Decision Trees

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. E 3 Decision Trees C 4 F A D 10 • 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 B 5

4. Simple Example 3 E C 70% 4 F A 10 D 30% B 5 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 Strong Growth Move Weak Growth Strong Growth Hackers’ Computer Store Expand Weak Growth Expand Wait and See Strong Growth Do nothing Weak Growth

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

8. Revenue Revenue Revenue – Expand Cost Revenue – Expand Cost Revenue - Move Cost Revenue - Move Cost Rev – Expand Cost Add in Probabilities Strong Growth Move 0.55 Weak Growth 0.45 Strong Growth 0.55 Hackers’ Computer Store Expand Weak Growth 0.45 Expand Wait and See Strong Growth Do nothing 0.55 Weak Growth 0.45

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. 843 765 365 863 413 850 525 Compute Payoff Values Strong Growth Move 0.55 Weak Growth 0.45 Strong Growth 0.55 Hackers’ Computer Store Expand Weak Growth 0.45 Expand Wait and See Strong Growth Do nothing 0.55 Weak Growth 0.45

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. 843 765 365 863 413 850 525 Pruning Branches Strong Growth Move 0.55 Weak Growth 0.45 Strong Growth 0.55 Hackers’ Computer Store Expand Weak Growth 0.45 Expand Wait and See Strong Growth Do nothing 0.55 Weak Growth 0.45

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. 765 365 863 413 850 843 525 Expected Values $585,000 Strong Growth Move 0.55 Weak Growth 0.45 660,500 Strong Growth 0.55 Hackers’ Computer Store Expand Weak Growth 0.45 Expand 703,750 Wait and See Strong Growth Do nothing 0.55 Weak Growth 0.45

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. 428,487 166,544 535,116 240,429 556,630 529,874 343,801 Decision Tree-NPV $310,613 Strong Growth Move 0.55 Weak Growth 0.45 402,507 Strong Growth 0.55 Hackers’ Computer Store Expand Weak Growth 0.45 Expand 460,857 Wait and See Strong Growth Do nothing 0.55 Weak Growth 0.45

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. 843 820 525 820 525 863 365 765 413 Decision Trees 0.25 Strong $465,000 Move 0.75 Weak Hackers’ Computer Store 0.25 Strong 533,000 Expand Weak 0.75 Expand 604,500 0.25 Strong Wait and See Do nothing Weak 0.75 598,750 0.25 Strong Do Nothing Weak 0.75

21. Real Options • If we didn’t have the wait and see option, we would Do Nothing. • Option to wait and see is worth $5,750 604,500 Wait and See $5,750 598,750 Do Nothing 533,000 Expand 465,000 Move

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