Assume that Ambrose Motor Corp. (AMC) estimates next year’s earnings before interest payments as $100 million, provided it does not lose a product liability lawsuit. The probability of a lawsuit is .02 and the payment if it occurs is estimated to be $1 million. From its $100 million in earning, Ambrose expects to pay $60 million on its interest and principal payments, leaving $40 million for shareholders - again provided the company does not lose a product liability suit. Ambrose is trying to decide how to finance risk associated with the potential liability suit.
A) What is the expected value of loss associated with the product liability lawsuit?
B) In a perfect market without transactions costs (taxes are among potential transactions costs) where AMC does not value insurer services, how much would AMC’s shareholders want AMC to pay for $50 million of product liability insurance?
C) Would an insurer be willing to provide this policy for the price AMC would be willing to pay? Explain.
D) Next, suppose that AMC’s insurer has an in-house legal expert on product liability who can reduce the probability of losing the lawsuit from .02 to .01. If the insurer’s premium loadings add an additional amount to the premium of 30% of the losses and loss adjustment expense, how much is the premium for $50 million of coverage, and would AMC be willing to pay it?