Volume 5
2015

Cost-Benefit Analysis of Mixed Measurement Model
YOSHINORI KAWAMURA*
Graduate School of Accountancy,
WASEDA UNIVERSITY

ABSTRACT
Since the current financial reporting uses various measurement attributes for measuringassets and liabilities, it is often referred to as the “mixed measurement model.” This
paper addresses the issues related to why and how different measurement attributes,
notably fair value and historical cost, are used in financial statements. The cost-benefit
analysis is adopted as a research methodology throughout this paper by formalizing as
mathematical functions the preparer’s measurement cost and the users’ benefits ofaccounting information that the preparer produces.
The cost-benefit analysis suggests that the mixed measurement model can be justified
through the preparer’s economic incentives for minimizing cost. It also suggests thatthe cost-minimization solution in the marketplace would represent a consensus among
the interests of the preparer and the users within a constraint in which only one set ofaccounting information is provided. This paper also identifies the situations in which
providing two sets of accounting information is preferable.
Key Words: Cost-benefit Analysis; Mixed Measurement Model; Fair Value; Relevance;
Faithful Representation; Comprehensive Income*

Corresponding author. Address Waseda University, 1-6-1 Nishi-waseda, Shinjuku, Tokyo 169-8050, JAPAN.
Telephone +81-3-5286-2047 E-mail ykawamur@waseda.jp.
This paper is partly based on but is significantly extended from my earlier work written in Japanese: “An Implicationfrom Discourse Related to the Asset-Liability View: Cost Analysis of Fair Value Measurement and Historical Cost
Measurement,” Kaikei 185 ( January 2014): 46–62. The author is grateful for helpful comments from Professors
Hiromitsu Sato, Takanori Suzuki, Masashi Okumura, Tomoki Oshika (Waseda University), Hisakatsu Sakurai (Kobe
University), Tomo Suzuki, Richard Barker (University of Oxford), and Christoph Pelger (University of Cologne).

Received August 8, 2014; available online December 13, 2014 (Advance publication by J-STAGE)
DOI: 10.11640/tjar.5.2015.01

Copyright©2015 Research Institute for Economics & Business Administration – Kobe University.

2

The Japanese Accounting Review, 5 (2015), 1-19

1. Introduction
Since the current financial reporting uses various measurement attributes for measuringassets and liabilities in a set of financial statements, it is often referred to as the “mixed
measurement model.” Critics have stated that the mixed measurement model does not provide
consistency of measurements in financial reporting (Barth 2007), and imposes a cost on the usersof financial statements because those users are unable to identify whether a line item on thestatement of financial position represents a measurement of fair value or historical cost without
reading carefully the accompanying notes to the financial statements. This paper addresses theissues related to why and how different measurement attributes, notably fair value and historicalcost, are used in the financial statements. This paper provides a theoretical framework for theselection of fair value and historical cost in measuring assets and liabilities.
From time to time, accounting standard-setters, including the U.S. Financial AccountingStandards Board (FASB) and the International Accounting Standards Board (IASB), haveattempted to enhance consistency in financial reporting. For example, the asset and liability view
(FASB 1976) was adopted to provide a consistent set of the definitions of the elements offinancial statements (FASB 1985; IASC 1989). Although this view successfully has eliminatedthe items that do not meet the definitions of assets and liabilities from the statement of financial
position, it seems that the view still does not provide a consistent basis for the measurement of
those elements.
During the late 1990s and the 2000s, the standard-setters tried to introduce fair value
accounting for all financial assets and liabilities, stating that it is an ultimate goal for them (forexample, FASB 1998; IASB 2008). However, even for financial assets and liabilities, fair value
would not likely be a single measurement attribute in practice currently and in the foreseeable
future (IASB 2010a; FASB 2013).
The selection of measurement attributes for assets and liabilities has an effect on
determination of income. Generally, if an asset or liability is measured at fair value, the change infair value should be recognized through net income (profit or loss) for the period. If an asset or
liability is measured at historical cost, any change is not recognized until that item is removed
from the statement of financial position unless the transaction price is systematically allocated.
Measuring assets and liabilities at any attribute imposes a cost upon a reporting entity.
Although such a measurement cost may be ignorable for some assets and liabilities, it would beenormous for others. For example, measuring real estates or intangible assets at fair value would
require the entity to spend costs for training its employees or hiring an outside expert. The
benefits that users gain from accounting information should also be considered to determine theoptimal accounting policies in a social context. In this paper, the cost-benefit analysis is adopted
as a research methodology by formalizing as mathematical functions the preparer’s measurement
cost and the users’ benefits of accounting information that the preparer produces.
The cost-benefit analysis was developed originally in economics and has become one of themost popular theoretical methods of analysis in other social science disciplines (Layard andGlaister 1994, 1–56). It has also been applied to accounting research, especially in theagent-principal setting. In accounting standard-setting, the balance between cost and benefit isoften mentioned as a constraint for developing accounting standards for specific issues. For
example, the IASB’s and the FASB’s conceptual frameworks treat the cost constraint on reporting
certain information as a factor that should be justified by the benefits of reporting that

Kawamura: Cost-Benefit Analysis of Mixed Measurement Model3

information (IASB 2010b and FASB 2010a, QC35–39). However, the cost-benefit analysis inaccounting standard-setting does not seem to be consistently applied, partly because it is difficult
to formalize the cost and benefit functions that reflect differences in accounting policies.
The cost-benefit analysis is a tool for solving economic problems that are subject to given
constraints. If there was no constraint, the preparer could produce limitless volumes of
information and the users could utilize such information without considering any cost ofinterpretation. However, in the real world, accounting always faces cost-benefit issues, which areoften described as the tradeoffs between different objectives. For example, Dye and Sridhar(2004) focuses on the aggregation of information, which is treated as a constraint, and clarifies
that it creates tradeoffs between reliability and relevance.
The cost-benefit analysis suggests that the mixed measurement model can be justified by the
preparer’s economic incentives for minimizing measurement cost. It also suggests that the users’
benefits from relevance and faithful representation would affect the optimal scope of fair value
measurement, and the solution in the marketplace would represent a consensus among theinterests of the preparer and the users within the constraint of the single criterion regime, where
only one set of the scope of fair value measurement is selected. Next, the analysis is extended tothe multiple criteria regime, where two sets of the scopes of fair value measurement are selected.
This paper identifies situations in which the multiple criteria regime is preferable in terms ofachieving a more cost-saving solution in the marketplace as a whole.
The paper proceeds as follows. In the next section, I review recording systems in accounting
and typical accounting measurements, including historical cost and fair value. I also review thestatic and dynamic descriptions of firm value and discuss how accounting numbers are related tothose descriptions. In section 3, I develop a framework for the cost-benefit analysis of the mixed
measurement model by formalizing the preparer’s cost and the users’ benefits. In section 4, theconstraint is relaxed to the multiple criteria regime, and I discuss how and in what condition themultiple criteria should be adopted. Section 5 concludes the paper.

2. Accounting and Firm Valuation
2.1 Accounting Measurements: Historical Cost and Fair Value
Broadly stated, accounting has two different recording systems for the economic activities ofan entity. Firstly, the activities of an entity are generally recorded when transactions occur.
Transactions are easily observable by a measurer because, in a transaction, one party exchanges
goods or services with another party, where the transaction price is clearly stated in monetary
terms. Accounting uses the identification of goods or services exchanged and the monetary unit
stated in the transaction price for recording that transaction in double-entry bookkeeping. Such atransaction-based recording system is discrete because nothing is recorded until the nexttransaction actually occurs. This system also leads inevitably to delayed recognition and causes
conservatism (Beaver and Ryan 2000). Secondly, certain events related to an entity are recorded
when such events occur, even though they are not transactions between parties. For example, as
the market price of a certain asset changes, accounting might record such changes even though
the entity does not transact anything with the other party. Such event-based recording system iscontinuous, at least conceptually, because the events (e.g. price movements) occur continuously
and could be recorded continuously.
Those two recording systems would lead to the use of different measurements. In current

4

The Japanese Accounting Review, 5 (2015), 1-19

practice, a variety of measurement attributes are utilized. Examples include historical cost,depreciated cost, amortized cost, fair value, current cost, net selling price, net realizable value,present value of future cash flows, value in use, and so on.
In this paper, accounting measurement attributes are considered to be broadly categorized
into historical cost measures and current value measures. Historical cost measures are themeasures that are produced based on historical transaction data, which includes depreciated oramortized costs that utilize historical transactions data and a systematic periodic allocation.
Current value measures are measures that are produced based on the current market or
entity-specific data at the measurement date, where historical transaction data are ignored.
Current value measures include fair value, which uses current data that is agreed upon by themarket participants, and value in use (or entity-specific value), which uses current data that is
specific to the reporting entity itself (FASB 2000). In this paper, I focus on fair value incomparison with historical cost, because fair value is widely used for measuring assets andliabilities in practice by allowing the measurer to consider not only observable market data but
also his or her assumptions about the market participant’s view. I avoid using value in use in theanalysis, because it is based on the measurer’s own assumptions about the entity’s usage of theasset, which could make the value more subjective. More importantly, since value in use could beinterpreted as the joint value of the asset in question and its related intangibles, it would not beappropriate to assign such a joint value solely to that asset by ignoring the contribution by the
related intangibles.
Each of two recording systems has a preference in terms of selecting accounting
measurement attributes. The discrete recording system is more consistent with historical cost,because the system leaves the carrying amount of an asset or liability unchanged until theconsequent transaction occurs. Conversely, the continuous recording system is more consistent
with fair value, because the carrying value of an asset or liability can be tracked with movements
in fair value even before the consequent transaction occurs.

2.2 Static and Dynamic Descriptions of Firm ValueIn this paper, I extended the framework presented by Hitz (2007, 336–338). The firm valueof an entity can be described in a static manner as the sum of the fair values of
positions ofassets at date , which include identifiable assets as well as unidentifiable (not separable) assets.
To obtain fair values of unidentifiable assets, a complete market is assumed conceptually as astarting point. Liabilities are treated as the assets whose values are negative hereafter in this paper.
By setting the identifiable assets to havepositions ( ≤ ), the remaining unidentifiable
assets are supposed to have −positions.
In a more formal manner, the firm value of the entity at date , denoted as , can be
expressed as
=∑

,

=∑

,

+

(1)

( ∈ natural numbers) at date , anddenotesHere,, denotes the fair value of asset
the value of goodwill at date . This expression of firm value is static, because all variables are thevalue at the same date . If
is separated into the sum of the fair values of identifiable assets
represents the sum of the fair values of theand the goodwill, the value of the goodwill

Kawamura: Cost-Benefit Analysis of Mixed Measurement Model5

unidentifiable assets (∑, ).
Alternatively,
can be expressed as the sum of the values in use of all identifiable assets(Barth and Landsman 1995, 101), as
=∑

=∑

,

,

+

(2)

at date . Again, if theis separated into theHere,, denotes the value in use of asset
shouldsum of the fair values of identifiable assets and the goodwill, the value of the goodwill
represent the sum of the differences between the value in use and the fair value of eachidentifiable asset, which is generally termed as the present value of the entity’s excess earnings
power (∑ (, −, )). The value in use is fundamentally determined by discounting thefuture cash flows that are generated by the usage of each asset. The future cash flows are often
estimated as a joint product of the usage of an asset group. If we estimate the future cash flowsthat are generated by the usage of all assets of the entity, we can determine
as a discounted
value of the future cash flows. When the cash flow expected at date that the firm would] and the cost of capital is denoted
generate at the end of period + is denoted as [can be expressed asas(assumed constant),
=∑

[

]

(

(3)

)

Such an expression of the firm value is dynamic in the sense that the value is described by a seriesof variables at different dates in the future.
Next, according to many researchers (for example, Feltham and Ohlson 1995; Barker 2010),
an entity’s activities are generally categorized into two types of activities for valuation purposes:
financing activities and operating activities. In this paper, I would like to make rather a broadinterpretation that operating activities produce joint cash flows by business unit comprised ofidentifiable and unidentifiable assets, whereas financing activities produce cash flows
independently through the utilization or disposition of each asset. I assign
positions offinancing assets ( ≤ ≤ ) to the financing activities. For financing assets, no goodwill is
involved because the financing assets yield gains through the marketplace, independently from theentity’s other assets (especially, knowledge and other intangibles). Therefore, the value offinancing activities equals to the sum of the fair values of financing assets.
On the other hand, the remaining− positions of operating assets (assets ( + 1)
through ) are assigned to the operating activities. Inevitably, operating assets involve goodwill,
which is depicted here as differences between the value in use and the fair value of operating
assets. The value of the operating activities as a whole is not expressed by the sum of the fairvalues of operating assets, but rather it is expressed by the present value discounted atof thecash flowsthat are expected at date that the entity would generate at the end of,
period + from its operating activities that are comprised of the assets ( + 1) through .
The firm value at date is described as
=∑

,

+∑

,

(

)

(4)

6

The Japanese Accounting Review, 5 (2015), 1-19

Estimates of future cash flows are anchored to how well the operating assets are grouped intobusiness units. Therefore, determiningout ofpositions influences the users’ ability to
project the future cash flows expected to be generated by the operating assets. Because the cash
flows are generated jointly by utilizing a group of assets, estimating the cash flows is moredifficult if the group of assets is inconsistent with the management’s view on the grouping.1
Two terms of the firm value in equation (4) have different properties in terms of theaccounting information and its usage by its users.2 The first term, the value of financing activities,
can be provided directly as part of the accounting information, if the financing assets are carriedat fair value on the statement of financial position. The second term, the value of operating
activities, is not provided directly by accounting. Rather it is estimated by users who readaccounting information about the operating activities, as implied by the expected value [∙].
That accounting information is often characterized by accounting stocks and flows together in apersistent way in which the users would find them useful in estimating a series of future cash
flows.

3. Cost-Benefit Analysis of Accounting Measurements
3.1 Minimization of the Preparer’s Measurement Costs
As I discussed in the previous section, accounting measures are grouped into the twocategories of historical cost and fair value, which concur with discrete recording and continuousrecording, respectively. Therefore, the determination of the scope of assets measured at fair value
would broadly determine the accounting policies of an entity. For a perspective of firm valuation,
positions of financing assets would be a promising alternative for a scope of fair value
measurement. Theorists may contend that
positions of identifiable assets should be measured
at fair value. However, as is often observed in the standard-setting process, the preparers
necessarily agree neither on categorizing their activities into financing activities and operating
activities (FASB 2008) nor on measuring all financing assets at fair value. In order to observe thepreparers’ incentives, I would like to develop a framework for the cost-benefit analysis of theselections of accounting policies, focusing on the determination of the scope of assets that aremeasured at fair value.
To neutralize the size of the firms, I divide the positions of the assets by
and put thequotients on the horizontal axis.3 I thereby obtain = 1, = , and = , each of which
expresses certain percentage of positions in proportion to all asset positions of the entity( 0 ≤ ≤ ≤ 1 ). The vertical axis represents the measurement costs to produce certain
accounting information in any common scale (possibly, in a dollar amount).
1

However, it should be also noted that the basis of grouping is not limited to , as long as the cash flows from thegroup of assets that are not measured at fair value can be estimated. For example, if the positions of assets
should be estimable for valuation purposes.
( ≤≤ ) are measured at fair value,2
For example, Holthausen and Watts (2001) states that value relevance studies appear to use two different theories:
direct valuation theory and inputs-to-equity valuation theory. The former would concur with the first term and thelatter would concur with the second in equation (4).
3
In the previous section, “positions” could be defined as any physical or monetary units as longs as the fair value andthe value in use are attributable to each of them. Technically, in this section, positions should be defined morenarrowly, in order to describe the behavior of certain cost as a linear function based on the positions. For example,
they can be defined in terms of monetary units based on initial acquisition costs.

Kawamura: Cost-Benefit Analysis of Mixed Measurement Model

7

Then, I define a(0 ≤ ≤ 1) as the scope of fair value measurements. The remaining
1 − represents the scope of historical cost measurements. Assume that the costs change
continuously for , so that the costs can be differentiated on . The measurement costs in thisanalysis include various direct and indirect costs in the entity’s departments of accounting,internal control, and other functions that are necessary to measure the assets at a certain attributeand apply the related accounting policies to them. Any constant measurement costs against
areignored because they are indifferent in solving the cost minimization problem, although the totalof constant and variable costs should be overcome by the potential total benefits.
The cost of fair value measurement changes depending on the scope of fair value
measurement, , and therefore it can be expressed as a function of , which is denoted as( ). The cost of historical cost measurement changes depending on the remaining scope ofhistorical cost measurement 1 − , and therefore it can also be expressed as a function of ,( ). The total cost of the measurement is denoted aswhich is denoted as( ). Assuming> 0 and ≥ 0, those cost functions can be defined as
( )=

(5a)

( ) = (1 − )

(5b)

( )=

( )+

( )=

+ (1 − )(5c)In those settings, some strong assumptions are introduced. For the cost of fair value
measurement, it would be acceptable to assume that that cost for each asset position would be( ) > 0 and( ) > 0 when asset positions are sorted indifferent, 4 and thatascending order of the measurement cost. For the sake of simplicity, the measurement cost of fairvalue is described as a quadric function, in which the cost increases more steeply as
increases
toward one. The parameteris the measurement cost incurred when = 1 (all asset positions
are measured at fair values) and can be seen as the cost indicator of fair value measurement.
Historical cost is defined rather broadly in this analysis as transaction-based measurements,
including zero measurement (immediate expensing), depreciated or amortized cost, as well as
original transaction price. For the sake of simplicity, the cost function of historical cost( ) ≤ 0 andmeasurement is described as a linier function, which has a property that( ) = 0. The cost of historical cost measurement would likely decrease at a more stableproportion per position, because entities use transaction data for historical cost measurement
similarly for each asset position. The parameteris the measurement cost incurred when = 0(when all asset positions are measured at historical costs), and can be seen as a cost indicator of
historical cost measurement.
The theories of firm valuation indicate that clean surplus accounting may result in the samevalue regardless of differences in accounting policies (Peasnell 1982; Ohlson 1995). As a first step,
here I assume that the users enjoy the same benefit regardless of(i.e. I ignore the difference inthe users’ benefits regarding ). In this setting, the preparer would select a certainthat
minimizes his or her total measurement cost.
4

Fair values of asset positions are supposed to be measured in a certain frequency (e.g. daily, weekly, or monthly).

8

The Japanese Accounting Review, 5 (2015), 1-19

Therefore, the optimal scope of fair value measurement for the preparer, denoted asdetermined by solving the problem fortoMinimize( )=Subject to 0 ≤

≤ 1.

∗

, is

+ (1 − )(6)

Solving this problem, we obtain∗=, when<2

1, when≥2 .

(7)

Except for the extreme case where ≥ 2 , the result tells us that ∗ becomes larger as
becomes larger. More importantly, the result
becomes larger, and that ∗ become smaller as
indicates that, except for certain limited cases, the preparer has an economic incentive to adopt
the “mixed measurement model,” in which both fair value and historical cost are used in the same
set of financial statements (0 < ∗ < 1).
In order to confirm this, it would be useful to review the conditions for two extremes: the full
historical cost accounting and the full fair value accounting. Firstly, the full historical costaccounting, in which all assets are measured at historical cost, is described as ∗ = 0. Since> 0 is assumed,
should be zero. = 0 means that the measurement cost of historical costis indifferent regardless of . It could happen when every transaction is recorded at historical costanyway for the purpose of managing and safeguarding the entity’s assets. Secondly, the full fairvalue accounting, in which all assets are measured at fair value, is described as ∗ = 1. To achievethis, ≥ 2 is required. Since this condition seems unrealistic, the full fair value accounting
would not likely be the preparer’s voluntary choice.
Figure 1 demonstrates how the optimal solution ∗ is determined. ∗ represents the scopeof fair value measurement in which the total cost is minimized, and 1 − ∗ represents the scopeof historical cost measurement at the cost minimization. As Figure 1 suggests, the mixed
measurement model is justified from a perspective of cost-benefit analysis insofar as the total costfunction is convex downwardly for 0 ≤ ≤ 1.
It is also noteworthy that ∗ is determined independently from or( ≠ ∗;≠ ∗)because it is determined solely by the preparer’s incentive for cost minimization. Especially, thisresult indicates that the incentives for fair value measurement for financing assets are notpredetermined. Some entities might not want to measure certain financing assets at fair value, if∗< . Others would be motivated to measure more assets at fair value beyond the scope offinancing assets, if < ∗ . For those entities, the fair value option in the existing practice seems
to accommodate their needs for measuring more assets at fair value, resulting in assisting theircost minimizations.
If only identifiable assets are measured at fair value ( = ), the total cost of measurement( ) is usually smaller than the total cost of fair value measurement for all assets ( ( ) <(1) = ) as long as ∗ = <. If
is small enough to assure ∗ = > for certainKawamura: Cost-Benefit Analysis of Mixed Measurement Model

9

FIGURE 1: THE PREPARER’S COST MINIMIZATION
( )

=

−

1−

=

= − (1 − )∗Scope of fair value
measurement1
Scope of historical cost measurement

entities (for example, certain financial institutions), the total cost of fair value measurement for all
identifiable assets might be smaller than the total cost of historical cost measurement for all assets( (0) = >( )). Especially, if ∗ ≥ , the fair value accounting for all identifiable assets
is supported.

3.2 Incorporating the Users’ Benefits into the Analysis
The analysis in the previous section has not considered the users’ benefits, or, stateddifferently, has considered that the users’ benefits as a constant regardless of . Here, I would
extend the framework of cost-benefit analysis so that the preparer’s costs of measurement and theusers’ benefits from the usage of information are both considered. The users’ benefits would
include, but not limited to, improvements over the users’ estimates for firm valuation. It would bereasonable to assume that the users’ benefits vary depending on . I discuss the behavior of theusers’ benefits from two different viewpoints: relevance and faithful representation.
3.2.1 Relevance
When contending that the fair values have relevance to the user’s firm valuation, such
relevance works directly to the users’ valuation in a sense that one unit increase in the fair value ofan asset would lead to an increase in the firm value by the same amount as was discussed in the

10

The Japanese Accounting Review, 5 (2015), 1-19

static description of firm value. Although in the IASB’s and the FASB’s conceptual frameworks,
relevance itself is interpreted more broadly as the capability of making a difference in thedecisions made by users (IASB 2010b and FASB 2010a, QC6–10), I use the term relevance in anarrower sense as a quality that helps the users evaluate the firm value more directly as discussed
above. Such relevance is generally observed in the fair value measurements of financing assets
because changes in fair value have a direct impact on the firm value. Therefore, the benefit
function of the relevance by fair value measurement( ) can be formalized as
( )=

.

(8a)

Where
is a benefit per position that the users enjoy when they obtain the information about( ) ≥ 0 andfair value ( ≥ 0). A linear relationship (i.e.
( ) = 0) can be assumed,
because incremental information about fair value would give the users a chance to revise theirvaluation equally for each asset position from a static view of the firm value.
3.2.2 Faithful Representation
Although the wider use of fair value measurement would likely serve the users more, somemight argue that it might impair the users’ ability to estimate the firm’s future cash flows. This
holds especially true when measuring certain components in the group of operating assets at fairvalue, which would not help the users estimate the future cash flows from the operating activities
because the cash flows are generated as a joint product of the group of operating assets, including
unrecognized intangibles. The group of operating assets should be accounted for as a cash
generating unit, and it would be better that each component asset is accounted for in a consistentmanner within the group. Moreover, others might argue that measuring certain assets at fair value
would introduce additional uncertainty in financial reporting (Landsman 2007) especially whenmeasuring the assets whose fair value is costly to measure. Such uncertainty in measurement
would impose more cost upon the users, because the users would have to adjust for theuncertainty in estimating the future cash flows. On the other hand, measuring financing assets atfair value would not be problematic in terms of difficulty in estimating the future cash flows or
uncertainty in measuring the fair values. Rather, the users would be better served if morefinancing assets are measured at fair value.
I would use the term faithful representation to describe such behavior of the users’ benefits inrelation to , because the financial statements would be most faithfully represented when thefinancing assets and operating assets are measured in concurrence with the economic usages ofthem by the entity. More specifically, the users’ benefits of faithful representation would be
maximized if = , where all financing assets are measured at fair value and all operating assets
are measured at historical cost, respectively. As
moves away from , the benefits will decrease.
In this paper, I assume that the benefits decrease along with the product of a constant( ≥ 0)and the square of the difference between
and . Therefore, the function of the users’ benefitsof faithful representation( ) can be expressed as( )=− ( − ) .
When

(8b)

< , a marginal increase in the scope of fair value measurement would increase the users’Kawamura: Cost-Benefit Analysis of Mixed Measurement Model11

benefit of faithful representation (i.e.
( ) ≥ 0 ). Conversely, when > , a marginalincrease in the scope of fair value measurement would decrease the users’ benefit of faithfulrepresentation (i.e.
( ) ≤ 0). In order to formalize the benefit of faithful representation, aquadric function is used in this analysis, because the errors in the users’ projecting the entity’s
future cash flows or the errors in the preparer’s measuring the fair values would likely impose acost that increases in proportion to the square of the distance betweenand .
can beinterpreted as another cost indicator that stems from faithful representation.
The IASB’s and the FASB’s conceptual frameworks give faithful representation a prestige offundamental qualitative characteristics. They state that useful financial information should
faithfully represent the phenomenon that it purports to represent, and that a depiction should becomplete, neutral, and free from error to be a perfect faithful representation (IASB 2010b and
FASB 2010a, QC12–QC16). That explanation does not define the benefit functions specifically,
but at least it seems to be consistent with the terminology in this paper because financing assets
and operating assets are both accounted for in accordance with the usages of the assets.
Then, we obtain a total benefit function( ) as
( )=

( )+

( )=

− ( − ) .

(8c)

To obtain a cost minimization in the marketplace as a whole, we have to define a net total cost( ) by subtracting the total benefit from the total cost, such asfunction
( )=

( )−

( )=

+ (1 − ) −+ ( − ) .

(9)In order to find the optimized scope of fair value measurement in the marketplace, which istodenoted as ∗∗ , we should solve the problem for( )=Minimize
Subject to 0 ≤+ (1 − ) −+ ( − )

≤ 1.

(10)

As is demonstrated in economics, it would be beneficial to discuss the problem in terms of
marginal cost and benefit. The functions of marginal total cost and marginal total benefit, which
are denoted as( ) and( ) respectively, are obtained by differentiating the functionsof total cost and total benefit, as shown in equations (5c) and (8c), on
as
( )=

( )

=2

( )=

( )

= −2

−

(11)
+

+2 .

(12)

At the optimized scope of fair value measurement ∗∗ in the marketplace as a whole, the( ∗∗ ) should concur with each other. Then, we obtain ∗∗ as( ∗∗ ) and
∗∗

=

(

)

1, when, when

+

+ +2

+2

< 2( + )≥ 2( + ).

(13)

12

The Japanese Accounting Review, 5 (2015), 1-19

FIGURE 2: THE MARGINAL TOTAL COST AND THE MARGINAL TOTAL BENEFIT
( )
( )

+2
=−2

∗

+ +2

∗∗

=2

−

1

−

+ +2 ≥
Since+ + 2 ≥ 0 and+ > 0 , always ∗∗ ≥ 0 . However, when∗∗),should remain one.
2( +Figure 2 illustrates the functions ofand, and shows an intersection point , atwhich the values of the two functions concur with each other and the net marginal cost is zero.
The optimal solution ∗∗ =is the abscissa at . If we ignore the users’ benefit)∗ (is shown as the intersection point ofand the horizontal( = 0, = 0), the solution
axis. It should be noted that ∗∗ ≠ ∗ , unless = 0 and = 0. This suggests that the preparer
would have to adopt the scope of fair value measurement that is different from the scope of its
own cost minimization. Therefore, some sort of regulation is necessary to require the preparer toadopt the scope of fair value measurement that realizes the cost minimization in the marketplace.
Figure 2 also demonstrates that as(cost indicator of fair value measurement) becomeslarger,should shift upward with steeper inclination, letting ∗∗ become smaller. As , ,or becomes larger, ∗∗ should become larger. As for , the effect is mixed because the changeinchanges both of the intercept and the inclination ofat the same time.

4. The Multiple Criteria Regime
So far, the framework of the cost-benefit analysis has provided a single optimal solution of
measurement criterion for 0 ≤ ≤ 1. A
can be interpreted as an overall accounting criterion,

Kawamura: Cost-Benefit Analysis of Mixed Measurement Model13

because it determines the scope of fair value measurement and, accordingly, the scope of historicalcost measurement, defining broadly other related accounting policies. As only one
isdetermined in the previous section, we could say that that framework belongs to the single
criterion regime. In that regime, we have to consider all the factors that affect the cost-benefit
analysis to find an optimal single criterion. As a result, an optimized solution would be achieved
as a consensus among the participants in the marketplace.
In this regard, one might argue that we could set forth more than one measurement criteria
and require the preparer to disclose more than one set of accounting information. The multiple
criteria regime might enhance the users’ benefits because different users have different interests
and those different interests could be served better with multiple sets of accounting information.
Of course, any increase in the preparer’s measurement cost by adopting the multiple criteria
regime should be considered.
A typical discussion of the multiple criteria regime can be found in AAA (1966), which
recommends that two sets of information of historical costs and current values be provided toaccommodate the various needs for information of various stakeholders. Also, FASB (2010b)
once proposed that both amortized cost and fair value would be presented on the face of thestatement of financial position for certain financial instruments. Another discussion can be foundin the standard-setting for reporting of financial performance. One of the most controversial
issues in reporting financial performance is whether one or two summary result(s) of financial
performance should be disclosed; i.e. whether only comprehensive income should be displayed ora pair of net income (profit or loss) and comprehensive income should be disclosed. Net income
and comprehensive income are determined based on two different criteria for the scope of fairvalue measurement. When the changes in fair value of certain investments are recognized throughother comprehensive income, such changes are not recognized in net income as if the investments
were measured at historical cost, although they are actually measured at fair value on thestatement of financial position. In this sense, two different criteria are applied to the reporting offinancial performance, although this is less obvious than in the proposals by AAA (1966) and
FASB (2010b).
To perform a cost-benefit analysis in the multiple criteria regime, I assume that a pair of twos,
can be selected (assume 0 ≤≤ 1; 0 ≤≤ 1;≤ ) in a manner in which
the net cost in the marketplace is minimized. Because two different scopes of fair value
measurement are selected, the asset positions that fall in the difference between two scopes shouldbe measured at historical cost by the first criteria and at fair value by the second criteria.
As≤ , the maximum scope of fair value measurement is, which determines the costof fair value measurement. Also, as 1 − ≥ 1 − , the maximum scope of historical costmeasurement is 1 − , which determines the cost of historical cost measurement. Therefore, thepreparer’s cost functions in ( , ) space are redefined as,

Measurement cost of fair value:,

Measurement cost of historical cost:

Total measurement cost:

,

=

(14a)
= (1 −=,+=+ (1 −

)

(14b)
,

).

(14c)

14

The Japanese Accounting Review, 5 (2015), 1-19

Next, we have to formalize the users’ benefit in ( , ) space. As≤ , the users useasthe criterion for relevance. In terms of faithful representation,
should be used for the analysis
that is specific in the multiple criteria regime.5 Thus, the users’ benefit functions are redefined as,

Benefit from relevance:

=

(15a)

,

Total benefit:

=− (

,

Benefit from faithful representation:
=

,

+

=

− (

− )

(15b)

,

− ) .

(15c)

From equations (14c) and (15c), the net total cost function in the marketplace in the multiple
criteria regime is formalized as
,

=
=

,
+

,
=

We have to solve the problem for,
Minimize<

Subject to

,

,

to
+

,

∗

1−

−

−2

=2

= 0.

−

,

+ (

(16)

− )
(17)

=− +2

=( +

− )

.

Therefore, the critical (minimum) point ( ∗ ,
∗

+ (

−

,
in (
, respectively, as

The critical point of
,
on
and
,

−
1−

).

,

) space is determined by differentiating

=0
(18)

∗

) is obtained as
(19)

∗ ∗
,
to become the optimal solution in the multiple criteria regime
Since the condition for
∗∗ ∗∗
∗
∗
,
is
< , the following inequality should be met as

+
5

<

.

(20)

Technically, | − | < −is a condition for usingas the criterion for faithful representation. However, if≤<(a condition for the multiple criteria regime as noted in the discussion about inequality (20)) is met,
always | − | < −is met.

Kawamura: Cost-Benefit Analysis of Mixed Measurement Model

15

This inequality suggests the circumstances where the multiple criteria regime would be preferable
to the single criterion regime. To stay in the multiple criteria regime, , , andshould besmaller, andandshould be larger. Inequality (20) also suggests that ∗ is always no less< .
than , because ≥ 0 and > 0. Therefore, when inequality (20) is met, always ≤This provides an interesting implication that at least all financing assets should be measured at∗∗ ∗∗fair value in the multiple criteria regime. The optimal solution,
is described as
∗∗

,

∗∗

=

+

,

, when

+

<

.

(21)

Although one might make a priori arguments that,should be (0,1), (0, ), ( , 1),( , ), or ( ∗ , ) in the multiple criteria regime,6 none of them seems to be justifiable by the
cost-benefit analysis.
If ∗ ≥ ∗ and ≤ ∗ (i.e. + ≥ ), then we have to minimize the net total costsubject to= . Thus, the problem is for,to,

Minimize=

Subject to

=

+

1−

+ (

−

.

− )
(22)

Solving this problem, we obtain the optimal solution as
∗∗

,

∗∗

=

(

)

,

(

, when

)

+

≥

.

(23)

This result is consistent with the optimal solution ∗∗ in the single criterion regime as in (13),=actually implies the single criterion regime.
because,space asIn summary, we have obtained the optimal solutions in
∗∗

,

∗∗

=

+

,

(

)

, when
,

(

)

+

<

, when +

≥

.

(24)

The discussion in cost-benefit analysis in the multiple (two) criteria regime is depicted in
Figure 3. If we try to draw the net total cost functions in,space, the indifferent contoursof the net total cost function are drawn as a set of ellipses that have the same center of ( ∗ , ∗ ) =( + , ) as
+
6

= .

(25)

For example, arguing that,should be (0,1) means that all assets should be measured at historical cost by
the first criterion and all assets also should be measured at fair value by the second criterion.

16

The Japanese Accounting Review, 5 (2015), 1-19

FIGURE 3: THE MULTIPLE CRITERIA REGIME

Maximum scope of fair value
measurement for Entity

andMaximum scope of historical costmeasurement for Entity≥ 0 is a constant that defines the height of the indifferent contour ellipses. As
becomessmaller, the indifferent contour ellipses become lower inand smaller in,space,∗ ∗,= ( + , ) and = 0. The
moving towards cost minimization at a point where
location of the ellipses in,space is defined by , , , , and , and the flatness of theellipses is defined byand , both of which reflect the business characteristics of the reporting
entities and the surrounding environment thereof. Figure 3 illustrates the business characteristics
by depicting each set of the indifferent contour ellipses that have theof entities , , andsame center of points , , and , respectively (although is assumed to be indifferent among
those entities in Figure 3). For example, some entities, like entity , which face strong demand
for fair value information by their users (larger ), would locate their set of contour ellipses
upward in,space. Other entities, like entity , with a larger cost of fair value,
spacemeasurement (larger ) would locate their set of contour ellipses downward inand shape them horizontally flat.

Kawamura: Cost-Benefit Analysis of Mixed Measurement Model17

In the area that meets ≤<(i.e. + <in the shaded area), the minimum∗∗ ∗∗point (like point ) should be the optimal pair,= ∗ , ∗ = ( + , ). This is thesolution in the multiple criteria regime. In this circumstance, two sets of accounting informationthat are prepared based on two different criteria, ∗∗ and ∗∗ , should be disclosed. When theminimum point, like points
and , is in the area that meets
≥
and ≤
(i.e.
+ ≥ ), the points
and , which represent the points of contact between the set ofcontour ellipses and the restriction line ( = ), should be the optimal scope of fair value
measurement ∗∗ = ∗∗ = ( ) . In this case, only one set of accounting information should
be provided. Such disclosure belongs to the single criterion regime.
The restriction≤
guarantees that every asset position is accounted for by historicalcost measurement or by fair value measurement, because (1 − ) +≥ 1. This characteristicof accounting can be described as completeness. Such completeness in accounting imposes somecost, which is represented by the excess of the net total cost that is realized by the optimized
solution in the single criterion regime (i.e.
( ∗∗ , ∗∗ ) where ∗∗ = ∗∗ ) over the lowest net∗ ∗total cost that would be realized (i.e.
( , )) if the completeness were ignored.
The result also implies that not all entities would be required to disclose two sets ofaccounting information. Like entities
and , in the case where + ≥ , entities would
not have to disclose two sets of accounting information. As discussed earlier, in the multiple
criteria regime, the entities should measure all financing assets at fair value. Even in the single
criterion regime, some entities, like entity , should measure all financing assets at fair value, butother entities, like entity , would not even have to measure all financing assets at fair value.

5. Conclusions
One of the challenges in financial reporting is optimizing the balance between various
often-conflicting interests in the marketplace. The balancing acts in such tradeoffs are afundamentally inevitable task needed to solve the problems in financial reporting. I demonstrated
a cost-benefit analysis for explaining the mechanism that determines the scopes of fair value
measurement and historical cost measurement by focusing on various parameters that affect the
incentives of the market participants. Accounting regulation is needed to achieve the optimal
solution in the marketplace, which is not the preparer’s voluntary choice. Adopting multiple
criteria regime that produces two different sets of accounting information would provide morecost-effective solution if a certain condition is met. This result implies that the regime chosen
depends on the parameters that describe the business characteristics and environment of thereporting entities, indicating that different accounting regulations are needed to encompass
differences in business models.

18

The Japanese Accounting Review, 5 (2015), 1-19

REFERENCESAMERICAN ACCOUNTING ASSOCIATION (AAA). 1966. A Statement of Basic Accounting Theory. Sarasota,
FL: AAA.
BARKER, R. 2010. The operating-financing distinction in financial reporting. Accounting and BusinessResearch 40 (4): 391-403.
BARTH, M. E. 2007. Standard-setting measurement issues and the relevance of research. Accounting andBusiness Research 37 (supplement 1): 7-15.
BARTH, M. E., AND W. R. LANDSMAN. 1995. Fundamental issues related to using fair value accounting
for financial reporting. Accounting Horizons 9 (4): 97-107.
BEAVER, W. H., AND S. G. RYAN. 2000. Biases and lags in book value and their effects on the ability ofthe book-to-market ratio to predict book return on equity. Journal of Accounting Research 38 (1):127-148.
DYE, R. A., AND S. S. SRIDHAR. 2004. Reliability-relevance trade-offs and the efficiency of aggregation.
Journal of Accounting Research 42 (1): 51-88.
FELTHAM, G. A., AND J. A. OHLSON. 1995. Valuation and clean surplus accounting for operating andfinancial activities. Contemporary Accounting Research 11 (2): 689-731.
FINANCIAL ACCOUNTING STANDARDS BOARD (FASB). 1976. Conceptual Framework for Financial
Accounting and Reporting: Elements of Financial Statements and Their Measurement. Discussion
Memorandum. Stamford, CT: FASB.
FASB. 1985. Elements of Financial Statements—a replacement of FASB Concepts Statement No. 3. Statementof Financial Accounting Concepts No. 6. Stamford, CT: FASB.
FASB. 1998. Accounting for Derivative Instruments and Hedging Activities. Statement of Financial
Accounting Standards No. 133. Norwalk, CT: FASB.
FASB. 2000. Using Cash Flow Information and Present Value in Accounting Measurements. Statement of
Financial Accounting Concepts No. 7. Norwalk, CT: FASB.
FASB. 2008. Preliminary Views on Financial Statement Presentation. Discussion Paper. Norwalk, CT: FASB.
FASB. 2010a. Conceptual Framework for Financial Reporting—Chapter 1, The Objective of General Purpose
Financial Reporting, and Chapter 3, Qualitative Characteristics of Useful Financial Information (areplacement of FASB Concepts Statements No. 1 and No. 2). Statement of Financial Accounting
Concepts No. 8. Norwalk, CT: FASB.
FASB. 2010b. Proposed Accounting Standards Update—Accounting for Financial Instruments and Revisions to
the Accounting for Derivative Instruments and Hedging Activities—Financial Instruments (Topic 825)
and Derivatives and Hedging (Topic 815). Exposure Draft. Norwalk, CT: FASB.
FASB. 2013. Proposed Accounting Standards Update—Financial Instruments—Overall (Subtopic 825-10):
Recognition and Measurement of Financial Assets and Financial Liabilities. Exposure Draft. Norwalk,
CT: FASB.
HITZ, J-M. 2007. The decision usefulness of fair value accounting: a theoretical perspective. European
Accounting Review 16 (2): 323-362.
HOLTHAUSEN, R. W., AND R. L. WATTS. 2001. The relevance of the value-relevance literature forfinancial accounting standard setting. Journal of Accounting and Economics 31 (1): 3-75.
INTERNATIONAL ACCOUNTING STANDARDS BOARD (IASB). 2008. Reducing Complexity in Reporting
Financial Instruments. Discussion Paper. London, U.K.: IFRS Foundation.

Kawamura: Cost-Benefit Analysis of Mixed Measurement Model

19

IASB. 2010a. Financial Instruments. IFRS 9. London, U.K.: IFRS Foundation.
IASB. 2010b. The Conceptual Framework for Financial Reporting. London, U.K.: IFRS Foundation.
IASC. 1989. Framework for the Preparation and Presentation of Financial Statements. London, U.K.: IASC.
LANDSMAN, W. R. 2007. Is fair value accounting information relevant and reliable? Evidence from capital
market research. Accounting and Business Research 37 (supplement 1): 19-30.
LAYARD, R., AND S. GLAISTER. 1994. Cost-Benefit Analysis. 2nd ed. Cambrige, U.K.: Cambridge
University Press.
OHLSON, J. A. 1995. Earnings, book values, and dividends in equity valuation. Contemporary Accounting
Research 11 (2): 661-687.
PEASNELL, K. V. 1982. Some formal connections between economic values and yields and accounting
numbers. Journal of Business Finance and Accounting 9 (3): 361-381.