1. Warm-up Problem Random variable X equals 0 with probability 0.4, 3 with probability 0.5, and -10 with probability 0.1. –E[X] = 0.5 –What is Var[X]? E[X+Y] = ? Var[X+Y] = ?

2. Agenda Show machine tools decision tree Caveats to this approach Risk and uncertainty

3. 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 Year 1 is –standard tools $13.5m –custom tools at $3m 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?