Insurance Analysis

A machine shop recently bought a new CNC mill, and is performing a risk and cost analysis to determine if insurance is necessary. The shop paid $100,000 for the tool. The annual cost for the insurance premium is $2,000, with a $1,000 deductible. After some initial analysis, the risk options to purchase or decline insurance are as follows:
  • 88% chance of no accident
  • 11% chance of a small $800 accident
  • 1% chance of a total loss for the CNC mill
Should the machine shop purchase insurance? Based on that decision, what is the max projected cost savings potential?

Hint
In a benefit-cost analysis, the benefits $$B$$ of a project should exceed the estimated costs $$C$$ .
$$$B-C\geq 0\; or \; \frac{B}{C}\geq 1$$$
Hint 2
Expected Value:
$$$EV=\sum (cost*probability)$$$
In a benefit-cost analysis, the benefits $$B$$ of a project should exceed the estimated costs $$C$$ .
$$$B-C\geq 0\; or \; \frac{B}{C}\geq 1$$$
Expected Value is:
$$$EV=\sum (cost*probability)$$$
Let’s first determine the projected total cost with insurance, then compare it to the projected total cost without insurance.
$$$EV_{insurance}=(Cost_{1}Prob_{1})+(Cost_{2}Prob_{2})+(Cost_{3}Prob_{3})$$$
$$$=(\$0\times 0.88)+(\$800\times 0.11)+(\$1,000\times 0.01)$$$
$$$=\$0+\$88+\$10=\$98$$$
Total annual cost with insurance premium: $2,000 + $98 = $2,098

$$$EV_{no\:insurance}=(Cost_{1}Prob_{1})+(Cost_{2}Prob_{2})+(Cost_{3}Prob_{3}) $$$
$$$=(\$0\times 0.88)+(\$800\times 0.11)+(\$100,000\times 0.01)$$$
$$$=\$0+\$88+\$1,000=\$1,088$$$
Total annual cost out of pocket: $1,088

Comparing the Expected Value with insurance to no insurance:
$2,098 - $1,088 = $1,010 savings by going with no insurance.
$1,010 savings by going with no insurance.