Question

Senior management of Super Oil Company is concerned about the potential loss that might occur in the event of fire at its refinery complex. The company estimates that the loss from one of these incidents could be as much $100 million, including losses due to service interruptions and damaged customer relations. Currently, the company estimates that there is only a 10% chance that a fire will break out over the next 10 years. The company is considering the installation of a new fire-prevention system at its refinery complex. If it is installed, the likelihood of any fire breaking out would be much longer – there would only be a 2% chance that a fire will break out over the next 10 years. The cost of the new system is $1.0 million (over the next 10 years). If fire were to break out (whether or not the fire-prevention system is installed), there is a 60% chance that it will only be a small one (in which case the losses will only be $1 million), there is a 30% chance of a medium fire (in which case the losses will amount to $10 million), and a 10% chance of a large fire (in which case the losses will amount to $100 million).

Determine whether the company should install the new fire-prevention system.

Answer 1

Lets take scenario A where we have no prevention system installed -

probability of fire breaking out = 10%

Lets split this probability into low, medium and high losses -

Probability of a small fire = 6%

Probability of a medium fire = 3%

Probability of a large fire = 1%

Lets note down the monetary losses for each case -

For a small fire = $1 million

For a medium fire = $10 million

For a large fire = $100 million

Expected monetary loss for scenario A -

0.06 * $1 million + 0.03 * $10 million + 0.01 * $100 million

= $1.36 million

Lets take scenario B where we fire prevention system installed -

probability of fire breaking out = 2%

Lets split this probability into low, medium and high losses -

Probability of a small fire = 1.2%

Probability of a medium fire = 0.6%

Probability of a large fire = 0.2%

Lets note down the monetary losses for each case -

For a small fire = $1 million

For a medium fire = $10 million

For a large fire = $100 million

Expected monetary loss for scenario A -

0.012 * $1 million + 0.006 * $10 million + 0.002 * $100 million

= $0.272 million

Comparing both the systems -

For scenario A

Switching cost + expected monetary loss

= 0 + $1.36 million = $1.36 million

For scenario B

Switching cost + expected monetary loss

= $1 million + $0.272 million = $1.272 million

Therefore, although fire prevention system requires a million dollars upfront, it is expected to reduce the cost of monetary loss by a margin of 0.088 million dollars more than its installation cost