Your firm faces a potential $10 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 $2 to the firm. Two policies are available: One pays $5 million and the other pays $10 million if a loss occurs. The insurance company charges 30% more than the actuarially fair premium to cover administrative expenses. To account for adverse selection, the insurance company estimates a 2% probability of loss for the $5 million policy and a 3% probability of loss for $10 million policy. Suppose the beta of the risk is -0.5, the risk-free rate is 1%, and the expected market return is 7%.
a. Which policy should the firm choose if its risk of loss is 2%? What’s the NPV of this choice?
b. Which policy should the firm choose if its risk of loss is 3%? What’s the NPV of this choice?