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Scott, Financial Accounting Theory, 6th EditioInstructor’s Manual Chapter 3
CHAPTER 3
THE D ECISIONU SEFULNESS A PPROACH TO FINANCIAL REPORTING
3.1 Overview
3.2 The Decision Usefulness Approach
3.2.mmary
3.3 Single-Person Decision Theory
3.3.1 Decision Theory Applied
3.3.2 The Information System
3.3.3 Information Defined
3.3.mmary
3.4 The Rational, Risk-Averse Investor
3.5 The Principle of Portfolio Diversification
3.5.mmary
3.6 The Optimal Investment Decision
3.6.mmary
3.7 Portfolio Risk
3.7.1 Calculating and Interpreting Beta
3.7.2 Portfolio Expected Value and Variance
3.7.3 Portfolio Risk as the Number of Securities Increases
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62 Scott, Financial Accounting Theory, 6th Edition Instructor’s Manual Chapter 3
3.7.mmary
3.8 The Reaction of Professional Accounting Bodies to the Decision Usefulness
Approach
3.8.mmary
3.9 Conclusions on Decision Usefulness
LEARNING O BJECTIVES AND S UGGESTED T EACHING A PPROACHES
1. Decisionefulness
The main purpose of this Chapter is to provide a framework for understanding the
concept of decision usefulness of financial reporting. Consistent with the conceptual
frameworks, I assume that the major decision problem to which financial reporting is
oriented is the investment decision. I then argue that if accountants are to produce
financial statements that are useful for investment decisions, they need to understand
how rational investors make such decisions.
2. Single-person Decision Theory
I use this theory, including the revision of beliefs by means of Bayes’ theorem, as a
model of rational investment decision making. Prior to getting into the theory itself, I
usually discuss with the class how they would proceed to make investment decisions if
they had a sum of money to invest, and steer the discussion to make the point that
single-person decision theory provides a systematic and formal way to do what many of
them would do anyway. Some instructors and students may disagree with this
argument, in view of increasing acceptance by academics that securities markets are
not fully efficient, and that investors may not be rational in an economic sense. These
issues are discussed in Section 6.2. I argue there that securities markets are sufficiently
close to full efficiency that the efficient markets model is still the most useful one to use
for studying the information needs of investors, and that the rational investment decision
model can explain security price behaviour that is often attributed to non-rational
investor behaviour. I also argue that to the extent securities markets are less than fully
efficient, the scope for decision useful information is increased.
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63 Scott, Financial Accounting Theory, 6th Edition Instructor’s Manual Chapter 3
I stick quite close to the text when illustrating the decision theory model, since this
model and the concepts that go into it are new to most students. I go over in detail
either the text example or some other similar example such as one of the end-of-
chapter problems. I always end up by asking the class how realistic they think the model
is (see point 4 below for additional discussion). If a student is particularly critical, I fall
back on asking again how he or she would make an investment decision under similar
circumstances. I do not particularly try to defend the extent to which the model can be
operationalized. However, as stated above, I do make the argument that whether it is
operational or not, it is a very useful conceptual device to help us understand what
information is and how investors may find financial statement information to be useful.
It is important to emphasize that the decision theory model is a model of an average
investor. There is no implication that all investors act this way. The real question is
whether investors on average behave as the model predicts or whether on average they
are biased away from the model’s predictions.
3. The Concept of an Information System
This is one of the most important concepts in the text. While the idea of the financial
statements being represented as a table of objective, conditional probabilities may take
some getting used to, the information system provides the crucial link between current
reported performance and the future performance of the firm. It conceptualizes the
quality of the financial statements with respect to their usefulness for investment
decisions.
Many reporting issues can be conceptualized by their effect on the main diagonal
probabilities of the information system. For example, a switch from historical cost to
current value accounting, or earlier recognition of revenue, increases these probabilities
by increasing relevance. This tightens up the relationship between current and future
performance and, other things equal, increases decision usefulness. However, to the
extent that fair value accounting and early revenue recognition are less reliable than
historical cost, this would have the opposite effect on the main diagonal probabilities.
The net effect on decision usefulness is thus not clear, but the information system is
helpful in conceptualizing the nature of the tradeoffs in accounting policy choice and the
concept of earnings quality--higher main diagonal probabilities, higher quality.
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64 Scott, Financial Accounting Theory, 6th Edition Instructor’s Manual Chapter 3
There are numerous ways of measuring earnings quality empirically, such as analyst
forecast revisions, market response, accruals. All of them can be tied back conceptually
to the main diagonal probabilities.
I find that the students’ understanding of the information system is helped if the
instructor spends some time on the two extremes — a perfect system and a useless
system. See Problem 1 of this chapter. This problem pushes understanding by showing
what happens when state probabilities are revised by Bayes’ theorem using the
conditional probabilities from the perfect and from the useless information systems.
I have structured the states of nature in Example 3.1 in terms of future firm
performance, rather than some more primitive states such as good economy or bad
economy. Future firm performance can be conceptualized in terms of future cash flows,
earnings, or dividends
Many discussions and models of firm performance and value are based on expected
future cash flows, particularly in the finance literature. I include future earnings as an
alternate measure of performance and value to be consistent with Ohlson’s clean
surplus theory, which is discussed in Section 6.5. The Ohlson theory shows that the
market value of the firm can equally be expressed in terms of expected future dividends,
cash flows or financial statement variables. Since this is an accounting text, it seems
natural to take financial statement variables such as earnings as a fundamental
determinant of firm performance and value, on an equal footing with cash flows and
dividends. Also, because of the Ohlson theory, prediction of future earnings is becoming
more common in empirical accounting research. Empirical implications of clean surplus
theory are discussed and illustrated in Section 6.5.4.
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65 Scott, Financial Accounting Theory, 6th Edition Instructor’s Manual Chapter 3
4. Does it Work?
While, as stated above, I do not particularly try to defend the decision theory model as
an operational way to make decisions, I do spend some time discussing with the class
whether they would be willing to make an investment decision this way. The following
notes, which could be distributed to the students, discuss some of the issues in applying
the procedure.
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66 Scott, Financial Accounting Theory, 6th Edition Instructor’s Manual Chapter 3
Issues in Applying the Decision Theory Model
Specifying the states of nature. States of nature are specific to the decision problem at
hand. For example, if my decision is whether or not to take my raincoat, relevant states
would be rain or no rain. That is, the relevant states of nature are simply those random
events whose outcome matters to the decision at hand. In an investment context, these
can be taken as different levels of future firm performance, since it is future performance
that determines investment payoff.
Specifying prior probabilities of the states of nature. These capture everything the
decision maker knows up to the beginning of the decision analysis. There are
techniques to help specify these probabilities. One technique is to conceptualize an urn
containing 100 coloured balls, of which a certain number are red and the remainder
black. To illustrate, suppose an investor wants to assess his/her prior probability of high
future firm performance next year. Envisage a bet of, say, $50 on this state—if future
performance is high you win $50, otherwise you lose $50. Now consider another bet.
You will draw 1 ball from the (opaque) urn. If you draw a red ball you win $50, otherwise
you lose $50. How many red balls should there be in the urn so that you are indifferent
between the 2 bets? Suppose you decide you would be indifferent if the urn contains 6
red balls. Then, your subjective probability of high future firm performance is 0.06.
Since prior probabilities are subjective, we cannot say that this probability is “correct.”
The point is, however, that in deciding on the number of red balls you are forced to
consider everything you know about the firm’s future prospects.
Specifying payoffs. For each state of nature, specification of your payoff if a particular
state happens should be relatively straightforward. For example, suppose you invest
$10,000 in shares of X Ltd. and the high performance state happens. Analysis of past
share price behaviour of X Ltd. when the firm is performing well may reveal an average
share return of 16%, that is, a net payoff of $1,600.
Of course, if you decide to invest your $10,000 in a riskless asset instead, the states of
nature for X Ltd. do not affect your payoff—if you buy a government bond yielding 2 ¼
%, your payoff will be $225 regardless of X’s performance. That is, states of nature only
apply to decisions with uncertain payoffs. Nevertheless, in deciding between a risky and
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67 Scott, Financial Accounting Theory, 6th Edition Instructor’s Manual Chapter 3
a riskless investment, you need to evaluate the payoff from the risky asset even if your
decision turns out to be to buy the riskless one. In other cases, your decision may be
between 2 or more risky investments. Then, the same set of states applies to each
possible investment. Text problems 11 and 17 illustrate this situation.
Specifying your utility function. Since most decision makers are risk averse, the
expected utility of a risky payoff depends on how risky it is. The text uses the device of a
utility function to calculate expected utility. There are techniques available to interrogate
yourself to estimate your utility function. A related approach is to estimate your expected
utility for a given risky investment directly. For example, suppose you are facing a
gamble of a 0.30 probability of a payoff of $1,600 and a 0.70 probability of a payoff of
zero. Ask yourself, what certain payoff would you need to be indifferent between this
payoff and the risky gamble just described? Suppose you feel the certain payoff is $200.
Then, you would use $200 as your expected utility for the risky gamble. If an alternative
investment yields a certain payoff of $225, your expected utility for this “gamble” is
$225, since no risk is involved. Then, you would choose the riskless decision
alternative.
Versions of this approach are used by investment advisors, who ask clients whether
their tolerance for risk is low, medium, or high.
The information system. If you decide to gather more information before acting,
specification of the information system is the most difficult aspect of your decision
problem. Unlike prior probabilities, information system probabilities are objective. If your
additional evidence is to be obtained from financial statements, the information system
probabilities are determined by the quality of GAAP. Thus, if X Ltd. is in the high
performance state, the probability that the financial statements show GN will be higher
the higher is the quality of GAAP. Nevertheless, it is still possible that the financial
statements show BN since GAAP cannot completely rule out errors and biases in
accounting estimates.
One approach to estimating information system probabilities is to use a sampling
approach to analyze the past relationship between financial statements and subsequent
firm performance. When past financial statements have shown GN, how many times
has next year’s firm performance been high, etc.? Another approach is to estimate
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68 Scott, Financial Accounting Theory, 6th Edition Instructor’s Manual Chapter 3
information system probabilities based on analyst reaction to the financial statements,
as outlined in Section 3.3.2 of the text. The stronger is analyst reaction per dollar of GN
or BN, the higher the information system main diagonal probabilities.
Conclusion. You may feel that there are so many issues surrounding the inputs into the
decision theory model that the procedure is not viable. If so, ask yourself how else you
would make a decision under uncertainty. By forcing careful consideration of the
variables that really matter to a decision, the decision theory approach may well lead to
better decision making on average.
Of course, you may instead turn your decision making over to an expert, such as a
financial institution or advisor. However, if you do, you still face a decision problem--
which financial advisor, how much to invest, do you accept the advisor’s advice, etc.
The issues described above still apply.
Finally, whether or not you accept the model, a major argument of Chapter 3 is that the
model reasonably captures the behaviour of the average investor, even though
individual investors may not follow the procedures exactly. As such, the model provides
guidance to accountants about the information needs of investors and the crucial role of
information in facilitating these decisions.
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69 Scott, Financial Accounting Theory, 6th Edition Instructor’s Manual Chapter 3
5. Portfolio Theory and the Optimal Individual Investment Decision
The text then goes on to illustrate a number of standard concepts and results from
portfolio and investment theory in Sections 3.5 to 3.7, incl. In response to several
comments from users of earlier editions about the technical nature of much of this
material, I have added a note in the text that this material can be skipped without
substantial loss of continuity, and have made some small changes in the following
chapters as a result.
I treat this material, Sections 3.5 to 3.7, as a specialization of single-person decision
theory to the investment decision. The main point I make is that the theory implies that
useful information is information that helps investors estimate expected returns and
betas (i.e., risk) of securities.
Other than a brief, intuitive discussion of risk aversion in Section 3.4, I usually do not
spend much class time on the material in Sections 3.4 to 3.7. Many students will already
have seen this theory in other courses. For those who have not, the text discussion is
designed to be self-contained, with liberal use of a running example.
6. Back to the Real World
At this point, it is important to bring the students back to the “real world” of accounting. I
do this by demonstrating that the draft joint IASB/FASB Conceptual Framework
(Chapters 1 and 2) has “bought” the decision usefulness approach. The main difference
from the decision theory model presented in the text is that the word ‘rational” does not
appear as an investor characteristic. Presumably, this is because of the theory and
evidence from behavioural finance that disputes rationality. Also, the Framework
envisages the role of financial reporting as providing information to a wide variety of
constituencies, not just to investors. Since “true” net income does not exist, and since
different users have decision needs, it is not clear to me how a single set of financial
statements can cater to different user constituencies. Nevertheless, the role of financial
reporting as conveying useful information to decision makers comes through clearly in
the framework.
The word “rational” is used in SFAC 1, being Chapter 1 of the original FASB conceptual
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framework. Since SFAC 1 is still in effect, and will presumably remain so until
IASB/FASB agreement is reached on the new version, some instructors may be
interested in the route by which such an abstract theory as the theory of rational
decision entered into the FASB concepts statements. The source appears to be the
American Institute of Certified Public Accountants Study Group on the Objectives of
Financial Statements, “Objectives of Financial Statements,” (New York, NY: AICPA,
1973), also known as the Trueblood Report. According to Zeff in his article “The
Evolution of the Conceptual Framework for Business Enterprises in The United States,”
(Accounting Historians Journal (December, 1999)), the Trueblood Report provided a
“blueprint” for the FASB concepts statements. This can be seen with particular clarity in
Volume 2: Selected Papers of the Trueblood Report, which contains several studies on
the use of accounting information in normative models of investor
consumption/investment decisions. See, in particular,
Ronen, J., “A User Oriented Development of Accounting Information
Requirements,” in J. J. Cramer and G. H. Sorter, editors., Objectives of
Financial Statements: Volume 2 / Selected Papers (The Trueblood Report)
(New York, NY: American Institute of Certified Public Accountants, 1974),
pp. 80-103.
Ronen, J. and G. H. Sorter, “The Descriptive and the Normative,” in J. J.
Cramer and G. H. Sorter, editors., Objectives of Financial Statements:
Volume 2 / Selected Papers (The Trueblood Report) (New York, NY:
American Institute of Certified Public Accountants, 1974), pp. 24-29.
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S UGGESTED SOLUTIONS TO Q UESTIONS AND P ROBLEMS
1. Perfect or Fully-Informative Information System
CuFrnantatlInfnrtmation
GN BN
State of nature High 1 0
(future profitability)
Low 0 1
Here, each state produces a different message with probability 1. Thus, if the
state is H, the financial statements will show GN for certain, and so forth.
Prior probabilities of the states of nature are:
0.30P(H)
0.7=P(L)
(any other set of prior probabilities with P(H) > 0 would do)
Suppose that GN is observed. Then, by Bayes’ theorem:
P(H)P(GN / H)
P(H /GN)
P(H)P(GN / H) P(L)P(GH / L)
0.301.00 1.00
(0.301.00) (0.700)
P( ) (GN L/ )
P( /GN ) P(H ) (N H/ ) L ( ) (L / )
0.70 0 0
(0.30 1.00) (0.70 0)
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Thus, with a perfect information system, the information perfectly reveals the true
state of nature.
If BN is observed, similar calculations give P(H/BN) = 0, P(L/BN) = 1.
Non-Informative Information System
Current Financial Statement Information
GN BN
State of nature High 0.8 0.2
(future profitability) Low 0.8 0.2
Here, both rows of the information system are the same. Any system with both
row probabilities the same would do.
Note: Students have a tendency to use 0.5 probability in each row. This is OK,
but instructors may wish to point out that other probabilities, such as those used
above, also produce a non-informative system as long as the probabilities in
each row are the same. More generally, the information system is non-
informative if the row probability vectors are linearly dependent.
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73 Scott, Financial Accounting Theory, 6th Edition Instructor’s Manual Chapter 3
Suppose that GN is observed. Then, by Bayes’ theorem:
P(H /GN) P(H)P(GN / H)
P(H)P(GN / H) P(L)P(GN / L)
0.300.80
0.30
0.300.80 0.700.80
P(L)P(GN / L)
P(L/GN)
P(H)P(GN / H) P(L)P(GN / L)
0.700.80
(0.300.80) (0.700.80) 0.70
The posterior probabilities are the same as the prior probabilities in this case,
which is what we would expect if the information system is non-informative. That
is, regardless of which is the true state, the state probabilities are the same after
the financial statements as before. In effect, the information cannot discriminate
between states. Thus, it is non-informative, or useless.
A similar result holds if BN is observed.
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74 Scott, Financial Accounting Theory, 6th Edition Instructor’s Manual Chapter 3
2. The utility function of a risk-taking investor would appear as the solid line below:
U((x)
2566
76.88
5.0625
x(payyof))
0 2255 480 1,6000
Compared with Figure 3.3, the utility function is convex, rather than concave.
Thus, as the payoff x increases, utility increases at an increasing rate, rather than
at a decreasing rate.
A specific example of a risk-taking utility function is:
2
U ( ) x
10,000
yielding the utilities shown on the vertical axis of the above figure.
Consistent with Example 3.1, suppose a risky investment offers a payoff of
$1,600 with probability 0.30 and $0 with probability 0.70, giving an expected
return of $480. Our risk-taking investor's expected utility for this investment is 256
× 0.30 + 0 × 0.70 = 76.80. The utility of the risk free investment, which offers a
payoff of $225 for sure, is only 5.0625. Thus, for the same prior probabilities and
payoffs, the risk-taking investor prefers the risky investment whereas Bill
Cautious, who is risk averse, prefers the risk-free investment.
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75 Scott, Financial Accounting Theory, 6th Edition Instructor’s Manual Chapter 3
A risk-taking investor will specialize (that is, buy only one security) — the one
with the highest risk for a given expected return. There is no incentive to diversify
for an investor who likes risk.
A risk-taking investor needs the same information as any other investor —
information that will be useful in assessing expected returns and risks of
securities. However, risk-taking investors will use the information differently. They
will seek to find the securities that, for a given return, have the highest risk.
3. aor 2 to yield the same utility as a ,1we must have:
3x 1/2 2 2.384
2 x
30.801/2 2 2.384
x
2
Soflving x :
1/2 2 2.400 2.384
x
0.016
x 0.032
A risk-averse investor trades off risk and expected return. An investment act with
a lower expected return must also have lower risk if it is to give the same
expected utility. As shown in the calculation, the risk of a (0.032) is less than that
2
of a1 (0.512) in order to compensate for the reduction in expected return from
0.88 to 0.80.
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76 Scott, Financial Accounting Theory, 6th Edition Instructor’s Manual Chapter 3
4. From Figure 3.5, we have:
2
at Z : x 0.1075, x 0.0020
2
at M : x 0.0850, x 0.0009
Toni’s utility at Z: Ui(Z) = 1/2 × 0.1075 - 16 × 0.0020 = 0.0218
Toni’s utility at M: U (M) = 1/2 × 0.0850 - 16 × 0.0009 = 0.0281
i
Thus, Toni no longer prefers Z over M, as she did in the illustration of Figure 3.5,
because she is now more risk averse. She therefore would not want to increase
her risk by borrowing at the risk-free rate to buy more of the market portfolio. (In
fact, she would probably want to reduce her risk, say, by moving to point Y in
Figure 3.5.)
5. a. The beta of the market portfolio is 1, since the covariance of a random
variable with itself is the same as its variance.
b. The beta of the risk-free asset is zero. The return on the risk-free asset is
a constant and the covariance of a random variable with a constant is zero.
c. We can think of portfolio A + B as a single asset and calculate the
covariance of its payoffs with those of the market portfolio much like we would for
a single security. However, a simpler way is to use the fact that the beta of a
portfolio is a weighted sum of the betas of the securities in the portfolio.
From Example 3.3, Toni invests $200: $120 in A, and $80 in B. Therefore, the
weights of each security in the portfolio are:
: A 120 0.60
200
80
: B 0.40
200
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77 Scott, Financial Accounting Theory, 6th Edition Instructor’s Manual Chapter 3
The betas of each security are given in Section 3.7.1:
βa= 2.6667
β = 1.5556
b
Then:
β = 0.60β + 0.40β
a+b a b
= 0.60 × 2.6667 + 0.40 × 1.5556
= 1.6000 + 0.6222
= 2.2222
6. The variance of the return (that is, the risk) of a portfolio is a weighted sum of the
return variances of the securities in the portfolio and the pairwise covariances of
the returns for each pair of securities in the portfolio. As the number of securities
in the equally weighted portfolio (n) increases, the weights attached to each
2 2
security variance 1/n decreases. Due to the n term in the denominator, the
weight rapidly decreases as n increases.
This rapid decrease captures the fact that firm-specific risk (a security’s variance
is a measure of its firm-specific risk of return) diversifies away as the number of
2
securities in the portfolio gets large. Since 1/n becomes quite small for as few as
n = 10 securities, most of the benefits of diversification can be attained with
relatively few securities.
No, the risk of return does not approach zero as the number of securities in the
portfolio gets larger. This is because the returns on the securities are correlated,
due to economy-wide or systematic risk, which affects the returns on all risky
securities. Then, the portfolio variance also includes all the pairwise covariances
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78 Scott, Financial Accounting Theory, 6th Edition Instructor’s Manual Chapter 3
of return of the securities in the portfolio. While the weights attached to these
2
covariance terms ( 2) also decrease with n, the number of covariance terms
n
n(n 1)
increases rapidly ( ) . Thus, unlike the variance terms, the sum of the
2
covariance terms does not decrease to zero as n increases. This sum captures
the systematic risk of the portfolio, which cannot be diversified away.
7. The argument is probably made because of the lumpiness of certain cash
receipts and disbursements. Cash payments for major purchases such as capital
assets, and for borrowings such as loan proceeds, tend to occur at discrete
intervals in large amounts. As a result, a firm could have what appears as a
favourable cash flow, but one which results, for example, from the proceeds of a
large borrowing rather than from recurring operating transactions. Since financial
statement users are primarily interested in the firm’s ability to generate cash from
operations, it would be necessary to separate out the effects on cash flows of
major transactions such as these.
Even within the category of operating cash flows, there can be lumpiness of
receipts and payments -- for example, a large collection on account may come in
shortly after year end. Under a strict cash basis, this would not appear as a cash
flow in the year. Under accrual accounting, of course, the account receivable (an
accrual) and revenue from such a transaction would be included in the financial
statements regardless of whether the cash was collected yet or not.
In effect, the Framework argues that accrual accounting enables a better
prediction of average or longer-run future operating cash flows or, more
generally, of future firm performance, by recording the inflows (revenues) and
outflows (expenses) in the period in which the major economic activity relating to
those flows takes place. This seems reasonable since accruals anticipate
operating cash inflows or outflows. The recording of accruals results in a more
timely recognition of these cash flows.
8. The reason for the Kim and Cross finding is that net income is determined on an
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79 Scott, Financial Accounting Theory, 6th Edition Instructor’s Manual Chapter 3
accrual basis. Since accruals anticipate future cash flows, they remove the
lumpiness that operating cash flows often exhibit. For example, revenue
recognized from a large sale near the end of the period may not be collected in
cash by the end of the period, yet all or most of the cash outflows associated with
the sale may have been incurred. Then, operating cash flows for the period
would not predict future cash flows as well as net income for the period.
Note: A superior answer would point out that if the firm is in steady state, cash
collections next period from current period sales would be counterbalanced by
cash collections at the beginning of the period from previous period’s sales.
However, these collections may not cancel out completely, even for a firm in
steady state. Also, if the firm is growing, the effect described in the previous
paragraph would continue to apply.
9. Toni’s utility function is , where x and 2 are the mean and variance of
the rate of return of her portfolio, respectively. Toni can borrow an unlimited
amount at 4% to invest in the market portfolio. Then, the expected return on her
portfolio is:
200 .085 1085z 1.4z 200
x
200
17 .045z
200
where $200 is the amount of her own investment, z is the amount borrowed, and
0.085 is the expected return on the market portfolio.
From Section 3.6, Toni has a 0.80 probability that the market portfolio will
increase by 10%, giving a return of:
0.10200 0.06z 20 0.06z
200 200
She has a 0.20 probability that the market portfolio will increase by 2 1/2%, giving
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a return of:
0.025 00 0.015z 5 .015z
200 200
Then, the variance of Toni's return is:
2 2
2 20 0.06 z 17 0.045 z 5 0.015 z 17 0.045 z
200 200 0.80 200 200 0.20
which reduces to
1 2
(360.36z 0.0009z )
40,000
Toni's utility, as a function of z, is thus
U i x 2 2(170.045 )z 1 (36 0.36z 0.0009z )
200 40,000
Then, the sufficient condition for maximum utility is
dU iz) 0.36 0.0018z
dz 0.00045 40,000 40,000 0
which gives z = $9,800
The utility of this investment is
2(170.045 ,800) 1 2
Ui(9,800) [360.369,8000.0009(9,800) ]
200 40,000
4.582.25
2.33
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81 Scott, Financial Accounting Theory, 6th Edition Instructor’s Manual Chapter 3
10. Off-main diagonal probabilities of an information system are non-zero when
conditions are not ideal. Specifically, low earnings quality, that is, low relevance
and/or low reliability will increase these probabilities, resulting in less
informativeness or, equivalently, greater noise or less transparency in the
system. This reflects the fact that when conditions are not ideal, the financial
statements do not provide perfect information about the true state of the firm.
Lower off-main diagonal probabilities or, equivalently, higher main diagonal
probabilities, produce a more informative information system. That is, a given
message results in a better ability to discriminate between states of nature as the
noise produced by the off-main diagonal probabilities decreases. In the limit, the
off-main diagonal probabilities go to zero and the information system becomes
perfectly informative (see Question 1).
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82 Scott, Financial Accounting Theory, 6th Edition Instructor’s Manual Chapter 3
11. a. The decision-usefulness approach to accounting theory is an approach
which deduces the information needs of financial statement users by studying
their decision problems.
b. The two questions which arise are:
i) Who are the users (or constituencies) of financial statements?
ii) What are their decision problems?
c. According to the draft joint Conceptual Framework, the primary
constituency of financial statement users is present and potential equity
investors, lenders, and other creditors who make decisions in their capacity as
capital providers. This constituency is called the primary user group.
According to the draft joint Conceptual Framework, the primary user group needs
information about the amount, timing and uncertainty of the firm’s future cash
flows.
d. The basic characteristic is that financial statement information should be
capable of making a difference in the decisions made by users. For this, financial
statements should provide an informative information system. To maximize
informativeness, the financial statements need the most decision useful trade-off
between characteristics of relevance and reliability.
e. Investors are assumed to be risk averse. Investment theory tells us that
risk-averse investors trade off risk and expected return of securities in making
their investment decisions. Specifically, a risk-averse investor will only be willing
to accept higher risk if the expected return is also higher, and vice versa. To do
this, they need information about the riskiness of securities.
Copyright © 2012 Pearson Canada Inc
83 Scott, Financial Accounting Theory, 6th Edition Instructor’s Manual Chapter 3
12. a. Mr. Smart derives the following utilities from the payoffs:
2 ln(8,000) = 17.97
2 ln(1,000) = 13.82
2 ln(5,000) = 17.03
2 ln(2,000) = 15.20
Based on his prior probabilities, Mr. Smart has the following expected utilities for
the two actions:
EU (common) = (0.50 × 17.97) + (0.50 × 13.82) = 15.90
EU (mutual fund) = (0.50 × 17.03) + (0.50 × 15.20) = 16.12
Thus, to maximize expected utility, Mr. Smart should buy the mutual fund.
b. Let:
G = good state of the economy
B = bad state of the economy
S = evidence obtained from financial statements
Then, by Bayes’ theorem, the posterior probability of the good state is:
P( ) ( / )
P ( / ) P( ) ( / ) P B( ) ( / )

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