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Decision Trees
Dr. Ron Lembke
Operations Management
Decision Trees
 Consider different possible decisions, and
different possible outcomes
 Compute expected profits of each decision
 Choose decision with highest expected
profits, work your way back up the tree.
Decision Trees
 Decision point
 Chance events
 Outcomes
 Calculate expected value of each chance
event, starting at far right
 Working our way back toward the
beginning, choosing highest expected
outcome at each decision
A
B
3
4
10
5
C
D
E
F
Simple Example
A
B
3
4
10
5
C 70%
D 30%
E
F
Expected value of A: 0.7*4 + 0.3*10 = 2.8 + 3 = 5.8
Expected value of B: 5
Choose A?
Decision Trees Example 2
 Computer store thinks demand may grow.
 Expansion costs $87k, new site $210k, and would cost
same if wait a year
 New site:
 55% chance of profits of $195k.
 45% chance of $115k profits.
 Expand Current
 55% chance of $190k profits
 45% chance of $100k profits
 Wait and see- enlarge store next year if demand grows
 If high demand, $190k with expanded store
 If high demand, $170 with current store
 If weak demand, $105k with current store
 Find the expected profits over 5 years, choose best one.
Basic Structure of Tree
Weak Growth
Weak Growth
Strong Growth
Strong Growth
Move
Expand
Wait
and
See
Weak Growth
Strong Growth
Expand
Do nothing
Hackers’
Computer
Store
Outcomes in each scenario?
Weak Growth
Weak Growth
Strong Growth
Strong Growth
Move
Expand
Wait
and
See
Weak Growth
Strong Growth
Expand
Do nothing
Hackers’
Computer
Store
Revenue - Move Cost
Revenue - Move Cost
Revenue – Expand Cost
Revenue – Expand Cost
Revenue
Rev – Expand Cost
Revenue
Add in Probabilities
Weak Growth
Weak Growth
Strong Growth
Strong Growth
Move
Expand
0.45
0.55
0.55
0.45
Wait
and
See
Weak Growth
Strong Growth
0.55
0.45
Expand
Do nothing
Hackers’
Computer
Store
Revenue - Move Cost
Revenue - Move Cost
Revenue – Expand Cost
Revenue – Expand Cost
Revenue
Rev – Expand Cost
Revenue
5 year Revenues and Costs
 Move, growth: 195*5 – 210 = 765
 Move, low: 115*5 – 210 = 365
 Expand, growth: 190*5 – 87 = 863
 Expand, low: 100*5 – 87 = 413
 Wait, strong, expand: 170+190*4-87=843
Sales of 170, then 4 years of 190
 Wait, strong, do nothing: 170*5 = 850
Sales of 170 every year
 Wait, low, do nothing: 105*5 = 525
Compute Payoff Values
765
365
863
413
Weak Growth
Weak Growth
Strong Growth
Strong Growth
Move
Expand
525
843
850
0.45
0.55
0.55
0.45
Wait
and
See
Weak Growth
Strong Growth
0.55
0.45
Expand
Do nothing
Hackers’
Computer
Store
Making the Decision
 Starting at the far right, look at the “Wait
and See” option. If demand is strong, we
would obviously not expand.
 $850k is better than $843.
 Eliminate the “Expand option”
Pruning Branches
765
365
863
413
Weak Growth
Weak Growth
Strong Growth
Strong Growth
Move
Expand
525
843
850
0.45
0.55
0.55
0.45
Wait
and
See
Weak Growth
Strong Growth
0.55
0.45
Expand
Do nothing
Hackers’
Computer
Store
Expected Values
 Move:
0.55* 765 + 0.45*365 = $585,000
 Wait and See:
0.55*850 + 0.45*525 = $703,750
 Expand:
0.55 * 863 + 0.45 * 413 = $660,500
 Highest expected value is to Wait and see,
and either way, do nothing!
Expected Values
765
365
863
413
Weak Growth
Weak Growth
Strong Growth
Strong Growth
Move
Expand
525
843
850
0.45
0.55
0.55
0.45
Wait
and
See
Weak Growth
Strong Growth
0.55
0.45
Expand
Do nothing
Hackers’
Computer
Store
$585,000
660,500
703,750
Other Criteria
 Another criteria to use is to pick the one
with the highest down side.
Best guaranteed result
Under this, do nothing still wins.
 Expected Value is not the only criteria you
might want to use
 Which has the best possible outcome?
Expand, if sales are good, $863.
Is Dollar next year =$1 Today?
 Another criteria to use is to pick the one
with the highest down side.
Under this, do nothing still wins.
 We could also consider the expected
value of the future cash streams.
 PV = $100/(1+r) = $100/(1.16)=$86.27
Present Values – Appendix C
 At 16%, Next year is worth 0.862
=(1+rate)^(-years)
Year 2: 0.743
Year 3: 0.641
Year 4: 0.552
Year 5: 0.476
 195 per year for 5 years: 195 * (3.274)
=638.43
Decision Tree-NPV
428,487
166,544
535,116
240,429
Weak Growth
Weak Growth
Strong Growth
Strong Growth
Move
Expand
343,801
529,874
556,630
0.45
0.55
0.55
0.45
Wait
and
See
Weak Growth
Strong Growth
0.55
0.45
Expand
Do nothing
Hackers’
Computer
Store
$310,613
402,507
460,857
Real Options
 Assess the value to me of being able to
change my mind in the future
 Changed problem slightly -
Reduced benefit doing nothing, high demand
Decision Trees
765
365
863
413
Weak
Strong
Move
Expand
525
843
820
0.25
0.75
Wait and See
Expand
Do nothing
Hackers’
Computer
Store
Weak
Strong0.25
0.75
Weak
Strong0.25
0.75
$465,000
533,000
604,500
820
525
Weak
Strong0.25
0.75
Do Nothing
598,750
Real Options
 If we didn’t have the wait and see option,
we would Do Nothing.
 Option to wait and see is worth $5,750
Move
Expand
Wait and See
465,000
533,000
604,500
Do Nothing 598,750
$5,750
Summary
 Building decision trees
What are decisions, chance events, what is
the sequence?
Costs of revenues of each sequence?
 Calculating Expected values
 Deciding a course of action
 Just for your Edification
Time Value of Money
Real Options

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04 2-decision trees-2016-09-23

  • 1. Decision Trees Dr. Ron Lembke Operations Management
  • 2. Decision Trees  Consider different possible decisions, and different possible outcomes  Compute expected profits of each decision  Choose decision with highest expected profits, work your way back up the tree.
  • 3. Decision Trees  Decision point  Chance events  Outcomes  Calculate expected value of each chance event, starting at far right  Working our way back toward the beginning, choosing highest expected outcome at each decision A B 3 4 10 5 C D E F
  • 4. Simple Example A B 3 4 10 5 C 70% D 30% E F Expected value of A: 0.7*4 + 0.3*10 = 2.8 + 3 = 5.8 Expected value of B: 5 Choose A?
  • 5. Decision Trees Example 2  Computer store thinks demand may grow.  Expansion costs $87k, new site $210k, and would cost same if wait a year  New site:  55% chance of profits of $195k.  45% chance of $115k profits.  Expand Current  55% chance of $190k profits  45% chance of $100k profits  Wait and see- enlarge store next year if demand grows  If high demand, $190k with expanded store  If high demand, $170 with current store  If weak demand, $105k with current store  Find the expected profits over 5 years, choose best one.
  • 6. Basic Structure of Tree Weak Growth Weak Growth Strong Growth Strong Growth Move Expand Wait and See Weak Growth Strong Growth Expand Do nothing Hackers’ Computer Store
  • 7. Outcomes in each scenario? Weak Growth Weak Growth Strong Growth Strong Growth Move Expand Wait and See Weak Growth Strong Growth Expand Do nothing Hackers’ Computer Store Revenue - Move Cost Revenue - Move Cost Revenue – Expand Cost Revenue – Expand Cost Revenue Rev – Expand Cost Revenue
  • 8. Add in Probabilities Weak Growth Weak Growth Strong Growth Strong Growth Move Expand 0.45 0.55 0.55 0.45 Wait and See Weak Growth Strong Growth 0.55 0.45 Expand Do nothing Hackers’ Computer Store Revenue - Move Cost Revenue - Move Cost Revenue – Expand Cost Revenue – Expand Cost Revenue Rev – Expand Cost Revenue
  • 9. 5 year Revenues and Costs  Move, growth: 195*5 – 210 = 765  Move, low: 115*5 – 210 = 365  Expand, growth: 190*5 – 87 = 863  Expand, low: 100*5 – 87 = 413  Wait, strong, expand: 170+190*4-87=843 Sales of 170, then 4 years of 190  Wait, strong, do nothing: 170*5 = 850 Sales of 170 every year  Wait, low, do nothing: 105*5 = 525
  • 10. Compute Payoff Values 765 365 863 413 Weak Growth Weak Growth Strong Growth Strong Growth Move Expand 525 843 850 0.45 0.55 0.55 0.45 Wait and See Weak Growth Strong Growth 0.55 0.45 Expand Do nothing Hackers’ Computer Store
  • 11. Making the Decision  Starting at the far right, look at the “Wait and See” option. If demand is strong, we would obviously not expand.  $850k is better than $843.  Eliminate the “Expand option”
  • 12. Pruning Branches 765 365 863 413 Weak Growth Weak Growth Strong Growth Strong Growth Move Expand 525 843 850 0.45 0.55 0.55 0.45 Wait and See Weak Growth Strong Growth 0.55 0.45 Expand Do nothing Hackers’ Computer Store
  • 13. Expected Values  Move: 0.55* 765 + 0.45*365 = $585,000  Wait and See: 0.55*850 + 0.45*525 = $703,750  Expand: 0.55 * 863 + 0.45 * 413 = $660,500  Highest expected value is to Wait and see, and either way, do nothing!
  • 14. Expected Values 765 365 863 413 Weak Growth Weak Growth Strong Growth Strong Growth Move Expand 525 843 850 0.45 0.55 0.55 0.45 Wait and See Weak Growth Strong Growth 0.55 0.45 Expand Do nothing Hackers’ Computer Store $585,000 660,500 703,750
  • 15. Other Criteria  Another criteria to use is to pick the one with the highest down side. Best guaranteed result Under this, do nothing still wins.  Expected Value is not the only criteria you might want to use  Which has the best possible outcome? Expand, if sales are good, $863.
  • 16. Is Dollar next year =$1 Today?  Another criteria to use is to pick the one with the highest down side. Under this, do nothing still wins.  We could also consider the expected value of the future cash streams.  PV = $100/(1+r) = $100/(1.16)=$86.27
  • 17. Present Values – Appendix C  At 16%, Next year is worth 0.862 =(1+rate)^(-years) Year 2: 0.743 Year 3: 0.641 Year 4: 0.552 Year 5: 0.476  195 per year for 5 years: 195 * (3.274) =638.43
  • 18. Decision Tree-NPV 428,487 166,544 535,116 240,429 Weak Growth Weak Growth Strong Growth Strong Growth Move Expand 343,801 529,874 556,630 0.45 0.55 0.55 0.45 Wait and See Weak Growth Strong Growth 0.55 0.45 Expand Do nothing Hackers’ Computer Store $310,613 402,507 460,857
  • 19. Real Options  Assess the value to me of being able to change my mind in the future  Changed problem slightly - Reduced benefit doing nothing, high demand
  • 20. Decision Trees 765 365 863 413 Weak Strong Move Expand 525 843 820 0.25 0.75 Wait and See Expand Do nothing Hackers’ Computer Store Weak Strong0.25 0.75 Weak Strong0.25 0.75 $465,000 533,000 604,500 820 525 Weak Strong0.25 0.75 Do Nothing 598,750
  • 21. Real Options  If we didn’t have the wait and see option, we would Do Nothing.  Option to wait and see is worth $5,750 Move Expand Wait and See 465,000 533,000 604,500 Do Nothing 598,750 $5,750
  • 22. Summary  Building decision trees What are decisions, chance events, what is the sequence? Costs of revenues of each sequence?  Calculating Expected values  Deciding a course of action  Just for your Edification Time Value of Money Real Options