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 C D E F

Simple Example A B C 70% D 30% E F Expected value of A: 0.7* *10 = = 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 Strong Growth Move Expand Wait and See Weak Growth Strong Growth Expand Do nothing Hackers’ Computer Store

Outcomes in each scenario? Weak Growth Strong Growth Move Expand Wait and See Weak Growth Strong Growth Expand Do nothing Hackers’ Computer Store Revenue - Move Cost Revenue – Expand Cost Revenue Rev – Expand Cost Revenue

Add in Probabilities Weak Growth Strong Growth Move Expand Wait and See Weak Growth Strong Growth Expand Do nothing Hackers’ Computer Store Revenue - Move 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: *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 Weak Growth Strong Growth Move Expand Wait and See Weak Growth Strong Growth 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 Weak Growth Strong Growth Move Expand Wait and See Weak Growth Strong Growth Expand Do nothing Hackers’ Computer Store

Expected Values Move:  0.55* *365 = $585,000 Wait and See:  0.55* *525 = $703,750 Expand:  0.55 * * 413 = $660,500 Highest expected value is to Wait and see, and either way, do nothing!

Expected Values Weak Growth Strong Growth Move Expand Wait and See Weak Growth Strong Growth Expand Do nothing Hackers’ Computer Store $585, , ,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  =(1+rate)^(-years)  Year 2:  Year 3:  Year 4:  Year 5: per year for 5 years: 195 * (3.274)  =638.43

Decision Tree-NPV 428, , , ,429 Weak Growth Strong Growth Move Expand 343, , , Wait and See Weak Growth Strong Growth Expand Do nothing Hackers’ Computer Store $310, , ,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 Weak Strong Move Expand Wait and See Expand Do nothing Hackers’ Computer Store Weak Strong Weak Strong $465, , , Weak Strong 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, , ,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