## 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**

**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**

**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:

$$$EV=\sum (cost*probability)$$$

Letâ€™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.