Chapter 2 Supplement 2: Decision Analysis

1
Chapter 2 Supplement 2 Decision Analysis

• Quantitative decision-making techniques
• for situations where uncertainty exists

2
Decision Making Criteria Under Uncertainty

• Our decision making may differ from others and
  also under different circumstances, depending
  upon levels of risk, reward, and conditions.
• Example
• Win 1 OR one chance in 10 of winning 10
• Win 1M OR one chance in 10 of winning 10M

3
Decision Making Criteria Under Uncertainty

• Maximax criterion
• Choose decision with the maximum of the maximum
  payoffs
• Maximin criterion
• Choose decision with the maximum of the minimum
  payoffs
• Minimax regret criterion
• Choose decision with the minimum of the maximum
  regrets for each alternative

? high-stakes gambler
? risk-averse
? minimum regret
4
Decision Making with Probabilities

• Risk involves assigning probabilities to states
  of nature
• Expected value is a weighted average of decision
  outcomes in which each future state of nature is
  assigned a probability of occurrence

5
Expected Value
where
xi outcome i p(xi) probability of outcome i
6
Decision Analysis

• Weve dealt with states of nature, and
  probabilities of outcomes
• What about situations that are far more complex?
  Where there are more steps in a situation
  analysis?

7
Sequential Decision Trees

• A graphical method for analyzing decision
  situations that require a sequence of decisions
  over time
• Decision tree consists of
• Square nodes - indicating decision points
• Circles nodes - indicating states of nature
• Arcs - connecting nodes

8
Simple Decision Tree
OUTCOME
DECISION POINT
ARCS CONNECTING NODES
OUTCOME
9
Simple Decision Tree
STATE or OUTCOME A
probability ofoutcome A
DECISION POINT
probability ofoutcome B
STATE or OUTCOME B
10
Expected Value Class Experiment
EV 1 .01 0.01
guaranteed P1.00
3 in a row P?
3H/T
EV ? .08 0.01
11
Expected Value Class Experiment
EV 1 .10 0.10
guaranteed P1.00
3 in a row P?
3H/T
EV ? .80 0.10
12
Expected Value Class Experiment
EV 1.00
guaranteed P1.00
3 in a row P?
3H
EV 1.00
13
Sequential Decision Tree
C
A
DECISION POINT
D
B
14
Sequential Decision Tree Education Decisions
yes
MBA
MBA?
yes
Stay in school?
BS/BA
no
no
HS diploma
15
Decision Analysis Replace Tire?
There are two states of nature flat and no
flat With probabilities of 0.1 and 0.9
respectively
new
Cost 50
YES
replace tire?
flat
Cost 50 (tire) 100 (tow)
NO
Probability 0.1
Probability 0.9
no flat
Cost 0
16
Decision Analysis Investment
Up
0.2
Purchase mutual fund
Mod
0.6
0.2
Down
Stock split
0.2
Invest?
Up
0.2
0.8
Purchase Individual stock
0.6
Mod
No split
0.2
Down
17
Decision Analysis Investment
Probabilities on any branch must sum to 1.0
0.2
Purchase mutual fund
0.6
0.2
Stock split
0.2
Invest?
0.2
0.8
Purchase Individual stock
0.6
No split
0.2
18
Decision Analysis Investment
120
Investment growths at each leaf are states
of nature
0.2
110
100
Purchase mutual fund
0.6
0.2
90
110
Stock split
0.2
Invest?
140
0.2
0.8
Purchase Individual stock
0.6
115
100
100
No split
0.2
75
19
Decision Analysis Investment
EV probability x growth x 100 EV
(0.2)(1.2)(100) EV 24
120
0.2
110
100
Purchase mutual fund
0.6
0.2
90
110
Stock split
0.2
Invest?
140
0.2
0.8
Purchase Individual stock
0.6
115
100
100
No split
0.2
75
20
Decision Analysis Investment
120
EV probabilityGrowth x growth x
probabilitySplit x growthSplit EV
(0.2)(1.4)(0.2)(1.1)(100) EV 6.16
0.2
110
100
Purchase mutual fund
0.6
0.2
90
110
Stock split
0.2
Invest?
140
0.2
0.8
Purchase Individual stock
0.6
115
100
100
No split
0.2
75
21
Decision Analysis Investment
120
24
0.2
110
100
Purchase mutual fund
0.6
66
0.2
90
110
18
6.16
0.2
Invest?
Stock split
140
0.2
0.8
Purchase Individual stock
0.6
115
100
100
22.40
69
0.2
No split
75
15
22
Decision Analysis Investment
120
24
0.2
110
100
Purchase mutual fund
0.6
66
108
0.2
90
110
18
6.16
0.2
Invest?
Stock split
140
0.2
112.56
0.8
Purchase Individual stock
0.6
115
100
100
22.40
69
0.2
No split
75
15
23
Decision Analysis Buying a Car

• Situation analysis Need a car
• Have up to 7,000 to spend
• Expect to keep it 5 years
• Decisions to be made
• New or old? What make? Warranty?
• Whether to / how to finance?
• Caveats
• This example based on 2005 data
• Does not factor
• costs assigned to unreliability
• benefits assigned to newness factor

24
Decision Analysis Buying a Car

• States of nature (financial)?
• Expense
• New cars higher than used cars
• Depreciation rate
• New car depreciation higher, varies among makes
• Repair cost
• Higher for older vehicles, varies among makes
• Cost-of-money
• If auto loan is needed

25
Honda Civic
Porsche 911
Chevy Cavalier
Buick Regal
years to 50
n
4
3
7
9
0 1 2 3 4 5
6 7 8 9 10
11
Ref http//www.kbb.com/
26
Decision Analysis Buying a Car

• User choices narrowed to
• 2005 Honda Civic Coupe EX 18,150
• 2 door, automatic, 4 cylinder, 1.7 liter VTEC
• bucket seats, CD, cruise, AC, AB, custom wheels,
  keyless entry
• 1995 Honda Civic Coupe EX 6,695
• 84,000 miles
• 2005 Chevy Cavalier LS Sport 17,975
• 2 door, automatic, 4 cylinder, 2.2 liter
• bucket seats, CD, cruise, AC, AB, custom wheels,
  keyless entry
• 1998 Chevy Cavalier LS Sport 6,695
• 72,000 miles

27
Decision Analysis Buying a Car
First two decisions
new
new or used
Honda Civic EX
used
which make?
new
new or used
Chevy Cavalier
used
28
Decision Analysis Buying a Car
Additional Decision Path for Used Cars
Y
warranty cost
warranty?
used
P1
repair cost 1
N
P2
repair cost 2
29
Decision Analysis Buying a Car
Complete Decision Tree
new
Y
warranty cost
new or used
Honda Civic EX
warranty?
used
which make?
new
Y
N
new or used
repair costs
Chevy Cavalier
warranty?
warranty cost
used
N
repair costs
30
Honda Civic
Chevy Cavalier
0 1 2 3 4 5
6 7 8 9 10
11
Ref http//www.kbb.com/
31
Decision Analysis Buying a Car
Assumed Repair Costs for Used Cars
Y
1695
warranty?
used
P0.20
5000
N
repair cost
P0.80
1000
32
Decision Analysis Buying a Car
C 18,150
C 6,695 D 1,100 RC 1,800 I 5,000
D 7,130
new
Y
1695
new or used
I 7,500
Honda Civic EX
warranty?
used
95
which make?
C 17,975
P0.20
5000
D 10,345
new
Y
N
1695
new or used
repair cost
I 7,500
Chevy Cavalier
warranty?
P0.80
1000
used
98
P0.20
5000
C 6,695 D 2,935 RC 1,800 I 5,000
C cost of purchase D depreciation I
insurance RC repair (non-warranty option)
N
repair cost
P0.80
1000
33
Sequential Decision Tree
AC Expected Accumulated Cost per 5 years
(non-financed) after sale of car
AC 14,630
new
Y
AC 7,795
new or used
Honda Civic EX
warranty?
used
which make?
AC 17,845
new
Y
N
AC 7,900
new or used
Chevy Cavalier
warranty?
AC 9,735
used
N
AC 9,630
34
Sequential Decision Tree
NC Expected Net Cost per 5 years 5 year loan
available at 6 APR after sale
NC 16,230
new
NC 7,795
new or used
Honda Civic EX
warranty?
used
which make?
NC 19,445
new
N
NC 10,145
NC 7,900
new or used
Chevy Cavalier
warranty?
used
N
NC 10,250
35
Decision Analysis Buying a Car
Cost of Vehicle for Five Years
depreciation, insurance, financing, repair
36
Decision Analysis Life Insurance

• Decision
• Buy whole life insurance
• Higher cost
• Provides accumulated cash value
• Covers until old age
• Buy term life insurance
• Lower cost
• No cash value
• Limited term
• States of nature
• ROI from whole life insurance
• ROI from investing the difference between whole
  term
• ROI from investing the difference in 401K

37
Decision Analysis Home Purchase

• Decision
• Rental housing
• Lower initial cost
• Limited term
• More flexibility
• No tax savings
• Buy home
• Higher initial cost, lower long term cost
• Provides accumulated equity
• Provides unlimited term living
• Potential large tax savings
• States of nature
• Home appreciation rates
• Rental rate increases
• Mortgage rates

38
Rent or Buy Housing?

• States of nature
• Family income of 60,000/year
• Tax bracket 50
• Condo rental 2000/month
• Home purchase 3000/month, of which 1500 is
  interest payment and deductable at 50 rate
• Home appreciation
• 5 chance of no appreciation
• 25 chance of 10,000 appreciation per year
• 50 chance of 20,000 appreciation per year
• 20 chance of 40,000 appreciation per year
• Long term cost of home purchase 1400 per
  month