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Your firm faces an 8% chance of a potential loss of $50 million next year. If your firm implements new safety policies, it can reduce the chance of this loss to 3%, but the new safety policies have an upfront cost of $250 000. Suppose that the beta of the loss is 0 and the risk-free rate of interest is 5%.
-Assuming that your firm will purchase insurance, what is the minimum-size deductible that would leave your firm with an incentive to implement the new safety policies? Show your calculations.
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Question

Quizplus · Accepted Answer

The Answer is If the firm is fully insured (no deductible), the insurance company will pay for the loss regardless of whether the safety program is in force or not. Therefore, the end-of-period cash flows will be identical with or without the program and the NPV is -$250 000 reflecting the cost of the safety program.
In order to give the firm the incentive to buy the insurance, the NPV of the safety program must be positive.
Another way of looking at this is to find the point where the PV of the expected deductible equals the cost of the safety program. Mathematically, we have:
(0.08 - 0.03)= $250 000, solving for the Deductible = = $5 250 000
To show that this indeed is the correct answer:
(0.08)= (0.03)- $250 000

Use the Information for the Question(s)below