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whether to purchase insurance. The construction company paid $100,000 for the loader he A construction company bought a new rubber-tire loader and is performing a risk analysis abou annual cost for the insurance premium is $2,000, and the deductible is $1,000. The risk options to purchase or not to purchase insurance are as follows: 0.88 probability of no accident 0.11 probability of a small accident at a cost of $800 • 0.01 probability of a total loss for the loader The best option and projected cost savings are: Ο Α. O B. purchase insurance and save $990 SHOTA purchase insurance and save $1,088 do not purchase insurance and save $1,010 do not purchase insurance and save $2,098 O C. O D.

User Mjolinor
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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.

User Waxwing
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