© 2006 Pearson Education Canada Inc.3-1 Chapter 3 The Decision Usefulness Approach to Financial Reporting

© 2006 Pearson Education Canada Inc.3-2 Single-Person Decision Theory Perfectly Specified Decision Process

© 2006 Pearson Education Canada Inc.3-3 Motivation for Decision Theory Model A model of rational decision making in the face of uncertainty Other ways to make decisions? Captures average investor behaviour? Helps us understand how financial statement information is useful

© 2006 Pearson Education Canada Inc.3-4 Example Perfectly Specified Decision Process –A game against Nature. “Nature does not think” –NB: Concept of an “Information System”

© 2006 Pearson Education Canada Inc.3-5 Perfectly Specified Decision Process Consider an investor with $10,000 to invest in one of the following mutually exclusive acts: a 1 : buy shares of x Ltd. For $10,000 a 2 : buy Canada Savings Bonds (CSB) for $10,000 Let there be 3 “states of nature”: θ 1 : shares fall 10% in market value θ 2 : shares hold steady θ 3 : shares rise 80%

© 2006 Pearson Education Canada Inc.3-6 Perfectly Specified Decision Process, Cont. Payoff TablePrior Probabilities Outcome θ1θ1 θ2θ2 θ3θ3 a1a a2a P(θ 1 ) =.05 P(θ 2 ) =.70 P(θ 3 ) =

© 2006 Pearson Education Canada Inc.3-7 Perfectly Specified Decision Process, Cont. Assume the investor uses expected monetary value as a decision criterion (EMV) EMV (a 1 ): (.05)(-1000) (8000) = 1950 EMV (a 2 ): (.05)(1000) +.70(-1000) +.25 (1000) = 1000 Therefore, if investor acts now, should take a 1. But: May be worthwhile to secure additional information.

© 2006 Pearson Education Canada Inc.3-8 Decision Problem Think of the financial statements of X Ltd. as an information system conveying information about probabilities of θ. Assume the financial statements will give one of the following 3 mutually exclusive messages:

© 2006 Pearson Education Canada Inc.3-9 Decision Problem, Cont. The information system can be characterized by the following table: P(m 1 /θ)P(m 2 /θ)P(m 3 /θ) θ1θ Θ2Θ θ3θ These conditional probabilities, or likelihoods, are the probabilities of receiving the various messages conditional on each state being true.

© 2006 Pearson Education Canada Inc.3-10 Decision Problem, Cont. Now, for any message, the decision maker can revise his/her prior probabilities using Bayes’ Theorem. Suppose that m 1 was received from the financial statements. =P(m 1 ) =.85 = Then: Similarly:

© 2006 Pearson Education Canada Inc.3-11 Decision Problem, Cont. Note the EMV of each act is So if m 1 were received act a 2 would be chosen.

© 2006 Pearson Education Canada Inc.3-12 Decision Problem, Cont. You should verify that if m 2 was received: where And the optional act is then a 1 with EMV of $

© 2006 Pearson Education Canada Inc.3-13 Decision Problem, Cont. Similarly, if m 3 was received: where

© 2006 Pearson Education Canada Inc.3-14 The Information System One of the Most Important Text Concepts Conditional on Each State of Nature (i.e., future firm performance), gives Objective Probability of the GN or BN in the Financial Statements

© 2006 Pearson Education Canada Inc.3-15 The Information System, Cont’d. Translation of First Entry in Information System Example in Table 3.2 of Text: –If future firm performance is going to be good, the probability that the current financial statements will show GN is 0.80

© 2006 Pearson Education Canada Inc.3-16 Information Defined Information is Evidence that has the Potential to Affect an Individual’s Decision –An ex ante definition –Individuals receive information all the time –Individual-specific –Are financial statements information?

© 2006 Pearson Education Canada Inc.3-17 Does it Work? Problems of Implementing Model –Specify states of nature –Prior probabilities of states (subjective) –Payoffs –Information system s/b objective Forces Careful Consideration How Else to Decide? Captures Average Behaviour

© 2006 Pearson Education Canada Inc.3-18 The Rational Investor Definition –Maximizes expected utility, using the single- person decision theory model –May be risk averse Then, will diversify Needs information about risk as well as expected return

© 2006 Pearson Education Canada Inc.3-19 Beta Definition –Standardized covariance between return on share and return on market Only Relevant Risk Measure for a Reasonably Diversified Investor –Why? Because firm specific risk diversifies away.

© 2006 Pearson Education Canada Inc.3-20 Decision Theory Model Underlies Concepts Statements Rationale for Concepts Statements Examples –FASB SFAC No. 1 –FASB SFAC No. 2 –CICA Handbook, Section 1000