1. Warm-up Problems Consider the oil well example. P(rich)=0.5. Now assume the test is not perfect: P(test - | rich) = 0.1 and P(test + | poor) = 0.3. What is P(rich | test +)?

2. Option to Delay Consider the oil well example without testing. Suppose you could delay drilling the oil well for 1 year. If you delay, the discounted profits may go up or down 30% with equal probability. Describe how this would change the decision tree.

3. Capacity Decision Demand for your product per year may be –1 million units per year (with probability 30%) or –2 million units per year (with probability 50%) or –3 million units per year (with probability 20%). –It will be the same in all 5 years of this project. You can build capacity to produce 1, 2, or 3 million units per year. The required investment is $10 million per 1 million units/year of capacity. Each year, you sell as many units as you can, given that you can not sell more units than are demanded, and you can not sell more units than you can produce. The cashflow in a year will be $5 per unit sold. The discount rate is 10%. What initial capacity should you choose?

4. Option to Expand At (the end of) Year 1, you will know the level of demand, and you will have the option to increase (but not decrease) your production capacity, by making an additional investment. Each additional 1 million units / year of capacity cost $10m as before.

5. Machine Tools Example You are planning to create a facility for producing a motor. You can choose to invest in standard machine tools or in custom machine tools (specially designed to produce this particular motor’s parts). Initial investment is $15 million. The project will last 10 years. Fixed costs will be $1.5 million per year. The price at which you sell each motor will be $500. Salvage value at the end of Year 10 will be zero. The variable costs per motor will be $260 if you use standard tools and $250 if you use custom tools. Sales are uncertain. They will be constant each year, but you are not yet sure whether sales will be 10,000 motors or 20,000 motors or 30,000 motors. Each of these scenarios is equally likely. You will learn the level of sales during Year 1. The discount rate is 15%. Should you do this project with standard tools, or with custom tools, or do nothing?

6. Option to Abandon You also have the option to abandon the project at (the end of) Year 1, after receiving the cashflow in Year 1. The salvage value of the standard tools at Year 1 would be equal to $13.5 million. The salvage value of the custom tools at Year 1 would be $3 million.