Description

QUESTION 1

You invest 500 in a fund this month. For the next following 5 months, you will receive 90, 100, 110, 120, 130, respectively. Suppose the monthly interest rate is 2%, what is the net present value for this investment?

-16.29

-16.61

16.61

16.29

1 points

QUESTION 2

Based on the decision tree on the last page of the slides, what is the expected monetary value if the decision-maker chooses to invest in the new business? Assume that we want to maximize the expected monetary value.

31.5

31

30

29

2 points

QUESTION 3

Based on the decision tree on the last page of the screen, should the decision-maker sells the new business? Assume that we want to maximize the expected monetary value.

True

False

1 points

QUESTION 4

Expected monetary value can take an individual risk attitude into consideration.

True

False

Decision Analysis Ã¢â‚¬â€œ

Decision Tree

Dr. Hao-Wei Chen

1

Modeling in Decision Analysis

Ã¢â‚¬Â¢ Modeling Decisions

Ã¢â‚¬Â¢ Elements of Decision Problems

Ã¢â‚¬Â¢ Modeling Uncertainty

Ã¢â‚¬Â¢ Modeling Preference

2

Basic Elements of Decision Problems

Ã¢â‚¬Â¢ When facing a difficult decision problem, it is important to first

thought through the problem and identify

Ã¢â‚¬Â¢

Ã¢â‚¬Â¢

Ã¢â‚¬Â¢

Ã¢â‚¬Â¢

Values and objectives

Decisions

Uncertain events

Consequences

3

Value and Objectives

Ã¢â‚¬Â¢ Values Ã¢â‚¬â€œ things that matter to us

Ã¢â‚¬Â¢ Objectives – what we specifically want to achieve

Ã¢â‚¬Â¢ Most people do not make the effort or take the time to define values and

objectives explicitly, systematically and consciously.

Ã¢â‚¬Â¢ Focus on the available alternatives and try to find the best one.

Ã¢â‚¬Â¢ What Ã¢â‚¬Å“bestÃ¢â‚¬Â mean is not carefully defined.

4

A Special Objective Ã¢â‚¬â€œ Increase Monetary value

Ã¢â‚¬Â¢ In modern society, it seems like making money (increase monetary

value) is the objective for most of the decision problems.

Ã¢â‚¬Â¢ Why is that?

Ã¢â‚¬Â¢ Proxy objective

Ã¢â‚¬Â¢ Pricing out

5

A Special Objective Ã¢â‚¬â€œ Increase Monetary value

Ã¢â‚¬Â¢ Advantages to using money as an objective:

Ã¢â‚¬Â¢ Universally understood

Ã¢â‚¬Â¢ Measurable

Ã¢â‚¬Â¢ Simplifies trade-offs because it allows different objectives to be put on the same scale

via pricing out

6

A Special Objective Ã¢â‚¬â€œ Increase Monetary value

Ã¢â‚¬Â¢ Disadvantages:

Ã¢â‚¬Â¢ Monetary values cannot be assigned to all values and objectives.

Ã¢â‚¬Â¢ Safety, family, lives, environment

Ã¢â‚¬Â¢ Can you name some others?

7

Decisions

Ã¢â‚¬Â¢ A decision exists if there are at least two alternatives

Ã¢â‚¬Â¢ Immediate decisions: Many situations have decisions that need to be made

right away.

Ã¢â‚¬Â¢ Identify these decisions immediately

Ã¢â‚¬Â¢ Some decisions are not urgent. These can wait.

Ã¢â‚¬Â¢ Identify alternatives

Ã¢â‚¬Â¢ Timing Ã¢â‚¬â€œ When does the decision have to be made?

Ã¢â‚¬Â¢ Information Ã¢â‚¬â€œ You may have to make the decision with less information than you would

like to have.

Ã¢â‚¬Â¢ Often a trade-off between timeliness and information

8

Sequential Decisions

Ã¢â‚¬Â¢ Sequential Decisions: Problems often involve multiple decisions to be made

over time, not all at once.

Ã¢â‚¬Â¢ Identify in what order they need to be made

Ã¢â‚¬Â¢ Which ones need to be made immediately?

Ã¢â‚¬Â¢ One decision may trigger another

Ã¢â‚¬Â¢ A decision may depend on what happened due to a prior decisions

Ã¢â‚¬Â¢ Called dynamic decision situations

9

Uncertain Event

Ã¢â€“Âª Uncertainty: decisions may have to be made without knowing exactly

what will happen in the future or exactly what the ultimate outcome

will be

Ã¢â‚¬Â¢ Less information that would prefer

Ã¢â€“Âª Not all future events are relevant. Determine which ones are; ignore

the rest.

Ã¢â‚¬Â¢ Relevant future events are those that will impact one or more of your

objectives.

Ã¢â‚¬Â¢ Information availability should not determine which future decisions you

focus on.

10

Dovetailing uncertain events

Ã¢â€“Âª Dovetailing: match relevant future uncertain events with the

decisions for your case.

Ã¢â‚¬Â¢ This is critical because it helps you to know at each decision exactly what

information is available and what remains unknown.

11

Consequence

Ã¢â€“Âª Each objective in the decision context will have a final consequence.

Ã¢â‚¬Â¢ Multiple objectives mean multiple consequences.

Ã¢â€“Âª Determine measures for each consequence so you can determine the

extent to which each objective was met.

Ã¢â‚¬Â¢ Monetary or non-monetary consequences?

Ã¢â‚¬Â¢ Can you price out any of the non-monetary consequences?

Ã¢â‚¬Â¢ What are the trade-offs between various objectives?

12

The Time value of Money

Ã¢â‚¬Â¢ A stream of cash flows is the most common consequences in personal and

business decisions.

Ã¢â‚¬Â¢ Ã¢â‚¬Å“A dollar today is worth more than a dollar tomorrow.Ã¢â‚¬Â

Ã¢â‚¬Â¢ Trade-offs between current dollars and future dollars

Ã¢â‚¬Â¢ Why?

Ã¢â‚¬Â¢ Due to interest rates

Ã¢â‚¬Â¢ What is the interest rate that you could get for investing your money in the next best

opportunity?

13

Good Deal or not?

Ã¢â‚¬Â¢ A friend wants you to invest his business

Ã¢â‚¬Â¢ You pays him $425 now

Ã¢â‚¬Â¢ One year later, he will pay you $110

Ã¢â‚¬Â¢ Two years later, he will pay you $121

Ã¢â‚¬Â¢ Three years later, he will pay you $133.10

Ã¢â‚¬Â¢ Four years later, he will pay you $146.41

Ã¢â‚¬Â¢ Total $510.51, which is greater than $425

Ã¢â‚¬Â¢ Assume that a savings account at 10%, compounded

14

Net Present Value

N PV

=

x0

x1

xn

+

+ Ã‚Â·Ã‚Â·Ã‚Â· +

0

1

(1 + r )

(1 + r )

(1 + r ) n

n

=

i= 0

N PV

=

=

xi

(1 + r ) i

Ã¢Ë†â€™ 425 100.00 121.00 133.10 146.41

+

+

+

+

0

1

2

3

(1.1)

(1.1)

(1.1)

(1.1)

(1.1) 4

Ã¢Ë†â€™ 25

15

Use ExcelÃ¢â‚¬â„¢s NPV Function

Ã¢â‚¬Â¢ = -425 + NPV(0.1,B3:B6)

16

Example

Ã¢â‚¬Â¢ A friend asks you for a loan of $1,000 and offers to pay you back at

the rate of $90 per months for 12 months.

Ã¢â‚¬Â¢ Using a annual interest rate of 10%, find the net present value

17

Decision Tree

18

Example

Ã¢â‚¬Â¢ The decision maker wants to decide whether to invest his $50k saving

in a new business to maximize his return on investment for a two

years period.

Ã¢â‚¬Â¢

Ã¢â‚¬Â¢

Ã¢â‚¬Â¢

Ã¢â‚¬Â¢

If the business succeeds (prob. 0.3), you will get $100k back.

If the business fails (prob. 0.7), you will get $0 back

If do nothing, you will have $60k in your saving after two years.

Assume all monetary values provided are NPV.

Identify the decision elements for the above question.

19

Construct A Decision Tree

Ã¢â‚¬Â¢ Decision Three

Ã¢â‚¬Â¢ From left to right (norm)

Ã¢â‚¬Â¢ Square : decision nodes

Ã¢â‚¬Â¢ Circle: chance nodes

20

Example 1 Ã¢â‚¬â€œ Decision Tree

success

New Business

Invest?

Y

$100k

0.3

fail

0.7

$0k

N

$60k

21

Decision Tree Ã¢â‚¬â€œ Hurricane Example

22

Decision Tree Ã¢â‚¬â€œ Uncountable Event

23

Decision Tree Ã¢â‚¬â€œ common mistakes

Ã¢â‚¬Â¢ Out of sequence/ordering

Ã¢â‚¬Â¢ Probability for each chance node is not sum to 1

Ã¢â‚¬Â¢ Probability for each chance node is not correct

Ã¢â‚¬Â¢ Are two events independent?

Ã¢â‚¬Â¢ If not, what are condition probabilities?

24

Solving A Decision Tree

Ã¢â‚¬Â¢ We construct a tree from left to right (from a root to several leafs)

Ã¢â‚¬Â¢ We solve a tree from right to left (solving sub-tree first)

Ã¢â‚¬Â¢ If the sub-tree is based on a decision node

Ã¢â‚¬Â¢ Choose the alternative with a higher expected value*

*Assume the objective is to maximize the payoff

Ã¢â‚¬Â¢ If the sub-tree is based on a chance node

Ã¢â‚¬Â¢ Calculate the expected value

25

Review: Expected Value

The weighted average of all possible values a random variable can take on.

What?

Sum over all

Possible

outcomes

x P(X = x)

How?

Value (outcome)

of the random

variable

How likely the

value would

occur

xP(X = x)

0

0.3

(0)(0.3) = 0

1

0.5

(1)(0.5) = 0.5

2

0.2

(2)(0.2) = 0.4

Sum over all

possible

values of X

E(X) = 0.9

E(X) = (0)(0.3) + (1)(0.5) + (2)(0.2) = 0.9

26

Calculate the Expected Value

Ã¢â‚¬Â¢ In a game, there is a 30% chance to lose 50 dollars and a 70% chance

to win 100 dollars. What is the expected payoff of this game?

Let X be the payoff of the game

x

P(x)

-50

0.3

100

0.7

E(X) = (-50)(0.3) + (100)(0.7) = -15 + 70 = 55.

27

Solving a Decision Tree – Example

28

Expected Monetary Values – Issues

Ã¢â‚¬Â¢ Repeatability is an abstract concept; Many decisions are

one-time decisions

Ã¢â‚¬Â¢ EMVs is convenient, but it can lead to decisions that may

not seem intuitively appealing

Ã¢â‚¬Â¢ Example

Game 1

Win $30 with probability 0.5

Lose $1 with probability 0.5

Game 2

Win $2000 with probability 0.5

Lose $1900 with probability

0.5

EMV(Game 1) = 14.50

EMV(Game 2) = 50.00

Which game do you prefer?

29

Quiz

Sale it

$100k

Y

success

New Business

Invest?

Y

N

0.3

$180k

0.5

fail

0.7

$0k

0.5

$30k

N

$31k

30

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