Fact: Your firm produces and leases vehicles while reimbursing customers for the cost of fuel of these vehicles. Each customer pays you $2,000 a year to operate a vehicle for ten years. Over the life of a vehicle, the customer drives 20 miles a day for 300 days a year for ten years before scrapping the vehicle (for 60,000 miles in total). The price of gas is now $2 a gallon. The steel vehicle consumes 0.04 gallons per mile (or 25 miles per gallon). So the firm pays $4,800 for fuel over the course of ten years. Since the cost of producing a vehicle is $10,000, the company’s profit per customer is $2,000*10 - $4,800-$10,000 = $5,200. You are designing the new version of the vehicle. You could leave the vehicle unchanged and have the company earn $5,200 per customer. Or you could use aluminum. Aluminum reduces weight but increases the cost of making the vehicle by $3 per pound of weight saving. The steel vehicle weighs 3000 lbs. You can only reduce the vehicle weight by 50% using aluminum. Assume that a 50% reduction in vehicle weight leads to a 50% reduction in the number of gallons consumed per mile. Suppose that you had to make the decision on whether to use steel or aluminum two months from now. But one month from now, you would get a perfect forecast about whether oil prices will change. Since you are doing you planning today, you do not know what the forecast will predict. You only know that there’s a 50% chance the forecast will predict that oil price increase. There is also a 50% chance the forecast predicts no change. If it predicts no price increase, then you will make more profit from using steel. [In real applications, it is often important to discount future profits to reflect the value of getting money now versus getting money a month from now. You do not need to do that there.]
What is the expected profit from this decision tree (where you knew whether oil prices would increase before you had to decide on using steel or aluminum.? [Remember that a perfect forecast does not mean that you get to assume that the most favorable event happened. It just means that you learn about the outcome of the uncertainty prior to making your decision.]
How much does your expected profit --- when you have this forecast --- differ from the expected profit you computed when you had no forecast (which was computed in addressing the eighth item in this assignment)? This is the value of the perfect forecast. It represents the maximum amount you would be willing to pay for the forecast.