Question

1. Bart Simpson, Inc., is considering the possibility of building an additional factory that would produce a new addition to its product line. The company is currently considering two options. The first is a small facility that it could build at a cost of $6 million. If demand for new products is low, the company expects to receive $10 million in discounted revenues (present value of future revenues) with the small facility. On the other hand, if demand is high, it expects $12 million in discounted revenues using the small facility. The second option is to build a large factory at a cost of $9 million. Were demand to be low, the company would expect $10 million in discounted revenues with the large plant. If demand is high, the company estimates that the discounted revenues would be $14 million. In either case, the probability of demand being high is 0.40, and the probability of it being low is 0.60. Not constructing a new factory would result in no additional revenue being generated because the current factories cannot produce these new products. Construct a decision tree to help Bart Simpson make the best decision.

Answer 1

Three cases are considered: First case is to construct a small factory, second is to construct a large factory and third is to do nothing.

Construct a Small Facility is the most suitable option from the business perspective which makes case 1 recommended.

Step-by-step explanation:

Case 1 - Construct a small facility

Return = [P(High Demand) x Revenue in case of High Demand] + [P(Low Demand) x Revenue in case of Low Demand] - Cost of Setup

= [ 0.4 x 12 ] + [ 0.6 x 10 ] - 6 = $ 4.8 million

Case 2 - Construct a Large Facility

Return = [P(High Demand) x Revenue in case of High Demand] + [P(Low Demand) x Revenue in case of Low Demand] - Cost of Setup

= [0.4 x 14] + [0.6 x 10] - 9 = $ 2.6 million

Case 3 - Do Nothing

Return = 0