DISCUSSION PAPER

Report No,: DRD84

The Algebra of Inflation Accounting

James Tybout

July 1984

Development Research DepartmentEconomics and Research Staff

World Bank

The views presented here are those of the author, and they should not beinterpreted as reflecting those of the World Bank

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AR-01 2a/JTD /#3

THE ALEORA F INFLATION ACCOUNTING

by

James Tybout

The World Bank

July 1984

This papcr vas prepared for World 1,1atk research project "liberalization and

Stabilizatio J in the Souithen Coe" (R.10 T7h-85), Te author is grateful to

Jaitr,c de2 Mejo lor con umts on an earl:.Lr drft. The views and interpretations

pre,cated h arevi ar v th-oc of the puthor e,ri should not be< attributed to the

World Bjunk or tsc njffilin:s.

Abstract

This paper develops algebraic representations of the various possible

distortions that inflation can introduce in financial statements, and of the

associated corrections that have been develODed by accountants. Adjustments

to balance sheets and income statements are presented for two basic cases:

general inflation, and inflation cum changing relative prices. Empirical

evidence concerning the impact of these adjustments is reviewed, and it is

noted that when inflation rates are substantial, the change in accounting

figures can be quite dramatic.

AR-012a/J'TD//3 - 1 -

OVERVIEW

In developing countries, analyses of the corporate sector often must

proceed on the basis of inflation-distorted financial statements. If these

distortions are ignored, findings regarding firms' financial structures and

earnings rates may be grossly in error. What appears to be an insolvent firm

may be simply an illiquid one; what appears to be a negative net profit rate

may be positive; and what appears to be a positive gross earnings stream may

be negative. Misreadings of these conditions can lead to inappropriate policy

recommendations and major resource misallocations.

To aid researchers who must interpret inflation-distorted financial

statements, this paper develops an algebraic exposition of the biases in

statements that firms have prepared according to traditional accounting

techniques, and of the methods available for their correction. Section I

introduces a simple representation of financial statments which do not suffer

from inflation distortions. Using this representation as a reference point,

section II demonstrates how traditional accounting practices lead to biases

when general inflation is present. Also, empirical evidence regarding the

impact of corrections for such biases is reviewed. Section III extends the

framework developed in previous sections to accomodate the possibility that

relative price changes accompany general inflation, and reviews additional

empirical evidence. Finally, section IV summarizes the four basic distortions

discussed in this paper and offers some general observations on the

circumstances under which they are likely to be significant.

I. FINANCIAL STATEMENTS IN A WORLD OF STABLE PRICES

A. Balance Sheets

Corporations regularly prepare two basic financial statements. The

AR-012a/JTD///3 - 2 -

first is a balance sheet,, which reports stocks of assets and liabilities.

From this statement, inferences can be drawn regarding such things as the

quality of a corporation's assets, the ease with which these assets can be

liquidated, and the distribution of claims on these assets between creditors

and shareholders. For expository purposes. a highly simplified balance sheet

is presented in table 1. Notice that all physical magnitudes are measured in

units that have a value of one base-period currency unit, and that all price

indices are defined with reference to this period (i.e., PO= P = P = 1).

Because each item in the balance sheet is expressed in terms of its value at

time T, this statement is "undistorted" and will serve as a reference point in

sections below.

B. Income Statements

The second basic financial statement prepared by corporations is an

income statement. This item-by-item summary of revenues and costs allows one

to isolate the sources of fluctuation in a corporation's net income stream,

and to formulate opinions regarding future performance. A highly simplified

income statement is presented in table 1. 1/ Bere, too, physical magnitudes

are measured in units that sell for one base period currency unit. Output is

assumed to sell at the general price level, PT, and inputs are assumed to sell

xat the inventory price, P . So long as prices are stable over the life of the

firm, entries in this statement may be interpreted to represent real

magnitudes. Accordingly, as with the balance sheet introduced above, this

1/ Note that to economLze on notation, labor costs have not been separatedout. The reader should either view "sales revenue" as net of thesecosts, or view "other expenses" as inclusive of them. Taxes have alsobeen ignored.

AR-012a/JTD/113 3 -

Table 1: The Structure of "Undistorted" Financial Statements

Balance Sheet at time T Income Statement for the Period 0 to T

C DT Gross Sales Revenue QPT

P XT Cost of Sales PT[X +U-XT]

k KPT WT Initial. Inventories X0

Purchases UPX

Closing Inventories XT T

Depreciation yKOPk

Other Expenses EPT

Net Income [Q-E]PT - [XO+U-XT]PT - yKOPk

Ct = monetary assets at time t: cash, deposits, net receivables

D t= monetary liabilities at time t: total debt

X = inventories at time t

K = fixed capital stock at time t

W = net worth at time t

Q = physical sales volume between time 0 and time T

U = volume of inputs purchased between time 0 and time T

E = real volume of other expenses between time 0 and time T:interest, overhead, administrative and marketing costs

Y depreciation rate per fiscal period on fixed capital

P = general price level at time t

P = price of inventories at time t

Pik price of fixed capital at time tt

AR-012a/JTD/#3 - 4 -

income statement will be used as an "undistorted" reference point in sections

that follow.

There exists a close relationship between balance sheets and income

statements. Specifically, when a corporation pays no dividends and neither

retires nor issues shares, the change in its net worth from one fiscal year to

the next coincides with its net income. To see why, note that whenever

revenues accrue, these are either used to defray production costs (i.e.,

wages, materials, interest, etc.), to acquire assets, or to retire debt.

Hence asset acquisitions plus debt retirements represent revenue in excess of

production costs, or net income. But clearly, from table 1, they also -

represent the change in net worth. This link between income statements and

balance sheets will prove central to the discussion that follows.

II. FINANCIAL STATEMENTS IN THE PRESENCE OF GENERAL INFLATION

Firms must somehow.estimate the conceptual magnitudes introducee in

table 1. For expository purposes, suppose they do this using a pure "historic

cost" (HC) accounting system. (Variants of this system are quite common among

developing countries.) Then each item reported in their financial statements

is a simple cumulative reflection of previous transactions. For example,

abstracting from depreciation adjustments, a balance sheet entry of 20 pesos

for fixed capital may reflect a 5 peso capital expenditure 3 years ago, and a

15 peso expenditure last year. Similarly, in the income statement, each flow

entry is calculated as a simple aggregation over the recorded valies of all

outlays or receipts of a given variety: A gross sales figure of 24 may

reflect the receipt of 2 pesos at the end of each month In the fi3cal year.

So long as all prices are stable, the [ntertemporal aggr!gation

implied by HC accounting norms is justifiable, and the conceptual magnitudes

AR-012a/JTD///3 - 5 -

introduced in table 1 are well approximated by recorded figures. However, in

an environment where the price level is rising, this accounting method leads

to a number of potentially important distortions. These distortions, and the

accounting system that has been developed to deal with them, are now reviewed

for the case in which all prices in the economy are rising at the same

(perfectly observable) rate.

A. General Inflation and Balance Sheets

To explain the bias that inflation creates in HC balance sheets, it

is first necessary to distinguish between "monetary" and "nonmonetary"

items. The former are assets and liabilities whose value is fixed by contract

or statute in terms of the domestic currency, such as deposits, accounts

receivable, and debts. The latter are all other items except net worth, or

for present purposes, inventories and capital. (Net worth is a residual

account.) Recorded values of monetary items are not distorted by inflation

under an HC accounting system because changes in the price level do not affect

their nominal value. However, nonnmonetary items generally increase in

nominal value during inflationary periods, and therefore tend to be carried on

HC books at less than their current worth. This is the esssence of the

inflation distortion.

Understatement of nonmonetary items means that firms' financial

status is misrepresented in several respects. First, firms appear to have

smaller and more liquid asset stocks than they actually do. Second, the

fraction of total assets which is debt-financed is exaggerated. Finally,

because net worth growth is understated, nominal and real income measures

based on this statistic are too low.

AR-012,/JTD///3 - 6 -

Accountants have developed a system for rectifying these inflation-

induced misrepresentations in KC financial statements. This system -- known

variously as "historic cost/constant dollar," "general purchasing power," or

"constant purchasing power" (CPP) accounting -- is based on a straightforward

principle: historic values of nonmonetary items should be brought forward to

imputed current values using a general price inflator. More precisely, each

nonmonetary asset should be valued at its historic cost, weighted by the ratio

of the current price level to the price level on its acquisition date.

If fixed capital and inventory prices are not changing relative to

the price level, and if the general rate of inflation is accurately observed,

this adjustment will yield the conceptually correct balance sheet introduced

in table 1. Moreover, because CPP-corrected net worth figures will represent

the nominal wealth of shareholders under these assumptions, growth in net

worth over the fiscal period will be interpretable as nominal income.

To illustrate the calculation of corporate incoma from CPP-corrected

balance sheets, table 2 presents these statements for the fiscal years ending

at times t=O and t=T. Here, to isolate net worth on the right hand side of

each statement, gross monetary assetL and liabilities have been replaced by

net monetary assets (M,=C,-D t), which may be of either sign. Also, because it

is assumed that all price indices are growing at the same rate, the general

index, Pt, has been used in place of Px and Pk. Finally, notice that nominalt te

income, expressed in terms of the various balance sheet items, has been decom-

posed into two components. The first is real income, and the second, termed

"capital maintenance", is the amount by which net worth at time 0 would have

had to grow in order to be undiminished ir real terms at time T, or

w0 [(PT/Po)-1'

AR-012a/JrD/#3 - 7 -

Table 2

CPP-Corrected Balance Sheets and Associated Net Income

Balance Sheet at Time 0 Balance Sheet at Time T

0 M

Xop0 1rPT

K 0P0 KPT WT

0 T W r - yK ]PT

T WO = 'MT - MO(PT/PO) + (XT - XO )PT+ l T

+ {XO T 0) + KO T 0) + M 0(P ) -1]}

= real income + capital maintenance

Mt = net monetary assets at time t; i.e., cash, net tradecredit, and other financial assets minus all debt

X = inventory stock at time t expressed in base period prices

K = fixed capital stock at time t in base period prices

W = net worth at time t

P = general price level at time t

y annual rate of depreciation of fixed capital

I = gross fixed investment during fiscal year, in base periodprices

= KT - (1-y)KO

AR-0J2a/JTD///3 - 8 -

B. General Tnflation and Income Statements

Intertemporal compartsons are embodied in income statements as well

as balance sheets and, in the presence of inflation, these result in several

additional distortions under the HC system. First, historic input costs are

understated relative to the sales revenues they generate because they are

recorded earlier. Second, depreciation costs are understated relative to

actual replacement costs because they are based upon the historic cost of the

capital stock. Finally, no recognition is made of the fact that monetary

items held over time do not maintain their real value. If these distortions

are left uncorrected, the contribution of various revenues and costs to net

income will be misrepresented. Moreover, the resultant net income figure will

not agree with the CPP-corrected figure derived in table 2 from balance

sheets. It is now explained how CPP accounting deals with these problems.

For reasons that should become apparent later, the discussion begins by

developing expressions for income statement items in midyear prices, then

these expressions are converted to year-end magnitudes.

1. Cost of Goods'hold

First consider the input cost distortion. If firms were to calculate

both input costs and the resultant sales revenues using prices prevailing when

the latter accrued, they would correctly record gross earnings between time 0

and T as total sales minus total costs, each in midyear prices. Assuming

physical sales and input acquisitions take place at the constant rates q=dQ/dt

and u=dU/dt, respectively, this gross earnings figure would be 1/

jO [q-u]Ptdt = [Q-U]PA'

1/ In this section the price level is represented as linear in time inorder to conform with the accounting literature.

AR-012a/JTD///3 - 9 -

where A = T/2. Unfortunately, it is not feasible to calculate the cost of

each input used on the basis of prices prevailing when the corresponding

output is sold. Instead, firms calculate the cost of goods sold as initial.

invenLories plus purchases, less closing inventories. This system often leads

to a systematic understatement of costs in an inflationary environment. For

example, suppose the physical inventory stock is constant at X throughout the

fiscal year, the average input remains in inventory for a period 2A before

use, and a "first-in, first-out" (FIFO) accounting rule is used. I/ Then the

calculated cost of goods sold is not UPA' but a figure smaller by the

amount X [P - P'], where P'=P and P' P_:T 0T T-A 0 -A

initial inventory XPOT

+ purchases fJOuPtdt

- closing inventory XPTT

Cost of goods sold UPA - X[PT -0

Clearly the understatement of input costs occurs because the increase

in the value of inventories due to inflation has been implicitly treated as a

capital gain and an increase in the earnings stream. An expression for income

which embodies this bias is presented in line 5 of Table 3, where the first 5

lines represent the basic items in an historic cost income statement. (It is

no longer assumed that inventory stocks are constant.)

1/ Under a FIFO valuation rule, each input taken from inventory for use isvalued at the price prevailing when the oldest good was placed ininventory.

Table 3- CUP Income Stactvent *

Item Mid-year prices Year end prices

(1) Sales QP

(2) Cost of Goods sold [(2.1)+(2.2)-(2.3)] X0 0 TPT + UP

(2.1) beginning inventories XPO

(2.2) purchases UPA

(2.3) closing inventories XTP'

(3) Other Operating Expenses EPA(overhead and interest)

(4) Depreciation yKO

(5) Historic Cosr Income [(1)-(2)-(3)-(4)] [Q-U-E]PA+XTP'-XOPO-YKO

(6) Adjustments for General Inflation [(6.1)+(6.2)] X0 A 0JT(A P'] + yKO [A-1

I

(6.1) cost of goods sold 0 0 A/PO) - 1]

K PT [(PA')- 1

(6.2) depreciation YYOPA- 1]

(7) Adjusted Income [(5)-(6)I (Q-U-E]PA T 0 A-KOPA [Q-U-E]P +[% -X 0 T-KOPT

(8) Inflation Loss on Monetary Assets ** MO(PT/PO) +[Q-E-U]P - I?

(9) Net Adjusted Income (7)-(8) [I-yK T

* Account format is from Scapens (1981); algebraic representation is the author's.

** Refer to table q.

P price level at time t Q - sales during year in base period prices

P - price level at time t-A U * intermediate good purchases during year in base period prices

T M time index at end of fiscal year E overhead and interest expenses during year in base period prices

0 M time index at start of fiscal year K 0 beginning of fiscal year capital stock in base period prices

A - T/2 Y - annual depreciation rate on capital stock

- 1/2 average time spent by a good in inventory M - net monetary assets at time t

I - grCss fixed investment during fiscal year, in base ?riod prices

AR-012a/JTD/#3 - 11 -

The undervaluation problem present in the top of Table 3 is

eliminated under CPP accounting norms by valuing inventories in terms of the

same prices as sales and purchases, i.e. by weighing the initial and closing

book values of inventories by P PO and PA /P , respectively. This

correction to historic cost of goods sold is typically entered as a separate

item in an."inflation adjustments" account (refer to line 6.1 of table 3).

If a "last-in, first-out" (LIFO) valuation procedure is used, and

inventory stocks are stable, no adjustment will be necessary. This because

under LIFO, the book value of inventories does not grow with inflation.

Rather, the "stock-at-beginning can be thought of as remaining untouched

throughout the year.. .forming a kind of permanent nucleus. At the end of the

year, still valued at its historical cost, it becomes stock-at-end" (Baxter,

1975, p. 84). For this reason, many have advocated the use of LIFO as a

simple means to eliminate understatement in the "cost of goods sold"

account. However, because it is an ad hoc "fix-up" that introduces new biases

in balance sheet inventory values and does not perform well when inventories

are not stable, some have argued in favor of the FIFO-plus-correction approach

(e.g., Baxter, 1975, Chapter 9).

2. Depreciation Costs

Biases in EC income statements because of inaccurate "cost of goods

sold" figures are very likely to be exacerbated by historic value depreciation

figures. Here the imputed reduction in physical capital due to wear and tear

is a fraction of the initial stock, valued at historical purchase prices, Sup-

pose the initial capital stock, K0 , is expressed in terms of base year prices

(perhaps it was purchased in Lhe base year), and that the fraction y of this

stock will be depreciaLed in the current year. Then at year end, the correct

value oE the capital stock in mid year prices is [I + (1-y)KO PA, where I is

AR-012a/JTD/#3 - 12 -

current year gross investment expressed in base year prices. The associated

correct value of depreciation is KO YPA . However, under HC bookkeeping

these items are recorded as IPA + K 0 (1-Y) and K0y, respectively, meaning

K (1-Y) and yK0 both should be adjusted by the factor P A Under CPP

accounting, the difference between historical depreciation cost and adjusted

depreciation cost, i.e., KO YPA- 1], is entered in the inflation adjustment

account along with the adjustment to "cost of goods sold" (see line 6.2 of

table 3). After netting out historical depreciation and these charges, income

in midyear prices becomes

(1) Y = [Q-U-E]PA + [XT 0 A- yKO A'

where E is "other expenses" of the fiscal year, expressed in base year prices.

Notice that because dividends and new share issues or retirements

have been disallowed, this partially corrected income measure must equal net

purchases of inventories, fixed capital, and net monetary assets. Also, be-

cause the average price during the year of the former two will be given byrPA,

the first term of equation I reflects the amount of earnings allocated to

gross fixed investment and net monetary asset purchases (i.e., IPAhMT .

It follows that the income measure in equation I may be rewritten as:

(2) Y = [M - M + [X -X P + [I - yK PT 0 T 0 A 0 A

This form of equation 1 will prove useful below, when the inflation loss from*

holding net monetary assets is discussed.

3. Loss Due to Net Monetary Asset Holdings

The final correction to HC statements deals with the fact that

AR-012a/JTD/#/3 - 13 -

monetary assets and liabilities shrink in real value over time. Without this

-correction, misleading conclusions regarding firm profitability are likely to

be drawn. For example, during inflationary times, nominal interest charges

include a premium to offset the expected decline in the real value of debts.

If the gain that firms enjoy from this decline is not recorded as a revenue,

but all of the nominal interest cost is recorded as a cost, the firm will

appear less profitable than it actually is. Similarly, if firms which carry

cash and interest bearing deposits were to record all financial revenues as

income, but not deduct from this the amount of income necessary to sustain the

real value of their monetary assets, they would be overstating profitability.

The CPP correction to HC accounts which adjusts for losses and gains

on monetary items may be viewed as a counterfactual exercise. It is an

approximate answer to the question: If all monetary assets and liabilities

had actually been perfect inflation hedges, how much more (or less) would the

firm have earned? This issue is addressed with calculations along the lines of

those presented Table 4.- First, initial net monetary assets, M0 , would have

grown to a value of MO(P T /P0) by the period's end if they had been perfect

hedges. Likewise, if the sales revenue accruing at time t had all gone into

perfect hedges it would have grown to [Pt q]T Pt) by period's end, making

total revenue simply FTQ, or PT /PA times recorded gross sales revenues.

Outlays for inputs and other expenses would have to have been realized by

liquidating hedges, and hence must also be scaled by PT /PA before subtracting

them. Finally, any fixed capital investments would have been an alternative

For a fuller discussion of these calculations, see Scapens (1981).

AR-012a/JTD/#3 - 14 -

Table 4 Net Inflation Loss on Monetary Items

(1) Net initial monetary assets m (P /Pwith perfect hedging

(2) Gross sales with perfect QPThedging

(3) Input and other expenseswith perfeet hedging [U+E]P

T(4) Fixed capital purchases IP

(5) Net end of period monetaryassets assets MT

(6) Inflation loss on monetaryassets [(1)+(2)-(3)-(4)-(5)] M0 T P0 )-T + [Q-U-E]PT -PT

* General format taken from Scapens (1981, table 4.4); algebraicrepresentation is the author's. See table 3 for variable definitions.

AR-012a/JTD/#3 - 15 -

to monetary asset accumulation and must be subtracted in year end prices. 1/

The resultant (hypothetical) net end-of-period monetary asset stock would have

been

M0 T/ 0 PT[Q-U-E] - IPT

If the actual end-of-period net monetary asset stock is subtracted from

thisfrom this figure, the difference may be viewed as that amount of earnings

which was foregone because monetary assets were not held in inflation hedges

(refer to line 6, table 4).

To arrive at a CPP-corrected income figure in year-end prices, one

first scales the income expression in equation 1 (or 2) up by the factor

PT /P . Then the monetary correction from Table 4, which is already in year-

end prices, is subtracted (refer to the right hand column of Table 3). To see

the logic of this, note that for nonmonetary items (inventories and

depreciation), this scaling roughly means reporting actual values at a later

point in time. But for cash flow items, it involves the assumption that all

flows accrue to, or are drawn from, inflation hedges. Hence scaling all items

in the income statement by PT /PA means assuming no monetary loss. Note that

after the monetary asset correction, we arrive at a net adjusted income (line

9) that corresponds exactly to the.CPP measure derived from balance sheet

items in Table 2.

Monetary loss accounts can, of course, also be used to arrive at an

adjusted income figure in mid-year prices. For this exercise the year-end

1/ Inventory investments are already included in total input purchases, andneed not be subtracted again.

AR-012a/JTD/#3 - 16 -

correction in line (6) of table 4 is weighted by (P /PA T

(3) 0 (PA/PO)M (PT' /PT)+PA[QUE]-IPA(3) M A 0 T PA T AQUE]IA)

then it is subtracted from the mid-year income figure (given in the left hand

column of Line 7, Table 3).

Some additional insight into the monetary correction item can be

gained by examining this mid-year variant. Recall from the discussion of

equation 2 above that the last two terms of (3) represent the actual change in

net monetary assets, or (y-MO). Hence (3) may be calculated as

(4) M - T PA /PT )M0 (PA /PO

or the nominal change in net monetary assets, less the real change in net

monetary assets, expressed in mid-year prices (e.g., Scapens, Note 10 to Table

6.18). This form of the monetary correction is easier to calculate than the

relatively cumbersome expression presented in Table 3, particularly when

sources and uses of funds are numerous. Accordingly, it is what is likely to

be used in practice.

One final observation on monetary corrections may be illuminating.

Converting (4) back to a year-end figure, line 6 of Table 4 may be expressed

as

(5) [M [M T A MT4O (P T O0

[14 T-M P T /PA )-t] + M [(P T ) - 11

AR-012a/JTD///3 - 17 -

'Here the first term represents losses on those net monetary assets which were

accumulated over the year (assuming dM/dt is constant), and the second term

represents losses on initial monetary assets.

C. Evidence on the Effects of Corrections for General Inflation

In the United States, the Financial Accounting Standards Board (FASB)

has required since 1979 that large firms prepare CPP accounts to augment HC

figures. 1/ The impact on reported profit rates has quite probably been

considerable. As reviewed by Scapens (1981), studies by Jones (1949),

Rosenfield (1969) and Pearcy (1970) compared CPP to conventional accounting

using various data bases and found (1) differences in profits during periods

of moderate inflation can be substantial, (2) the impact of CPP adjustments

varies considerably from company to company, and (3) CPP profit measures are

generally lower than unadjusted figures. More recently, Parker (1977)

obtained very similar results in his sample of 1050 U.S. firms for the period

1972 through 1974. Finally, using aggregate U.S. flow of funds accounts,

Cagan and Lipsey (1979) generated results qualitatively similar to those

obtained at the firm leval, but they found that during some recent periods

inflation-adjusted profits exceeded unadjusted figures considerably 2/

1/ These firms have also also been required to prepare supplemental figureson a "current value" basis, which will be discussed in section IIIbelow.

2/ In the Cagan and Lipsey (1979) study, inventory valuation adjustmentsranged from having virtually no impact on profits (1961 and 1962) tocutting profits by 60% (1974). Depreciation adjustments actuallyincreased profits by as muchas 7% in the mid-1960s, but decreasedprofits by up to 19% in the mid-1970s. Finally, adjustments for lossesor gains on net monetary assets had the largest impact of all during theinflationary period of the 1970s, increasing profits by nearly 69% in1974. (Clearly, firms were typically net debtors.)

AR-012a/JTD//#3 - 18 -

There is some empirical evidence suggesting that CPP adjustments

improve the correspondence between firms' financial statements and their

market performance. For example, Baron, Lakonishok and Ofer (1980) find that

the correlation between firms' "market beta" and "accounting beta" values is

stronger when the latter are estimated using CPP-adjusted financial

statements. 1/ Moreover, the distinction is sharpened when data are used that

span both low and high inflation periods. However, there is also evidence

that CPP statements do not contain much information beyond what financial

market participants were already capable of deducing. For example, Beaver and

Landsman (1982) fail to uncover a significant impact on security prices whem

firms begin reporting CPP-adjusted statements. Also, using discriminant and

logit models of bankrupcy prediction, Norton and Smith (1979) find no

additional predictive power in CPP relative to TIC statements. 2/

All of the above results must be viewed with caution inasmuch as

they are based on U.S. data, where financial markets are highly developed, and

inflation has been quite pedestrian by developing country standards. Although

"research on systems such as those in Argentina and Brazil seems absent from

American libraries and literature indexes" (Frishkoff, 1982), some preliminary

evidence on the importance of inflation adjustments is becoming available.

For example, de Melo and Veneroso (1984) found that public sector enterprises

in Portugal appeared to be doing quite poorly according to their uncorrected

1/ A firm's beta value is estimated by regressing its earnings rate on theearnings rate of a "market basket" (e.g., Fama, 1976), and is an indexof the riskiness of holding its shares. A perfect correlation between *market- and book value-based betas would indicate that books capture allinformation available to market participants. For a review of earlierstudies of the association between CPP-adjusted earnings and marketearnings, see Frishkoff (1982).

2/ See, however, the criticism of this work in Solomon and Beck (19R0).

AR-012a/JTD/#3 - 19 -

financial statements.!/ The average equity to debt ratio in their sample

during 1982 was .21 and combined net income was -35 billion es.cudos. However,

when adjustments were made to account for the effects of inflation (which was

22%), the equity-to-debt ratio increased to .28 and net income increased to -7

billion escudos. In another study, Petrei and Tybout (1984) found that high

inflation and nominal interest rates in Argentina during 1981 caused HC income

statements to register net income losses on the order of -30% to -60% as a

ratio to net worth. Yet because real financial cost were quite negative,

average earnings rates after correcting for net monetary losses ranged between

40% and 50% in some quarters21/

III. FINANCIAL STATEMENTS IN THE PRESENCE OF CHANGING RELATIVE PRICES

When the relative values of different balance sheet items are

changing -- for example, when inventory prices are rising relative to the

general rate of inflation -- the CPP approach to accounting will not yield an

accurate picture of either corporate income or its determinants. One simply

cannot arrive at the conceptually correct balance sheet in table I by applying

a general inflator to historical cost data. To deal with such an environment,

accountants have developed various systems of current value (CVA) accounting.

Because these systems differ in terms of the method by which items are

assigned values, it is worthwhile to review the alternatives before describing

the common characteristics of all CVA approaches.

The Portugese do adjust fixed capital stocks for inflation, but only witha lag.

2 The Argentine inflation rate was above 200% per annum during somequarters of 1981. "Corrected" net earnings rates should not be taken atface value because it was not possible to correct "cost of goods sold"for inflation biases. Still, the magnitude of the change in these ratessuggests the importance of correcting for gains on net monetaryliabilities.

AR-01.2a/JTD/#3 - 20 -

Current value accounting, like CPP accounting, requires that all

items in financial statements be expressed in terms of their current value at

some common point in time. However, rather than relying on a general price

index to calculate these values, CVA accounting dictates that items be valued

individually with reference to various types of auxillary data that reflect

the current economic environment, This means, inter alia, that each entry can

grow in value at its own rate, and in principle, the conceptual magnitudes in

Table 1 can be estimated. But once it has been acknowedged that relative

prices are changing, some difficult conceptual problems regarding the correct

valuation system must be faced.

There are three alternative approaches to assigning values under the

CVA system: (a) replacement costs, (b) resale or "realizable" value, and (c)

value of the discounted earnings stream they are expected to generate. 1/ A

detailed treatment of the merits of each system is beyond the scope of this

paper. It may be noted, however, that a case can be made for any of these

approaches, depending upon who is going to use the data, and the relative

magnitudes implied by each (e.g., Scapens, 1981, chaps 5 and 7). For example,

if an investor who views the firm as a going concern wishes to make decisions

based on accounting data, he may favor replacement costs as the best indicator

of claims on the firm's future gross earning stream (see Revsine, 1973). On

the other hand, creditors may view.assets as collateral, and prefer to know

the resale value. To further confound matters, sometimes a case can be made

for mixing valuation methods on a given balance sheet. For example, suppose

one adopts the rule that assets should be valued at the loss the owner would

1/ Of course in perfectly competitive markets with no transactions coststhe three concepts should coinctde.

AR-012a/JTD//3 - 21

suffer if deprived of them. Then if an asset is held for use, but has a

future earnings stream valued at less than its replacement cost, the former

magnitude might be viewed as the relevant one. Other assets held by the same

firm which have at earnings stream value greater than their replacement cost

might reasonably be valued accordhig to the latter concept, because this is an

upper bound on the loss owners would suffer if the assets were lost. Whatever

the method chosen, significant practical problems of gathering and processing

data are likely to be encountered. 1/

A. Relative Price Changes and Balance Sheets

Suppose agreement has been reached on an observable set of prices

with which to value inventories, fixed capital, and items that require a

general deflator. As in section I, call these prices at time t Px, Pk, and P

respectively. Then by reconstructing the balance sheet so that all items

reflect their current value on the closing date, one arrives at a year end CVA

adjusted statement which, in principle, coincides with table 1. Recognising

that the various price indices are no longer interchangeable, the net worth

growth decomposition between real income and capital maintenance is now more

complicated then the CPP version in Table 2:

(6) W -0 = {M - M (P/P) + T - X0 P(P /P A) + [I - yK k TP AT T 0 T 0OT0O T AKOPA(PT ~A

+ (P'x [(PX /Px ) P /P~'~ + P kK [(P k /P~ k (PT'/O)+ {PX T 0T 0 0KO 0 T 0

+ [XT - x JPX[(PX/Px) - (P /P )3 + [I -yK ]Pk[Pkk/P k (P /P)MT 0 A T A T A) 0 A T A T A

1/ See Fabricant (1978) for a sobering list of difficulties.

AR-012a/JTD/#3 - 22 -

+ (POXIOT(PT ) - 1] + Pk K[(PT/PO) - 1] + M (P/p) - 1}

The first bracketed term of this net worth change looks very much like CPP

income. The only difference is that now, net purchases of fixed capital and

inventories are expressed in specific prices, and brought to year-end values

using the general price inflator. Similarly, thb last bracketed term above

resembles the capital. maintenance term in Table 3; it is the amount that

initial net worth would have had to grow in order to maintain its real

value. The middle terms are peculiar to CVA accounting, and are the topic of

some controversy. They represent holding gains on non-monetary assets in

excess of those which would have occurred if all prices had risen at the rate

of general inflation. If income is defined to be net worth growth in excess

of that necessary to maintain real net worth value, these middle terms should

be combined with the first to comprise total adjusted income. (This "real

purchasing power" notion of income is used in the United States.) Alterna-

tively, if income is defined as net worth growth in excess of that necessary

to maintain the firm's productive capacity, it should be combined with the

third bracketed term to comprise total capital maintenance. (This "capacity

maintenance" notion of income is used in Great Britain.)

B. Relative Price Changes and Income Statement

A CVA-corrected income statement is presented in Table 5. Notice

that the first 9 items are analogous to those presented in Table 3, except Ln

that specific price indices are used. (This changes historic cost entries for

inventories and depreciation, as well as inflation adjustments for these

items.) The monetary correction account is constroeted, as before, under the

assumption that the opportunity cost of holding net monetary assets is

whatever capital gain they could have generated if they had been placed in a

TIable' 5: CVA Income3 Staemnt

Uidvear nrices Year-end Prices

(1) Gross Sales QP

(2) Cost of Gooda Sold xX P x

(3) Dapreciation TX

(4) Other Expenses EP

(5) H'storic Cost Income 1(1)-()()() [--Xp + XKT +U0 Kp 74 +upý

(6) Inflution Adjustments 1(6.1)+(6.2)] x0 !-P-P ]+ x' 0to Operating Profits ..

(6.1) Cost of Goods Sold XO Ppo - x T

(6.2) Depreciation yK[ A

............--------------------------------------------------------------------------(7) Adjusted Income [(5)-(6)1 [Q-E]PA+[XT-X]P -UP -KO A T A T A A7TA

k-TK0 iA iT

1iA>-YK>

k x(8) Loss from Rolding Net Monetary asets m AP lp T [AT -P -IP Hm TP lp T- T[_Fp-UP (PT

P (PT A

(9) Adjusted Income After Monetary Correction ML(P p )-H A/ F l 0 A+0 T 14 -M (iP )+[ x p(p lp A

+[I-TK /p(P )

(10) Cain oan Nonmanetary Assets [(10.1)+(10.2)] PA /?T) {XP -P(P /P -X -X (P p -P p H X

(101)Inenores(P/P T 0 T 0 + K T T 0 + K T 0 X(10.1) Inventories (P( 7/ (XTPT-X'PO(PT/P)) +K 1P lp )-(p /P ) ) K IpTK/P (P T /P)

_+KOpkiPk /Pk )-Ptpl + fI-K lp k UP klp k (P lp UL[TXO',xPTd'?,åJ LY A T i''A>~ 0A OA T A - Ak

(10.2) Fixed Capital (PA T) {KO T o

+[,-YKO'PA[(PT/PA)-(P'P)l)

(11)------- .ar.e.... ----ca---- ....u... af....../Qi 7/'I- - - -- - -(11) Cr Income Inclusive of Real Holding Cains MT(PA/PT)-MO A(P /P 01 [APT x A x T TT1(9)+(10)1 T 0 .0+TT(,F)Xp'PA', 0 XNX0PT/P 0 )+[Xi-X 0 Ipý+X0(PT-P0(TI 0

+ KP(P /p)-Ko p(P A )+[I-yK lP (PlpT + [-YK + KO '7TiPO<iT'O)l

p- inventory price level at time t

t

AR-012a/JTI)///3 - 24 -

general inflation hedge. Line 9, expressed in end-of-year prices, corresponds

to the first bracketed term in equation 6. Hence it corresponds to corporate

income measured on a capacity maintenance basis.

The major qualitative distinction between the CPP and the CVA income

statement is that the latter includes accounts for real gains on nonmonetary

assets. These accounts (i.e., items 10, 10.1 and 10.2) represent real holding

gains on initial nonmonetary assets, plus real holding gains on the net

accumulation of nonmonetary assets over the course of the year. As usual, it

is assumed that all physical asset stocks and prices are linear in time.

Notice that line 10, expressed in end-of-year prices, corresponds to the

second bracketed term In equation 6, which implies that line 11 is real

corporate income measured on a purchasing power maintenance basis.

C. Empirical Evidence on Relative Price Change Adjustments

When done on a replacements cost basis, CVA adjustments may be viewed

as a refinement on CPP adjustments. Accordingly, the impact of CVA

adjustments on net income is presumably comparable to that of CPP adjustments,

and the present discussion will be confined to the (relatively limited)

empirical literature concerning the information content of firm-specific CVA

figures.

With regard to tests of association between accounting and market

earnings rates, the evidence is so,ewhat weak and mixed. On the one hand,

Easman, Falkenstein and Weil (1979) find in their panel data study of U.S.

firms that CVA earnings rates are more closely associated with market rates

than are HC figures over the period 1972-1977. (Nonetheless, only 4% of total

market variation is explained.) On the other hand. Beaver, Griffia and

Landsman (1981) find that in cross section, IC earnings rates are actually

better predictors of stock returns than CVA-adjusted earnings. To further

AR-01.2a/JTD/#3 - 25 -

confound matters, each study based on a distinct set of adjustments, and

neither should be viewed as a complete CVA system./

With regard to the prediction of bankruptcy, only one major study

appears to deal with CVA data. This is Mensah's (1983), who finds that books

adjusted according to CVA norms contain only marginally better information

than HC figures. However, when a loss function is specified that attaches

relatively large costs to classify-ng bankrupt firms as non-bankrupt (as

opposed to classifying noubankrupt firms as bankrupt), the superiority of the

CVA books increases. Here too, no strong conclusions are warranted.

Because none of the above studies deals with fully adjusted CVA books

that were prepared by firms themselves, many open issues remain regarding the

value of such inflation corrections. Perhaps more importantly, as noted in

connection with CPP studies, almost all of the research deals with industrial-

ized countries where the inflation rate has been miniscule relative to that of

Latin Amerfea. I- short, personal biases still appear to play an inordinately

large role in the debate on the merits of CVA adjustments.

IV. SUMMARY:, APPLYING THE ALGEBRA

In sections II and III, 4 basic types of inflation bias were

identified in HC income statements: input cost understatement, depreciation

cost understatement, neglect of net monetary losses, and neglect of those

capital losses due to changing relative prices. These biases are represented

in their most general form by the various adjustments in Table 5 and, to

summarize and interpret the discussion of previous sections, they are now

1/ For example, unrealized holding gains and losses are not recognized.

For a review of other (also inconclusive) studies, see Frishkoff (1982).

AR-012a/JD/#3 - 26 -

reviewed.

The first bias, inxit cost understatement, is represented by line 6.1

of table 5. Its magnitude derends upon the inventory valuation system used,

the volume of inventories carried by the firm, and the rate of inflation. If

inventory stocks are stable and a LIFO valuation system is used, the

distortion disappears: Po' and P are replaced by some common price level

that reflects the average (historic) cost of the initial stock. On the other

hand, if inventory stocks are stable but a FIFO system is used, the bias will

be roughly the annual change in prices times the inventory stock.

The second bias, which is represented by equation 6.2, is due to the

basing of depreciation expenses on historic acquisition costs. Clearly, the

more fixed capital-intensive a firm, and the more the price of capital goods

has risen since the firm acquired its stocks, the more important this bias

becomes. It is worth noting that in countries without comprehens:ive inflation

accounting systems, the capital stock is sometimes adjusted for general

inflation. In such cases depreciation figures may be relatively free of

distortions.

The third bias results from ignoring the shrinkage in real value of

monetary items, which roughly amounts to treating nominal financial costs as

if they were real costs. It is represented by line 8 of table 5 or,

equivalently, by equation 4 in section II of the text. This distortion is

directly proportional to the inflation rate, and at a given inflation rate, to

the net monetary asset stock. In hyperinflated countries it can be the single

most important source of income misstatement. If no adjustment for this

distortion is made, "net income" figures represent not real income, but rather

AR-012a/JTD///3 - 27 -

the residual earnings flow that would be available to firms after retiring

real net monetary liabilities at the rate of inflation.

The final bias is really not due to general inflation; it is present

if and only if relative prices are changing (refer to lines 10, 10.1 and 10.2

of table 5). Accordingly, unlike other biases, this relative price distortion

need not be directly related to the inflation rate. Its magnitude is deter-

mined by the discrepancy between growth in the general price level and growth

in the prices of inventories and fixed capital. Given that there is no con-

sensus on the proper valuation system for nonmonetary assets, the importance

of this relative price distortion is to some degree a matter of personal

judgement: replacement costs may follow one trajectory relative to the

general price level, while net realizable values or discounted expected

earnings stream values may follow another.

AR-012a/JTD/#3 - 28 -

References

Baron, Arie, Josef Lakoniskov and Aharon R. Other, 1980, "The InformationContent of General Price Level Adjusted Earnings: Some EmpiricalEvidence, The Accounting Review, 55 (January), pp 22-35.

Baxter, W.T. 1975. Accounting Values and Inflation. London: McGraw-Hill.

Beaver, William 1. and Wayne Landsman, 1982, "The Incremental InformationContent of FAS 33 Disclosures" (July). Unpublished manuscript.

Beaver, William H., Paul A. Griffin and Wayne R. Landsman 1981. "TheCorrelation of Replacement Cost Earnings with Security Returns".Working Paper (revised). Stanford: Graduate School of Business,Stanford University (July).

Cagan, P. and R.E. Lipsey 1978. The Financial Effects of Inflation. NewYork: NBER.

de Melo, Martha and Frank Veneroso 1984. "Inflation Accounting and its PolicyImplications for Portugal's Public Enterprises." Unpublisheddocument, The World Bank.

Easman, William S., Jr., Angela Falkenstein and Roman L. Weil, 1979. "TheCorrelation between Sustainable Income and Stock Returns: Changes inSustainable Income..." Financial Analysts Journal(September/October), pp. 44-48.

Fabricant, Soloman, 1978. "Accounting for Business Income Under Inflation:Current Issued and Views in the United States." Review of Income andWealth. (March). pp. 1-24.

Fama, Eugene F., 1976. Foundations of Finance. New York: Basic Books.

Frishkoff, Paul, 1980. Financial Reporting and Changing Prices: A Review ofEmpirical Research. Stamford: Financial Accounting Standards Board.

Mensah, Yaw M., 1983. "The Differential Bankruptcy Predictive Ability ofSpecific Price Level Adjustments: Some Empirical Evidence. TheAccounting Review, 58 (April). pp. 228-246.

Norton, Curtis L. -nd Ralph E. Smith, 1979. "A Comparison of General PriceLevel and Historical Cost Financial Statements in the Prediction ofBankruptcy", The Accounting Review 54 (January), pp 72-87.

Parker, James E. 1977. "Impact of Price-Level Accounting." The Accounting (Review 52 (January), pp. 69-96.

Pearch, J. 1970. "Inflation and U.K. Published Accounts." Journal UEC(October), pp. 196-203.

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Petrei, A. Humberto and James R. Tybout 1984. "How the Financial Statementsof Argentine Firms Reflected Liberalization and Reform Attempts:1976-81." Unpublished document, The World Bank.

Resvine, L. 1973. Replacement Cost Accounting. Englewood Cliffs, N.J.:Prentice-Hall.

Rosenfield, P. 1969. "Accounting for Inflation - A Field Test." Journil ofAccounting (June), pp. 45-50.

Scapens, R.W. 1981. Accounting in an Inflationary Environment, 2nd edition.London: MacMillan.

Solomon, Ira and Paul J. Beck, 1980. "A Comparison of General Price Level andHistorical Cost Financial Statements in the Prediction of Bankrupt-cy: A Comment," The Accounting Review (July), pp 511-515.