Question 2.2: Suppose the risk of an airline accident for a major airline ...
Suppose the risk of an airline accident for a major airline is 1% per year, with a beta of zero. If the risk-free rate is 4%, what is the actuarially fair premium for a policy that pays $150 million in the event of a loss? What is the NPV of purchasing insurance for an airline that would experience $15 million in financial distress costs and $10 million in issuance costs if it were uninsured in the event of a loss?
Plan
The expected loss is 1% × $150 million = $1.50 million, but the total value to the airline is $150 million plus an additional $25 million in distress and issuance costs that it can avoid if it has insurance. The premium is based solely on the expected loss, as the PV of the expected loss shown in Eq. 2.1. Because the beta is zero, the appropriate discount rate is 4%.
Insurance Premium = \frac{Pr(Loss) \times E [ Payment in the Event of Loss ]}{1+r_{L}} (2.1)
Execute
The actuarially fair premium is $1.50 million/1.04 = $1.44 million.
The NPV of purchasing the insurance is the expected benefit, including avoiding the distress and issuance costs, net of the premium:
NPV = -1.44+1\%\times (150+25)/1.04=\$0.24 millionEvaluate
The insurance company charges a premium to cover the expected cash flow it must pay, but receiving the insurance payment may be worth more than the amount of the payment. The insurance payment allows the firm to avoid other costs, so it is possible for the premium to be actuarially fair and for the insurance to still be a positive-NPV investment.