Your firm faces a potential \($100\) million loss that it would like to insure. Because of tax benefits and the avoidance of financial distress and issuance costs, each \($1\) received in the event of a loss is worth \($1.50\) to the firm. Two policies are available: One pays \($55\) million and the other pays \($100\) million if a loss occurs.
The insurance company charges 20% more than the actuarially fair premium to cover administrative expenses. To account for adverse selection, the insurance company estimates a 5% probability of loss for the \($55\) million policy and a 6% probability of loss for the \($100\) million policy.
Suppose the beta of the risk is zero and the risk-free rate is 5%. Which policy should the firm choose if its risk of loss is 5%? Which should it choose if its risk of loss is 6%?