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

© 2006 Pearson Education Canada Inc.

3-1

Chapter 3

The Decision Usefulness Approach to

Financial Reporting


3-2

Single-Person Decision Theory

Perfectly Specified Decision Process


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


3-4

Example

• Perfectly Specified Decision Process

– A game against Nature. “Nature does not think”

– NB: Concept of an “Information System”

Bill Scott

Note to Instructors: This example is slightly simpler than the text example. here, the decision-maker is risk-neutral. Otherwise, the concepts are the same.


3-5

Perfectly Specified Decision Process

Consider an investor with $10,000 to invest in one of the following mutually exclusive acts:

a1: buy shares of x Ltd. For $10,000

a2: buy Canada Savings Bonds (CSB) for $10,000

Let there be 3 “states of nature”:

θ1: shares fall 10% in market value

θ2: shares hold steady

θ3: shares rise 80%


3-6

Perfectly Specified Decision Process, Cont.

Payoff Table Prior Probabilities

Outcome

θ1 θ2 θ3

a1 -1000 0 8000

a2 1000 1000 1000

P(θ1) = .05

P(θ2) = .70

P(θ3) = .25

1.00


3-7

Perfectly Specified Decision Process, Cont.

Assume the investor uses expected monetary value as a decision criterion (EMV)

EMV (a1): (.05)(-1000) + 0 + .25(8000) = 1950

EMV (a2): (.05)(1000) + .70(-1000) +.25 (1000)

= 1000

Therefore, if investor acts now, should take a1.

But: May be worthwhile to secure additional information.


3-8

Decision ProblemThink 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:

9.1/

05./":"1 CLCA

SENIpoorm

0.2/

12./":"2 CLCA

SENIfairm

2.2/

18./":"3 CLCA

SENIgoodm


3-9

Decision Problem, Cont.The information system can be characterized by the following table:

P(m1/θ) P(m2/θ) P(m3/θ)

θ1 .75 .20 .05

Θ2 .50 .30 .20

θ3 .10 .20 .70

These conditional probabilities, or likelihoods, are the probabilities of receiving the various messages conditional on each state being true.


3-10

Decision Problem, Cont.Now, for any message, the decision maker can revise his/her prior probabilities using Bayes’ Theorem.

Suppose that m1 was received from the financial statements.

09.

4125.

)75)(.05(.

/

//

1

11111

PmP

mPPmP

=P(m1) =.85

=.06

1.00

Then:

Similarly: )/( 12 mP

)/( 13 mP


3-11

Decision Problem, Cont.

Note the EMV of each act is

1000)(

390$)8000)(06(.0)1000)(09(.)(

2

1

aEMV

aEMV

So if m1 were received act a2 would be chosen.


3-12


You should verify that if m2 was received:

0000.1

1852.)/(

7778.)/(

0370.)/(

23

22

21

mP

mP

mP

2700.

)()/()( 22

PmPmPwhere

And the optional act is then a1 with EMV of $1444.48.


3-13


Similarly, if m3 was received:

0000.1

5512.)/(

4409.)/(

0079.)/(

33

32

31

mP

mP

mP

where 3175.)( 3 mP


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


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


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?


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

Bill Scott

Instructors using this slide may wish to refer to the Instructor's Manual, Chapter 3, teaching suggestion 4, for backup discussion.


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


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.


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

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

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