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

Question

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?

Accepted Answer

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%.

[latex]Insurance Premium = \frac{Pr(Loss) imes E [ Payment in the Event of Loss ]}{1+r_{L}}[/latex] (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:

[latex]NPV = -1.44+1\% imes (150+25)/1.04=\$0.24 million[/latex]

Evaluate

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.

Question 2.2: Suppose the risk of an airline accident for a major airline ...

Related Answered Questions

Bolt Industries is facing increased competition and wants to borrow $10 million in cash to protect against future revenue shortfalls. Currently, long-term AA rates are 10%. Given its credit rating, Bolt can borrow at 10.5%. The company is expecting interest rates to fall over the next few years, ...

Verified Answer:

Verified Answer:

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 ...

Verified Answer:

Verified Answer:

Consider the following data for Walmart Stores and Target Corporation ($ billions):Compare Walmart’s and Target’s operating margin, net profit margin, P/E ratio, and the ratio of enterprise value to operating income and sales. ...

Verified Answer:

Assess how Global’s ability to use its assets effectively has changed in the last year by computing the change in its return on assets. ...

Verified Answer:

The following table contains information about Walmart (WMT) and Nordstrom (JWN). Compute their respective ROEs and then determine how much Walmart would need to increase its profit margin in order to match Nordstrom’s ROE. ...

Verified Answer:

Assess Global’s ability to meet its interest obligations by calculating interest coverage ratios using both EBIT and EBITDA. ...

Verified Answer:

Compute Global’s accounts payable days, inventory days, and inventory turnover for 2016. ...

Verified Answer:

Suppose Global had an additional $1 million depreciation expense in 2016. If Global’s tax rate on pretax income is 26%, what would be the impact of this expense on Global’s earnings? How would it impact Global’s cash at the end of the year? ...

Verified Answer: