1. MBA 201A – Section Intro  Introduction  Section Agenda -Review Class Concepts -Review Homework -Answer Questions  Office Hours – Tuesday 11-1, Please come by!

2. This Week’s Topics  Review Class Concepts -Setting up Decision Trees - Expected Value, Backward Induction -Sensitivity - -Value of Information -Value of an Option – Present Value -Costs – Opportunity, Sunk, Fixed, Marginal  Review Homework  Questions

3. Class Concepts – Setting up Decision Trees  Node Types : Chance Node : Decision Node  Setting up a Decision Tree -Timeline -What has happened already?  Sunk Costs -What decisions do you need to make? What order do they occur in? -What are your other options?  Opportunity Costs

4. Class Concepts – Solving Decision Trees  Backward Induction  Start from the “leaves” of the tree and work toward the “root”  This is counterintuitive, but since each decision/chance node is independent of the others, we can start by solving the simplest decision, and work back toward the more complicated one we started with  Decision Nodes -Choose the best of the options  Chance Nodes -Find the expected value of the outcomes EV = 5*0.4 + -10*0.6 EV = 2 – 6 EV = 4

5. Class Concepts – Introducing and Valuing Information  The Value of Information -Question types: If you had the opportunity to receive perfect information for a given cost, should you take it? Would it change your decision? What is the most you would pay for perfect information? -Examples -There’s a storm coming, should you harvest your grapes now or wait until later? -You want to invest in a stock, should you buy or short?  Example: Applying to Business School -You are applying to three schools: Haas, UCLA, Stanford -You have a 15% chance of getting accepted at each school. -The probability of getting accepted at one school is independent of getting into any other school

6. Class Concepts – Introducing and Valuing Information  Information is often valuable if purchased earlier rather than later -Think about what you would pay to know what internship offers you will receive now versus after you have interviewed -When would it make sense to wait to pay for information?

7. Class Concepts – Decision Trees and Sensitivity  Sensitivity on a Cost or Revenue Value -Method: Recalculate payouts using an unknown value, and determine when your decision changes to the next best alternative -Example: WakTek cost of Safety Test, Freemark Abbey cost of Reputation  Sensitivity on a Probability -Method: Substitute probability with p and (1-p), and determine when your decision changes to the next best alternative -Examples: Freemark Abbey sensitivity to storm probability

8. Class Concepts – Calculating Present Value  How much would you pay to receive $100 in 1 year? -Discounting: C/(1+r) n -$100/(1+0.1) 1 = $90.91  How much would you pay to receive $100 a year forever if your first payment is one year from now. What if your first payment were today? -Perpetuity formula for payments beginning in 1 year: C/r -$100/0.10 = $1,000 -Perpetuity formula for payments beginning today: C + C/r -$100 + $1,000 = $1100 -Memorize this!

9. Class Concepts – Calculating a Derivative  We were introduced to derivatives with the concept that the derivative of Total Cost is Marginal Cost. So what is a derivative? -The derivative is the slope of a function. -The derivative of Total Cost is the amount it costs to make each additional unit  How to take a derivative -Total Cost = Bx + C -Derivative of Total Cost = Marginal Cost = B -General Formula: -Derivative of Ax 2 + Bx + C = 2Ax + B

10. Class Concepts – Costs  Sunk Costs  Opportunity Costs  Fixed Costs  Variable Costs

11. Homework – WakTek – Question 2a

12. Homework – WakTek – Question 2b -Regardless of what the cost of the safety test is, the Prototype is a better choice than the Production Line -When do we choose to do nothing?

13. Homework – WakTek – Question 2c -Simultaneous Information

14. Homework – WakTek – Question 2d

15. Homework – Chevron – Question 3 -Simultaneous Information

16. Practice Problems  Project Manager -You are a manager with the budget to fund one project, which should you choose? -Project 1: Will earn profits of $1M forever -Project 2: Will lose $8M in the first year, but then earn $2M forever -Project 3: Will earn $4M in profits for 5 years -Assume a 10% discount rate  Answer: -PV of Project 1 = $1M/0.1 = $10M (Perpetuity Formula) -PV of Project 2 = -$8M/1.1 + ( )/1.1 = -$7.2M + $18.18M = $10.9M -PV of Project 3 = $4M/1.1 + $4M/1.1 2 + $4M/1.1 3 + $4M/1.1 4 + $4M/1.1 5 = $15.2M -Choose Project 3!