Final answer:
After conducting a risk analysis, it is determined that the construction company should not purchase insurance for the new rubber-tire loader, as the expected cost savings is $934.10 by foregoing the insurance.
Step-by-step explanation:
The question at hand involves a risk analysis about whether a construction company should purchase insurance for a new rubber tire loader. To evaluate the best option and determine projected cost savings, we need to calculate the expected value of each scenario (purchasing or not purchasing insurance) based on the probabilities and costs given.
If the company does not purchase insurance, the expected cost due to accidents can be calculated by multiplying each scenario's cost by its probability:
- 0.88 (probability of no accident) × $0 = $0
- 0.11 (probability of a small accident) × $800 = $88
- 0.01 (probability of a total loss) × $100,000 = $1,000
The total expected cost without insurance is thus $1,088.
If the company purchases insurance for $2,000 annually with a deductible of $1,000, their only expected cost in the case of a small accident is the deductible: (0.11 × $1,000) = $110, plus the insurance premium of $2,000, totaling $2,110.
In the case of a total loss, the insurance covers the loader, so the company pays the insurance premium and deductible: $2,000 + $1,000 = $3,000.
Combining the expected costs:
- No accident: $2,000 (insurance premium)
- Small accident: $2,000 (premium) + $110 (deductible) = $2,110
- Total loss: $2,000 (premium) + $1,000 (deductible) = $3,000
The expected cost with insurance is:
- 0.88 × $2,000 = $1,760
- 0.11 × $2,110 = $232.10
- 0.01 × $3,000 = $30
The total expected cost with insurance is $2,022.10. Therefore, the company can save money by not purchasing insurance, and the savings will be the difference between the expected costs with insurance ($2,022.10) and without ($1,088), which equals $934.10.