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 = 5.8Expected value of B: 5Choose 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

WaitandSee

Weak Growth

Strong Growth

Expand

Do nothing

Hackers’ComputerStore

Outcomes in each scenario?

Weak Growth

Weak Growth

Strong Growth

Strong Growth

Move

Expand

WaitandSee

Weak Growth

Strong Growth

Expand

Do nothing

Hackers’ComputerStore

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

WaitandSee

Weak Growth

Strong Growth0.55

0.45

Expand

Do nothing

Hackers’ComputerStore

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 Values765

365

863

413Weak Growth

Weak Growth

Strong Growth

Strong Growth

Move

Expand

525

843

850

0.45

0.55

0.55

0.45

WaitandSee

Weak Growth

Strong Growth0.55

0.45

Expand

Do nothing

Hackers’ComputerStore

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 Branches765

365

863

413Weak Growth

Weak Growth

Strong Growth

Strong Growth

Move

Expand

525

843

850

0.45

0.55

0.55

0.45

WaitandSee

Weak Growth

Strong Growth0.55

0.45

Expand

Do nothing

Hackers’ComputerStore

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 Values765

365

863

413Weak Growth

Weak Growth

Strong Growth

Strong Growth

Move

Expand

525

843

850

0.45

0.55

0.55

0.45

WaitandSee

Weak Growth

Strong Growth0.55

0.45

Expand

Do nothing

Hackers’ComputerStore

$585,000

660,500

703,750

Other Criteria

Another criteria to use is to pick the one with the highest down side.Best guaranteed resultUnder 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: 0.743Year 3: 0.641Year 4: 0.552Year 5: 0.476

195 per year for 5 years: 195 * (3.274)=638.43

Decision Tree-NPV428,487

166,544

535,116

240,429Weak Growth

Weak Growth

Strong Growth

Strong Growth

Move

Expand

343,801

529,874

556,630

0.45

0.55

0.55

0.45

WaitandSee

Weak Growth

Strong Growth0.55

0.45

Expand

Do nothing

Hackers’ComputerStore

$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 Trees765

365

863

413

Weak

StrongMove

Expand

525

843

820

0.25

0.75

Wait and See

Expand

Do nothing

Hackers’ComputerStore

Weak

Strong0.25

0.75

Weak

Strong0.25

0.75

$465,000

533,000

604,500

820

525Weak

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 treesWhat 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 MoneyReal Options