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Department
Administrative Studies
Course
ADMS 1000
Professor
Yung Ching C Hing
Semester
Fall

Description
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 Copyright © 2012 Pearson Canada Inc 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. Copyright © 2012 Pearson Canada Inc 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. Copyright © 2012 Pearson Canada Inc 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. Copyright © 2012 Pearson Canada Inc 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. Copyright © 2012 Pearson Canada Inc 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 Copyright © 2012 Pearson Canada Inc 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 Copyright © 2012 Pearson Canada Inc 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. Copyright © 2012 Pearson Canada Inc 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 Copyright © 2012 Pearson Canada Inc 70 Scott, Financial Accounting Theory, 6th Edition Instructor’s Manual Chapter 3 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. Copyright © 2012 Pearson Canada Inc 71 Scott, Financial Accounting Theory, 6th Edition Instructor’s Manual Chapter 3 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)  0.301.00 1.00 (0.301.00)  (0.700) P( ) (GN L/ ) P( /GN ) P(H ) (N H/ ) L ( ) (L / )  0.70 0  0 (0.30 1.00) (0.70 0) Copyright © 2012 Pearson Canada Inc 72 Scott, Financial Accounting Theory, 6th Edition Instructor’s Manual Chapter 3 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. Copyright © 2012 Pearson Canada Inc 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) 0.300.80   0.30    0.300.80  0.700.80 P(L)P(GN / L) P(L/GN)  P(H)P(GN / H)  P(L)P(GN / L) 0.700.80  (0.300.80) (0.700.80)  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. Copyright © 2012 Pearson Canada Inc 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. Copyright © 2012 Pearson Canada Inc 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 30.801/2 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. Copyright © 2012 Pearson Canada Inc 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 Copyright © 2012 Pearson Canada Inc 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 Copyright © 2012 Pearson Canada Inc 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 Copyright © 2012 Pearson Canada Inc 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 1085z 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: 0.10200  0.06z 20 0.06z 200  200 She has a 0.20 probability that the market portfolio will increase by 2 1/2%, giving Copyright © 2012 Pearson Canada Inc 80 Scott, Financial Accounting Theory, 6th Edition Instructor’s Manual Chapter 3 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 (360.36z 0.0009z ) 40,000 Toni's utility, as a function of z, is thus U i  x   2 2(170.045 )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(170.045 ,800) 1 2 Ui(9,800)   [360.369,8000.0009(9,800) ] 200 40,000  4.582.25  2.33 Copyright © 2012 Pearson Canada Inc 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). Copyright © 2012 Pearson Canada Inc 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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