Nielson Motors has a debt-equity ratio of 1, an equity beta of 1, and a debt beta of 0. They are deciding if they wish to buy fire insurance against their factory burning down, which would result in loss of $110 million with probability 5%. Because the risk of fire is idiosyncratic, the beta of the loss is zero. The risk-free rate is 5%, and the expected market return is 15%. If the loss is insured, or if Nielson is unaffected, their capital structure remains unchanged (debt-equity ratio of 1, an equity beta of 1, and a debt beta of 0). If uninsured, the firm will have no difficulty raising debt to rebuild the factory, but extra debt will change the capital structure: given that they have to rebuild the factory, Nielson will have debt-equity ratio of 1.2, an equity beta of 1.5, and a debt beta of 0.24. Next year, whether or now Nielson is affected by a loss, they will evaluate the following projects, none of which would change Nielson's volatility.

a. What is the actuarilly fair insurance premium?

b. If the insurance company charges administrative expenses of 10% over the actuarilly fair premium, how much do they charge?

c. At this premium, what is the NPV of buying insurance?