a proposed modification to residual income -- interest adjusted income

A Proposed Modification to Residual Income -- Interest Adjusted IncomeAuthor(s): Keith ShwayderSource: The Accounting Review, Vol. 45, No. 2 (Apr., 1970), pp. 299-307Published by: American Accounting AssociationStable URL: http://www.jstor.org/stable/244381 .

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A Proposed Modification to Residual Income-Interest Adjusted Income

Keith Shwayder

R ECENTLYmanywritershavesuggested that residual income be substituted for or supplemented to return on in-

vestment analysis.' In a recent survey of over 1,000 large American firms reported by Mauriel and Anthony,2 27 percent of the respondent firms indicated that they used residual income in divisional performance evaluation.

I will discuss some of the limitations of residual income in internal reporting and then describe interest adjusted income, a modification of residual income, which mit- igates some of these limitations.

RESIDUAL INCOME VS. RETURN ON

INVESTMENT ANALYSIS

The residual income of a division is the net income of the division less the product of the capital of the division times a required rate of return. If a division had capital of $1,000,000 and net earnings of $300,000 and the firm required a return of 20 percent from the division, the residual income would be

$300,000- (20% X $1,000,000) = $100,000.

In other words, residual income is entity net earnings less an imputed interest cost. In the example, the imputed interest rate is being defined as equal to the required rate of return (both are 20%) and the imputed interest cost is $200,000.

Residual income is superior to the return on investment ratio in at least three re- spects.

1. Motivation of Divisional Manager. If ROI is used as a performance indicator a divisional manager may reject projects whose internal rate of return is higher than the firm's cost of capital but lower than the average internal rate of return of the division. Acceptance of the project would make the firm better off but would make the performance of the division look worse. Suppose the firm estimates its cost of capital at 20 percent, and there is a division where the average rate of return is 30 percent. The manager of this division is motivated to reject a project with a 25

I David Solomons, Division Performance: Measure- ment and Control (Financial Executives Research Foun- dation, 1965), pp. 60-64. See also: John Coughlan, "Contrast Between Financial-Statement and Dis- counted-Cash-Flow Methods of Comparing Projects," NAA Bulletin, (June 1960), p. 9; and William Furlong, "Risk Income and Alternative Income Concepts," Management Accounting, (April 1967), p. 25. Solomons (p. 63) credits the General Electric Company with giving the name "residual income" to this concept.

2 John Mauriel and Robert Anthony, "Misevaluation of Investment Center Performance," Harvard Business Review, (March-April 1966), pp. 98-105.

Keith Shwayder is Assistant Professor of Accounting at the University of Chicago.

299



300 The Accounting Review, April 1970

percent return. Acceptance would lower his average return on investment.3

The residual income figure explicitly combines the two factors (income and capital) in a form which makes the goals of the divisional manager congruent with the goals of the firm. If the firm's cost of capital is 20 percent, maximizing the firm's wealth would imply investing in all projects which yield at least a 20 percent return. (Modifications to this statement due to differences in the riskiness of divisional and corporate asset portfolios will be considered later in the paper.) A division following this policy would maximize its divisional residual income.

2. Evaluation of Divisional Manager. Un- less the relationship between the cost of capital and divisional income is made ex- plicit, as in residual income, it is difficult to compare two divisions. Suppose a firm with a cost of capital of 20 percent had three divisions which turned in the following performance for the year:

Division Capital Income ROI

A $1,000,000 $300,000 30% B 2,000,000 550,000 27.5% C 3,000,000 600,000 20%

All three divisions have return on investment ratios which are at least equal to the cost of capital. Is it possible to rank the three divisions with respect to the goal of the firm implied by the 20 percent cost of capital? (Increase capital intensity until the marginal internal rate of return is less than 20 percent.) Division A at first glance appears to have the best performance as it has the highest ROI. Yet if the cost of capital is 20 percent, B has performed better than A. B has used $1,000,000 more capital and has earned $250,000 more income than A. The ROI on this increment is 25 percent. B's greater capital intensity than A is justified. (This comparison mea- sures the joint effects of wisdom in capital

investment and efficiency in operations.) On the other hand B has also performed better than C. C has used $1,000,000 more capital and has earned only $50,000 more income than B. The ROI on this increment is 5 percent.

This comparison can be iterated for all divisions using just the capital income and cost of capital for each division. However, the ranking is made much easier (especially when there is a large number of divisions) and more direct by using residual income. (The residual income of divisions A, B, and C is $100,000, $150,000 and $0 respec- tively.) Moreover, a more precise evaluation of the difference in performance among each division is available using residual income. (B earned $50,000 more residual income than A. The analysis above merely indicates B performed better than A). This example reinforces the point made under (1), in that incentives resulting from the evaluation system may be inconsistent with the best interests of the firm. More- over, residual income not only provides more goal congruence between the divisional manager and the firm than ROI, but it also facilitates interdivision com- parisons of performance.

3. Sensitivity of Performance Indicator to Changes in the Cost of Capital. It is desirable that the performance evaluation of the division be sensitive to changes in the capital market so that changes in the cost of capital affect the actions of divisional managers. In residual income such sensitivity can be obtained by modifying the division's required rate of return as the firm's cost of capital changes.

$Morton Backer, "Additional Considerations in Return on Investment Analysis," NAA Bulletin, (Janu- ary 1962), pp. 57-62, has suggested a system of side payments to offset the reduction of a division's ROI when a project is accepted which has a ROI smaller than the division's average ROI but which also has an internal rate of return higher than the company's cost of capital. In the writer's opinion such a system of side payments would be very difficult to administer.



Shwayder: Interest Adjusted Income 301

ALLOCATING IMPUTED INTEREST

TO ACCOUNTING PERIODS

Despite its many advantages there are at least three limitations of residual income.

1. Residual income is subject to all the imperfections of historical cost net asset valuation. Mauriel and An- thony4 vividly describe some of the pitfalls in using residual income in conjunction with generally accepted accounting rules for performance evaluation. However, residual income can be used in conjunction with other accounting rules (e.g., replacement cost accounting), eliminating some of the problems described in the Mauriel and Anthony article.

2. The allocation of imputed interest to accounting periods is arbitrary under residual income in that all imputed interest is expensed. Some imputed interest may have future service potential and therefore should be capitalized.

3. The use of a required rate of return (which includes a risk component) puts the accountant in the undesirable position of attempting to measure that which, at the current state of econo- metric methodology, is often un- measurable.

Interest adjusted income can mitigate the latter two limitations of residual income. In this section the allocation of imputed interest to accounting periods will be compared for the two methods. In the next section the problem of risk measurement in the imputed interest rate will be discussed.

Interest adjusted income is a proposal for incorporating implicit interest into the financial statements. Interest adjusted income is similar to price level adjusted accounting in that a rate (the rate of change in the price level for price level adjusted

accounting: the interest rate in interest adjusted accounting) is used to comprehen- sively adjust the financial statements. An objective of price level adjusted accounting is to adjust the accounting accruals and deferrals to reflect changes in the purchasing power of the dollar. An objective of interest adjusted income is to adjust the accounting accruals and deferrals to reflect the fact that a dollar today is more valuable to the firm than a dollar tomorrow.

Interest adjusted income can be described by comparing it to price level adjusted accounting:

1. The technical procedures used are similar to those for making price level adjustments to financial statements. In this paper, the technical procedures advocated in Accounting Re- search Study No. 6 (ARS No. 6) will be used.,

2. Like price level adjusted accounting, several asset valuation rules can be used for interest adjusted income.6 In this paper, interest adjusted income is used with historical cost accounting.

3. The default free rate is used as the adjustment factor instead of the rate of change in a price level index as in price level adjusted accounting. The default free rate for the year is ap- proximated by the one year U. S. government bond rate in effect at the beginning of the fiscal year.

To illustrate interest adjusted income consider the following example where a monetary and nonmonetary item are held for one accounting period. At the begin-

4 Mauriel and Anthony, op. cit. 6 Reporting the Financial Effects of Price-Level

Changes, Accounting Research Study No. 6, (American Institute of Certified Public Accountants, 1963).

6 Keith Shwayder, "The Capital Maintenance Rule and the Net Asset Valuation Rule," THE ACCOUNTING REVIEW (April 1969), pp. 304-316.




ning of the accounting period the effective yield for a U. S. government note with a one year maturity is 5 percent.

Balance . Balance Sheet at Adjust- Sheet at

Beginning Factor End of of Year Fatr Year

Cash $1,000 1.00 $1,000 Land at Cost 1,000 1.05 1,050

Total Assets $2,000 $2,050

Capital $2,000 1.05 $2,100 Retained Earnings

(imputed holding loss from holding cash) -0- (50)

Total Equities $2 ,000 $2,050

The reader can compare this adjustment procedure with page 11 of A RS No. 6.7 The adjustment procedure is identical, except the rate of change in the price level is re- placed by the default free rate as the adjustment factor.

Let us focus on the adjustment factors in more detail. Monetary items are valued at historical cost. Nonmonetary items are

varie Implicit Portion Carrying Asset (beginning interest to be value (end

of period) expensed of period)

Cash $1,000 $50 $50 $1,000

Land $1,000 $50 -0- $1,050

valued at historical cost plus an imputed holding cost (the valuation of the asset times an interest rate). The basic assumption justifying the valuation of the asset at an amount greater than its cost is that management acted rationally in holding the asset. By holding the asset, some other cost in replacing the asset was obviated.

For example, management may hold inventories to speculate against future price rises or to smooth production. The implicit holdings cost thus has future service potential if management's expectations are realized.

In some cases immediate replacement of the asset at its original cost is feasible. A cost obviation assumption yielding a valuation larger than this cost is hard to justify in these situations. (That is, it appears that the implicit holding cost does not have future service potential.) Thus inventory is valued in interest adjusted income at the lower of replacement cost or interest adjusted cost. This is analogous to the valuation of inventories at the lower of replacement cost or price level adjusted cost advocated in ARS No. 6.8 Like price level adjusted accounting no attempt is made in interest adjusted income to measure the "current value" of assets. Un- expired future service potential is valued at historical cost times an adjustment factor.

Therefore, the analysis of the two assets would show:

Comments

Since the replacement cost of cash at the end of the period is $1,000 there is no future cost obviation for the implicit interest. It is assumed that management is holding land as an investment. If the expected replacement cost of the land at the end of the period is less than $1,050, management would not have held the land. On the other hand if land is being used as a productive asset, part of the implicit interest might be expensed.

Because in this example and the next example an interest adjusted capital maintenance rule is used, there is an adjustment to capital. In a previous article in this journal9 I have examined the possibility of

7 Reporting the Financial Effects of Price-Level Changes, Accounting Research Study No. 6, op. cit., p. 11.

8 Ibid., p. 39. Shwayder, op. cit.




combining several different asset valuation and capital maintenance rules. If an historical cost capital maintenance rule had been used, there would be no adjustment to capital.

The example above was designed to show similarities between the technical procedure of interest adjusted income and price level adjusted accounting. Consider now an example designed to show the different ways implicit interest is treated in residual income and interest adjusted income. Division S of firm P was started at the beginning of the year with $1,000,000 cash. Inventory costing $1,000,000 is im- mediately purchased. At this point of time a historical cost balance sheet for Division S would appear as follows:

A ssets Equities

Inventory $1,000,000 Contributed $1,000,000 Capital

Total Total Assets $1,000,000 Equities $1,000,000

No sales were made until just before the end of the period when the division sold inventory costing $400,000 for $600,000 cash. $100,000 of miscellaneous expenses were paid at the end of the accounting period. The annual imputed interest rate is 5 percent. (In the next section alternative methods of determining the imputed interest rate will be considered.) Under residual income the income statement for the division would show:

Sales $600,000 Cost of Goods Sold 400,000

Gross Margin $200,000 Less: Expenses 100,000

Income before Imputed Interest $100,000 Less: Imputed Interest 50,000

Residual Income $ 50,000

The balance sheet for Division S would show:

Assets Equities

Cash $ 500,000 Imputed Interest "Owed" to P $ 50,000 Inventory 600,000 Contributed Capital 1,000,000

Retained Earnings 50,000

Total Assets $1,100,000 Total Equities $1,100,000

Under interest adjusted income the income statement for Division S would show:

Unadjusted Adjustment Discussion Adjusted A mount Factor A mount

Sales $600,000 1.00 No adjustment needed since $600,000 sales occur at end of period.

Cost of Goods Sold 400,000 1.05 See subsequent text. 420,000

Gross Margin $200,000 $180,000 Less: Expenses 100,000 1.00 No adjustment needed since 100,000

expenses occur at end of pe- Interest Adjusted Income $100,000 riod. $ 80,000




The balance sheet for Division S would show:

Assets Equities

Cash $ 500,000 Contributed Capital $1,050,000 Inventory 630,000 Retained Earnings 80,000

Total Assets $1,130,000 Total Equities $1,130,000

In residual income all of the imputed interest for the period ($50,000) is expensed; under interest adjusted income some of the imputed interest may be capitalized. Under interest adjusted income the $50,000 is allocated between the ending inventory ($30,000) and the cost of goods sold ($20,000). This provides better matching in that the imputed holding costs attrib- utable to the inventory will be matched with the revenue from the sale of the inventory.

Under interest adjusted income the timing of the realization of the imputed interest follows the accruals and deferrals of balance sheet items. That is, the appor- tionment of the imputed interest to present and future periods depends upon the asset valuation rules. (If the ending inventory had been valued at $500,000 and the cost of goods sold had thus been $500,000, $25,000 of the imputed holding cost would have been allocated to the ending inventory and $25,000 would have been allocated to cost of goods sold.) Under residual income the timing of the realization of the imputed interest is relatively independent of the accounting accruals and deferrals.

In general, if one feels that the accounting accruals and deferrals provide good matching of costs with revenues, he will tend to favor interest adjusted income over residual income.10

CHARACTERISTICS OF THE DEFAULT FREE RATE

One of the main problems of implement- ing either residual income or interest ad-

justed income is the determination of the imputed interest rate. Because of measurement problems it may be desirable to ex- clude risk of default from the imputed interest rate.

Consider a capital market (say the market for corporate bonds) where investors require a given rate of return on securities. It is meaningful to divide this required rate of return into two components:

1. A TimePreference Component. The investor would have a time preference for cash even if there were no risk of default of the payment of the principal and interest. Thus, loans to es- sentially riskless borrowers (say to the U. S. government1' have a pos- itive interest rate.

2. A Risk Premium Component. For each borrower in the corporate bond market, there is a probability that this borrower will default on the in-

10 Unless he believes that the service potential of the imputed holding cost of an asset and the original service potential of the asset (whose surrogate is the asset's historical cost) expire in different accounting periods. In the example above, the purchases for the period, $1,000,000, are allocated between the balance sheet (ending inventory-$600,000) and income statement (cost of goods sold-$400,000). As mentioned above, if one accepts this allocation he would be likely to accept a similar allocation of the imputed holding cost. How- ever, as described earlier, sometimes there is evidence that the service potential of the imputed holding cost expires at an earlier time than the other service potential of the asset. If the replacement cost of the ending inventory is $600,000 there is evidence that the service potential of the imputed holding cost has expired by the end of the year.

11 The U. S. Government securities rate is a default free rate rather than a risk free rate in that security holders have no hedge against changes in the structure of interest rates. If the risk free rate can be determined, the dichotomy used in the portfolio theory literature, risk free rate and risk premium, should be used.




interest and/or the principal of the bond. The higher the risk, the greater the interest demanded by the lender. In addition to the risk of default there is the risk of fluctuation in the market value of the security. Similarly for securities in the stock market, the rate of return demanded for common stocks due to uncertainty concerning dividend payments is greater than the default free rate.

These two components of the required rate of return differ in at least three areas:

a) The time preference component is common to all securities; the risk premium component is peculiar to a particular security. The time preference component is a function of a particular state of the capital market at a particular point in time. The risk premium component is a function of the perceived risk of a particular security.

b) The time preference component is a function of the maturity of the security (and the risk of change in the default free rate); the risk premium component may or may not be afunction of the maturity of the security or investment. Fisher12 has shown that the time preference component depends upon the aggregate impatience of society for consumption goods, a function of time.

Robichek and Myers"3 have challenged the relevance of the commonly made implicit assumption that risk is always a function of time. They consider the example of an investor who has the choice of financing one of two voyages, one of one year, the other of two years. The voyages are fully insured against losses at sea but the value of the cargo brought back on each voyage is uncertain and will only be known when the ship returns. The expected discounted present value (at the default free rate) of each voyage is the same and the uncertainty associated with each voyage (the probability distribution of the value of the cargo) is identical. Then the investor should be indifferent to the

two voyages. Using the same risky discount rate to evaluate the two alternatives will not give this answer. The use of such a rate is based on the implicit assumption that risk is directly proportional to the length of time the cash is tied up. This assumption is incorrect for the two voyages.

The risk premium need not be expressed as a required increase in the rate of return; it may also be expressed as a required excess value or percentage of excess value. Thus, if a ten year U. S. government bond with a 5 percent coupon sells at 108.18 (to yield 4 percent) and similar obligations of a corporation sell at par (to yield 5 percent), the risk premium can be expressed as a 1 percent increase in the required rate of return, as a $8.18 required excess present value on each $100 bond or as a 7-1 percent excess present value percentage (8.18/ 108.18). If the risk premium is not a function of time, it is more convenient to ex- press it as a required excess present value. For example, such an approach makes the investment decision cited in the Robichek and Myers article easier to solve.

c) The time preference component can be objectively measured; there are severe es- timation problems in measuring the risk premium. The expected rate of interest on one year U. S. government bonds can be observed as a good surrogate to the expected one year default free rate.14 Due to the difficulty of determining the market's expectations concerning future dividends it is difficult to measure, ex ante, the risk

12 Irving Fisher, The Rate of Interest, (The Macmillan Company, 1930).

13 Alexander Robichek and Stewart Myers, "Concep- tual Problems in the Use of Risk-Adjusted Discount Rates," Journal of Finance, XXI, No. 4, (December 1966), pp. 727-730. A similar point is made in Harold Bierman, Jr. and Seymour Smidt, The Capital Budgeting Decision, (The Macmillan Company, 1966), pp. 322- 326.

14 The bond rate is a default free rate but is not a completely risk free rate because there is no hedge for changes in the default free rate. The ideal security for finding a risk free rate would be a U. S. bond of the same maturity whose interest rate was dependent upon the current U. S. bill rate. However, if the holding period of the investor is one year, the one year default free rate is equal to the riskless rate.




premium or alternatively the required rate of return of equity securities.

APPROPRIATENESS OF THE DEFAULT

FREE RATE FOR DIVISIONAL PER-

FORMANCE EVALUATION

Which imputed interest rate should be used to measure the performance of a division? Under certain conditions it is possible to estimate a cost of capital which is relevant to divisional performance evaluation by observing the market yield of the firm's equity and debt."5 A nonexhaustive listing of these conditions would include the following:

1. Debt and equity investors can ac- curately estimate the risk characteristics of the firm.

2. The accountant can estimate the future earnings projected by equity investors.

3. The risk characteristics of the division are identical to that of the firm.

4. The capital turnover of the division is comparable to that of the company. If the division had the same riskiness as the firm but a different capital turnover, then a different interest rate should be used for the division than for the company."6

5. The firm is not in a condition of capital rationing. Here the definition of capital rationing used by Bierman and Smidt is used. The firm can bor- row or lend any quantity of funds that it desires at a given market rate of interest."

It is unlikely that all these conditions will be met. An alternative approach is to incorporate the default free rate into divisional performance measurements and allow the user of the divisional performance measurements to attach his own risk penalty. Based on similar reasoning, Bierman and Smidt advocate the use of default free rate in discounting cash flows

for capital budgeting decisions and the making of risk adjustments separately.18

There are two aspects to determining a risk adjustment factor:

1. Determining the riskiness of the project or set of projects.

2. Assigning an adjustment factor based on the risk aversion of the user of the financial statements.

Unless a marketplace exists where the risk aversion of the user is revealed, it is very difficult for the accountant to measure this risk aversion. Often the accountant has more information than the user concerning the riskiness of the project. How- ever, this information is not useful unless the accountant is able to translate it into an appropriate adjustment factor or unless the accountant can transmit this information in a form the user can utilize in his adjustment factor.

INFORMATION LOST BY USING THE

DEFAULT FREE RATE

Having obtained an adjustment for risk, there is the problem of relating this adjustment to the other accounting data. The accountant has more information concerning the accounting accruals and deferrals than the user. How useful is this information with regard to the incorporation of the risk adjustment into the accounts?

In interest adjusted income, implicit interest is proportional to the unadjusted cost of the asset and to the length of time between the acquisition of the asset and the expiring of the asset's service potential. As described earlier, the default free component of the required rate of return follows this relationship while the risk component may or may not. That is, risk may not be directly related to time. If both

15 Ezra Solomon, The Theory of Financial Manage- ment (Columbia University Press, 1963), pp. 76-78.

16 Robichek and Myers, op. cit., p. 730. 17 Bierman and Smidt, op. cit., p. 181. 18 Ibid., pp. 326-331.




components are directly related to time then interest adjusted income with the firm's cost of capital as the implicit interest rate would give good results.

The user cannot make the interest adjustment himself. Earlier, the similarity between the procedures for interest adjusted income and price level adjusted accounting was shown. Consider the problem of the user attempting to make his own adjustment for price level changes to a series of historical cost financial statements. He cannot make this adjustment unless he can reconstruct a schedule of the acquisitions and disposals of assets and liabilities. The price level adjustment cannot be allocated among income statement and balance sheet items without this schedule because this adjustment is based on the accountant's accruals and deferrals whose precise timing is not given to the user in the traditional financial statements. Similarly, the user cannot make the interest adjustment to the financial statements without the accountant (unless the user can reconstruct the schedule of acquisitions and disposals of assets and liabilities).

If risk is not directly related to time, there is no reason to tie the realization of the risk penalty to the other accounting accruals and deferrals and the user can adjust the financial statements for the risk component as well as the accountant.

Summarizing, three problems in includ- ing risk in performance evaluation of divisions have been identified:

1. Measurement of risk. 2. Assigning a penalty to this risk based

on the risk aversion of the user (the evaluator of divisional performance.)

3. Matching the risk penalty with other accruals and deferrals.

The accountant can often estimate risk better than the user. However, it is usually very difficult for him to translate this estimate into an adjustment factor reflecting the risk aversion of the user due to a pauc- ity of market information. When risk is not a function of time the user can incorporate the adjustment factor into the accounts as easily as the accountant. There is, therefore, a strong argument for con- sidering the use of a default free imputed interest rate for divisional performance evaluation and letting the user make his own adjustment for risk.

CONCLUDING REMARKS

Interest adjusted income appears to be superior to residual income in that the realization of implicit interest is related to the timing of accounting accruals. Some implicit interest should be expensed, but in some situations part of the implicit interest should be carried forward as an asset. Moreover, for internal reporting it often makes sense to use the default free rate as the implicit interest rate. The case for the default free rate in external reporting is even stronger where comparatively more importance is given to objectivity'9 and comparability.

19 Here I am using the term objectivity in the sense that Yuji Ijiri and Robert Jaedicke ["Reliability and Objectivity of Accounting Measurements," THE Ac- COUNTING REVIEW, (July 1966), pp. 474-4831 use this word, as synonymous with sampling error.



a proposed modification to residual income -- interest adjusted income

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