic writing, even though Hicks himself pointed out its impracticability.'^

Economic income is generally defended as an ideal theoretical concept which is impractical to implement because of the difficulty in an uncertain world of measuring future cash flows. Not only is economic income an impractical concept, but it is also, in my opinion, an unsound theoretical model for accounting income measurements. In defending this opinion, I will analyse five situations where the

1. J. R. Hicks, Value and Capital, Oxford University Press, 1939, p 172. 2. Sidney Alexander, 'Income Measurement in a Dynamic Economy', Five Monographs in Business Income, New York, American Institute of Certified Public Accountants, 1948, as revised by David Solomons, in Studies in Accounting Theory, W. T. Baxter and Sidney Davidson (eds), Homewood, Illinois, Richard D. Irwin, Inc, 1962. 3. Palle Hansen, The Accounting Concept of Profit, Amsterdam, North-Holland Publishing Company, 1962, p 19. 4. David Solomons, 'Economic and Accounting Concepts of Income', The Accounting Review, July 1961, p 375. 5. Louis Goldberg, An Inquiry into the Nature of Accounting, American Accounting Association, 1965, p 247.

* The writer wishes to thank Professors Yuji Ijiri and Charles Horngren of Stanford University for their many helpful comments and suggestions.

KEITH SHWAYDER is Instructor in Accounting, Graduate School of Business, University of Chicago.

23

ABACUS

economic income method allocates income to accounting periods in a manner which violates our intuitive notions concerning periodic income:

1. A firm with a single venture. 2. A long lived firm. 3. A firm where the subjective rate of interest approaches zero. 4. A firm where the past is known with certainty and the future is highly

uncertain. 5. A firm where some future events are known with certainty and others are

uncertain.

Since the operational difficulties with economic income are recognized, the paper will deal only with theoretical problems.

'Economic Income'

'Economic income' usually denotes income as defined by economists. As accountants differ among themselves in measuring income, economists also have divergent income concepts and potentially there are as many definitions of economic income as there are economists. However, since the publication of Alexander's monograph, economic income has taken on a more restricted con- notation in accounting literature—income as defined by Hicks and modified in Alexander's monograph. Hicks defined income as the amount a man can consume during a period, and still remain as well off at the period's end, as he was at the period's beginning.^ Alexander adapted this concept to the corporation, describing income as the amount the firm could distribute to shareholders during a period and still remain as well off (have as much residual equity) at the end of the period as it was at the beginning of the period.'' 'Well-offness' was defined entirely in terms of cash flows discounted at subjective rates of interest.^ The timing and amounts of cash flows and the future subjective interest rates were assumed to be known with certainty. The subjective interest rate is the discount rate where the entity is indifferent to future money and current money. Alexander argued that if management was maximizing the owners' 'well-offness', this rate should be greater than or equal to the stockholders' time value of money.'

For example, suppose the firm knows with certainty the timing and amount of its future net cash flows from operations (the net cash flows from all sources except contributions from or distributions to residual equity shareholders). Let Pt be the present value at the beginning of period t of all of the future net cash flows of the firm, discounted at the appropriate future subjective interest rates. Economic income for period t then equals Pt+i — Pt -j- the net cash flows occurring during period O° Economic income is generally defended as a concept appropriate when the future is known with certainty, but difficult (though some- times possible) to apply in an environment where the future is uncertain." It is

6. Hicks, loc cit. 9. Ibid, p 149. 7. Alexander, op cit, p 139. 10. Ibid, p 142. 8. Ibid, pp 140-142. 11. See for example, Solomons, op cit, p 378.

24

ECONOMIC INCOME AS AN ACCOUNTING CONCEPT

argued that, in a world of certainty, a firm can only become better off by moving forward in time. If the firm's internal rate of return exceeds its subjective rate of interest, as it moves forward in time the present value of the future net cash flow increases. This increase is a function of the subjective rate of interest.

Case One: Single Venture, ex ante Certainty Let us now compute economic income in a concrete example, a firm with but

one venture. Suppose I start a firm and invest no capital in it. I do nothing for two periods. Shortly after the start of the third period, I invest $1,000 in the firm and buy some land for $1,000. Shortly after the start of the fourth period I sell the land for $2,000 and immediately withdraw the money from the firm. At the end of the fourth period I liquidate the firm. My subjective interest rate during the four periods is 5 per cent per annum.

-1- $2,000 Sell Land

Period 1 Period 2 Period 3 Period 4

— $1,000 Buy Land

Case One: Cash Flow from Operations

At the end of the fourth period I wish to prepare a set of periodic income statements to describe the economic history of the firm. From this certain net cash flow I can compute the economic income for each period as follows:

Present value of the cash flow at

Period the beginning of the period dis- counted at 5%

(t) (Pt)

Net cash flow occurring during

the period

(CF,)

Income for the period

Pt+i – Pt + CF,

Instantaneous profit recognized at the inception of the firm Period 1 $821 Period 2 $862 Period 3 $904 Period 4 $2,000

Total lifetime entity profit

-$1,000 +$2,000

$821 $41 $42 $96

$0

$1,000

TABLE 1 Calculation of Periodic Income Using the Economic Income Method

25

ABACUS

Opinion in accounting literature is divided as to whether instantaneous gain (such as the $821 in the above example) is income or merely the discovery of capital. 12 In this paper we will use Alexander's approach and treat instantaneous gain as a part of lifetime entity income." Under this formulation, lifetime entity income equals lifetime entity net cash fiow. Lifetime entity income can be divided into capital gain (instantaneous gain) and capital interest components. In the example above, the firm had a capital gain of $821 at the beginning of the first period. The firm earned $41 capital interest in the first period, $42 capital interest in the second period, etc.

Let us now consider additional information concerning the land venture which, although not necessary to calculate economic income (in fact ignored under the economic income method), may give us insight into evaluating the validity of the economic income method. Suppose the land purchase in period 3 was from a seller who had imperfect information concerning the market. The land was purchased for $1,000 when its 'market value' was $1,500. Suppose that in period 4, when I sold the land, I again found someone with imperfect market information who purchased the land for $2,000 when its 'market value' was $1,500.

From this information we can conclude that 1. there was a strong causal relationship between the firm's net cash flow and the bargain purchase and sale of land, and 2. there was a very weak relationship between the firm's net cash flow and the activities occurring in periods 1 and 2. With this data we can impute 100 per cent of the lifetime monetary profit to periods 3 and 4 (say 50 per cent to period 3 and 50 per cent to period 4). Such an imputed income reflects how much better off the firm is for having performed the activities which are temporally associated with the period, i"* Let us now compare the two periodic income allocations (economic income and 'imputed' income). (See Table 2.) The reader is asked to decide which allocation method gives the most reasonable economic history of the firm. If one is concerned with trends in profitability or with the relative performance of the firm in periods 3 and 4 as opposed to periods 1 and 2, imputed income seems to be the more valid measurement.

Why does the economic income method give such a distorted picture of the firm's activities?

1. All economic events relating to the firm are ignored except the timing and amount of net cash flow and the subjective interest rate. Thus, the income of the period does not reflect such important events as advantageous sales and purchases.

12. Alexander (op cit, p t30) considers instantaneous gain to be part of the lifetime income of the firm. Robert K. Jaedicke and Robert T. Sprouse (.Accounting Flows: Income, Funds and Cash, Prentice-HaU, Inc, 1966, p 22) and Maurice Moonitz and L. H. Jordan {Accounting: An Analysis of Its Problems, vol 1, revised ed. Holt, Rinehart and Winston, i963, p 134) on the other hand exclude such instantaneous gain from the lifetime income of the firm under their interpretation of the economic income method. 13. Alexander, loc cit. 14. This definition of imputed income is similar to Alexander's definition of activity profit. Activity profit refiects 'how much better oflE is the corporation for having performed certain activities which are somehow associated with the period'. (Alexander, op cit, p 173)

26

ECONOMIC INCOME AS AN ACCOUNTING CONCEPT

Period

Capital gains recognized at the beginning of period 1 Period 1 Period 2 Period 3 Period 4

Total lifetime income

Economic income

$821 $41 $42 $96 0

$1,000

^Imputed' income

0 0 0

$500 $500

$1,000

TABLE 2 Comparison of Periodic Income Figures under Economic Income and ^Imputed' Income Calculations

Such omissions result in patterns of periodic income allocations which distort the firm's economic history. Under the economic income method, over 85 per cent of the lifetime profit of the firm is allocated to the first accounthig period (capital gains of $821 and capital interest of the first period of $41). Yet, insignificant contribution to the lifetime profit of the firm occurred in this period. Only 10 per cent of the total profit is allocated to period 3, and only 0 per cent of the total profit is allocated to period 4. Yet, in these periods the most significant profit-producing events took place; in these periods the lifetime monetary income of $1,000 was actually earned by the firm.

2. A large portion of the lifetime income of the firm is allocated to the point in time when the firm obtained the information about the future profitable operations (82 per cent of the venture income is allocated to the inception of the firm when the knowledge concerning the future profitable operations was assumed to occur). The timing of the income realized under the economic income method describes the timing of our knowledge concerning future economic events; it does not describe the timing of the occurrence of the economic events.

3. The reported profitability of the firm is a function of the subjective interest rate rather than of the internal rate of return. Changes in the internal rate of return are suppressed.'^ In the land venture the internal rate of return jumped from 0 per cent to approximately 100 per cent between period 2 and period 3. This change was not recognized under the economic income method.

15. Here the writer assumes that it is meaningful to talk about changes in the internal rate of return at different points in the firm's history, even when the firm's future is known with certainty. In particular, this assumption is iustified when there is independence among the several accounting periods. In the example above, the first two periods are assumed to be independent of periods 3 and 4. The life of the firm could be meaningfully divided into two sections: a quiescent section (periods t and 2) where the internal rate of return was zero, and a trading section (periods 3 and 4) where the firm had a positive internal rate of return.

27

ABACUS

Case Two: A Firm With a Long Life, ex ante Certainty

Our previous example concerned a firm with a short life. Let us now consider a fiirm with a very long life. Only a limited class of such firms has a measurable economic income. More specifically, as the life of the firm approaches infinity, only firms with a growth rate of capital lower than the subjective rate of interest have a measurable economic income.

Assume the subjective rate of interest, I, and the internal rate of return, R, are constant in all periods. That is. It = Ii -t-1 = I and R, = Ri +1 = R for all i. Pt as before is the present value of the firm at the beginning of period t. The timing and amounts of future cash flows are known with certainty; CFi is the net cash flow of period i (assumed to occur at the end of the period). Ci is the cost of the net assets invested in the firm at the beginning of period i. Suppose the firm grows or declines (in terms of capital investment) at a constant rate. That is,

Ci+i = Ci (1 + Gi) and Gi = Gi+i = G for all i.

1. Present value of CFi evaluated

at time i + 1 = Q (R + 1) – Q (I + D = Q (R – I)

Ct+1 C "

+ ( t t+1

3. Pt = (R – I) I 1 . . . + Vd+i) (1+1)2

)

_ t Ct (1 + G) Ct (1 + G)2 Ct(l+G)°° 4. P' = ( R – I > ^ + + +

(1+G) no finite answer u > 1

(1 + I) Equation 6 converges to a finite answer if, and only if, the growth rate is strictly lower than the investor's subjective rate of interest. If the growth rate is higher than the subjective rate of interest, we cannot compute economic income. Economic income depends upon a comparison of beginning and ending present values. This comparison is impossible if these present values are not finite.

We rarely expect the subjective rate of interest greatly to exceed the market interest rate (M). If an entity's subjective interest rate exceeds the market rate, it should borrow until its time preference for cash approaches the market rate.

28

ECONOMIC INCOME AS AN ACCOUNTING CONCEPT

(Some small difference, D, between the market rate and the entity's time preference for cash can be maintained by the firm's being a poor credit risk, being averse to risk, etc.) The entity's subjective rate of interest for riskless projects should probably not greatly exceed say 7 per cent. Moreover, G must be at least zero for the firm to have a long life. Thus, there is a very restrictive set of going concerns which have measurable economic income. More specifically, only those long lived firms whose growth rate falls within the range:

O^G^I=M+D have a measurable economic income.

One of the difficulties in applying economic income to a going concern results from the extremely liberal realization criteria. The present value of net cash fiows resulting from projects started 25, 50 or 75 years in the future are capitalized (and are in this sense realized), even though the interdependence of these projects with the economic Gestalt of the current period is, at best, highly tenuous, and, more likely, is negligible.

Case Three: Zero Subjective Interest Rate, ex ante Certainty Previously we assumed that the entity had a strictly positive subjective interest

rate. However, it is possible for the entity to have a zero subjective interest rate. Consider an economy where the price level is falling and the real level of interest rates (adjusted for general price level changes) exactly offsets the price fall. The aggregate interest rate for the investors in the economy would, under these conditions, be zero. Suppose the opportunities available to the entity for investing capital were either to invest in the firm at an incremental rate of return of 0 per cent, or to lend the money at a zero interest rate. Moreover, suppose the time preference for consumer goods by the owners of the entity was equal to the real level of interest rates. It is apparent that the appropriate subjective rate of interest for the entity is zero.

If the firm has an indefinite life, it has a measurable economic income only if it maintains approximately a constant level of capital investment. Consistent with the reasoning of the last section (0 ^ G ̂ I = 0), the growth rate must be zero.

If the firm has a limited life and a zero subjective rate of interest, the economic income for all accounting periods, except the first period, is zero. All income is recognized as instantaneous gain at the firm's inception. That is, the present value of the total cash flow over the life of the entity does not change as the firm moves forward in time. Suppose, however, that this firm was profitable as determined by conventional accounting measurement rules (the internal rate of return was positive).'^ Clearly the continued operation of the firm is improving the share- holder's 'well-offness'—the internal rate of return is higher than the shareholder's

16. The firm could have a positive internal rate of return and a zero time preference for cash if, say, the average internal rate of return was positive, and the marginal internal rate of return was zero.

29

ABACUS

subjective interest rate. Yet none of this increase in 'well-offness' is recognized as the firm moves forward in time.

The above example vividly illustrates the peculiar way in which those who employ economic income attribute income to accounting periods. As indicated earlier, economic income is recognized when cash fiows are discovered rather than when they are created. Thus if I know with certainty that in ten years I will write a best-selling novel, receiving in the tenth year $50,000 in royalties, and if I have a very low subjective rate of interest (say 0 per cent), under the economic income method I would assign all income to the year in which I became aware I would write the novel, assigning no income to the year in which I actually did the work. That is, I impute greater importance to my knowledge that I will write the novel than to my actual labour in creating the book. Economic income describes the timing of our information about future events, rather than the timing of the economic events themselves, as we have already said.

Case Four: ex post Certainty In our previous discussion we considered certainty in an ex ante sense—the

timing and amounts of the firm's lifetime cash flow was known with certainty before the cash fiow occurred. It is interesting to look at certainty in an ex post sense—the timing and amount of the firm's lifetime cash flow are known with certainty, but after the cash fiow occurs. Ex post certainty of cash flow is approximated in some accounting measurements. For example, the lifetime cash flow from operations of a firm with complete records is known with certainty at the time of the firm's liquidation.

Under ex ante certainty there is some balance sheet justification for capitalizing the present value of cash flows known with certainty to occur in the future. Having complete confidence that the cash flows will occur increases the investor's psychological satisfaction. This information also has economic beneflts. The firm could be sold to another investor with an equal or lower time preference for cash for at least the discounted present value. We have merely attempted to argue that realizing income on this basis leads to unreasonable results in the income statement.

Under retrospective certainty of cash flows, however, even the balance sheet argument fails. Consider the land venture discussed in Case 1, dropping the assumption of ex ante certainty. Suppose the accountant at the end of period 4, after the liquidation of the firm, wished to reconstruct the firm's economic history. He knows the cash flow from operations and the subjective rate of interest with certainty. Under what justification can he capitalize the present value (as of the beginning of period 1) of the cash flows from periods 1 to 4? Even the 'well- offness' definition of Hicks will not support this balance sheet valuation. The investor derived no economic or psychological benefit from the firm until the land was purchased. He could not hypothecate the future earnings of the firm, since neither he nor the prospective purchaser could know at the beginning of

30

ECONOMIC INCOME AS AN ACCOUNTING CONCEPT

period 1 whether the timing and amount of cash flow from operations would be favourable.

But what is the relevant difference between ex ante and ex post certainty? It is not the accountant's measurement problem; the accountant can assign magnitudes to ex ante and ex post cash flows with equal reliability if they are both known with certainty. The difference occurs in the value of the cash flow to the investor. Because the investor cannot, in general, know future cash flows with certainty, he cannot derive economic benefits from the knowledge of these cash flows until they occur (or until their occurrence can be predicted with a sufficiently high a priori probability). However, many accountants only cite the measurement problem when discussing the difficulties of economic income."

Case Five: Partial ex ante Certainty

We have assumed so far that the future timing and amount of cash flow are either known with complete certainty or with complete uncertainty. Now we will examine economic income when the firm's ex ante knowledge concerning future cash flows is between these two extremes.

In the typical situation, the firm has high prior probabilities conceming some cash flows, and low prior probabilities concerning other future cash flows. For example, the firm has a high a priori confidence that the cash inflow from interest on United States Government Bonds will be of a certain amount at a certain time. There is comparatively higher uncertainty concerning the timing and amount of cash realized from a more speculative project such as the introduction of a new product. At least two factors influence the firm's ability to predict the future: 1. the mix of projects in the firm's investment portfolio (for example, the comparative amount of speculative projects and projects whose outcomes can be easily predicted), and 2. the amount of effort the firm invests in gathering infonnation for predicting the future. One would expect that these factors would change over time, and that such changes would materially affect the firm's ability to predict the future.

We will approximate the above situation by assuming that a firm knows some future events (the cash flows of periods t, t -(- 1, t -f 2, . . . , t -j- x) with certainty, and is completely uncertain about other future events (the cash flows of periods t -f X -f 1, t -f X + 2, . . . , N). We will further assume that x, the number of future periods into which the firm can forecast with certainty the timing and amounts of net cash flow, changes over time. This approximates the typical situation of the firm; there is a mix of certainty and uncertainty about the future, and this mix changes over time. Assume that the firm has a constant net cash flow from operations every year of $1,000, which it promptly distributes to its shareholders. The firm maintains a constant monetary level of owner's equity. Suppose X took on the following values for the first five periods of the firm's life:

17. See for example, Jaedicke and Sprouse, op cit, p 26, and Edward G. Philips, 'The Accretion Concept of Income', The Accounting Review, January 1963, p 17.

31

ABACUS

At beginning x (Number of periods in the future of period where net cashflows can be predicted

with certainty) equals

1 2 3 4 5 6

TABLE 3 Ability ofthe Eirm to Forecast Euture Cash Eiows

At a 5 per cent subjective interest rate, the capitalization under the economic income method at the beginning of each period would be as follows:

Period Present value at beginning of the period

1 1 1000(105)-! = $ 952 2 2 1000 (105)-i + 1000 (105)-2 =$1,859 3 3 1000 (105)-i + 1000 (105)-2 + 1000 (105)-3 = $2,723 4 3 1000 (105)-i + 1000 (105)-2 + 1000 (105)-3 = $2,723 5 2 1000 (105)-! +1000 (105)-2 =$1,859 6 3 1000 (105)-i + 1000 (105)-2 + 1000 (105)-3 = $2,723

TABLE 4 Calculation of Present Values

The economic income of the firm could then be easily calculated:

Period

(0 Beginning of period 1

1 2 3 4 5

Present value at the beginning of

the period

$ 0

$ 952 $1,859 $2,723 $2,723 $1,859

Present value at the end of the

period (Pi+i)

$ 952

Sl,859 $2,723 $2,723 $1,859 $2,723

Net cash flow during the

period (CFO

$ 0

$1,000 $1,000 $1,000 $1,000 $1,000

Economic income

(Pi+1 – Pi + CFi)

$ 952

$1,907 $1,864 $1,000 $ 136 $1,864

TABLE 5 Calculation of Economic Income

Notice the wide fluctuations in economic income. Such volatility does not seem consistent with the firm's constant armual net cash flow and constant internal rate of return.

32

ECONOMIC INCOME AS AN ACCOUNTING CONCEPT

This example illustrates an earlier point. Economic income describes the timing of changes in the firm's information (and therefore expectations) conceming the future. It does not describe the timing of changes in ibe firm's profitability (i.e. changes in the firm's internal rate of return). Fluctuations in reported periodic income were entirely due to the firm's varying ability to predict the future.

Although Solomons recognized this problem, he felt Alexander's concept of variable income could explain the effect of changes in expectations on economic income measurements.^^ Variable income was defined as 'equal to the net receipts from the security plus or minus any change in its value which was, at the beginning of the period, expected to take place during the period'.' ' Thus:

economic income = variable income + unexpected gains.^"

Some of the spurious variability in economic income created by changing expectations in an uncertain world would be explained by dividing economic income into variable income and unexpected gains. This dichotomy, however, does not completely solve the problem:

1. All variability in income caused by changing expectations is not factored out of variable income into unexpected gain. For example, Solomons states, 'We must include in variable income any change in the value of the enterprise which is the result of managerial activity during the year.'^* In the above example, x could well be a function of managerial activity (the selection of the asset portfolio or the determination of the extent of market research undertaken by the firm). If X is entirely determined by managerial policy, variable income equals economic income.

2. Although this paper is a critique of economic income as a theoretical concept, it is appropriate to note that variable income is even less operational than economic income. With economic income you merely have to predict future cash fiows. With variable income you have to segregate cash fiows into cash resulting from good luck and cash resulting from good judgment.22

Although ex ante certainty is never realized in actual measurement situations, some accountants have suggested that we try to estimate economic income as closely as possible with the information we have available. It is often pointed out that some cash fiows (i.e. interest from United

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