Delta Electric Service is an electrical-utility company serving parts of several states. It is considering replacing some of its equipment at generating substations and is trying to decide whether it should replace an older, existing PCB transformer. (PCB is a toxic chemical known formally as polychlorinated biphenyl.) Although the PCB generator meets all current regulations, if an incident such as a fire were to occur, and PCB contamination caused harm either to neighboring businesses or farms, or to the environment, the company would be liable for damages. Recent court cases have shown that simply meeting regulations does not relieve a utility of liability if an incident causes harm to others. In addition, courts have been awarding very large damages to individuals and businesses harmed by incidents involving hazardous material.

If Delta replaces the PCB transformer, no PCB incidents will occur, and the only cost will be the cost of the new transformer, estimated to be $85,000. Alternatively, if the company elects to keep the existing PCB transformer in operation, then, according to their consultants, there is a 50/ 50 chance that there will be a high likelihood of an incident or a low likelihood of an incident. For the case of a high likelihood of an incident, there is also a 0.004 probability that a fire will occur sometime during the remaining life of the transformer, and a 0.996 probability that no fire will occur. If a fire occurs, there is a 20 percent chance that it will be severe and the utility will incur a very high cost, whereas there is an 80 percent chance that it will be minor and the utility will incur a low cost. The high- and low-cost amounts, including both cleanup and damages, are estimated to be $100 million and $10 million, respectively, based on results from other incidents in the industry. For the case of a low likelihood of an incident, there is a 0.001 probability of a fire during the remaining life of the transformer, and a 0.999 probability of no fire. If a fire does occur, then the same probabilities exist for the severe and minor outcomes as in the previous case. In both cases, there will be no cost if no fire occurs.

a. Should Delta replace its old transformers?
b. What is the expected cost per transformer, under the optimal replacement strategy?