Your firm faces a potential $10 million loss that it would like to insure. Becau

Question

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?

Explanation / Answer

for $5 million policy , premium amount to $5 million*2% loss of prob. = $10000 + 30% = $13000

for $10 million policy , premium amount to $10 million*3% loss of prob. = $30000 + 30% = $39000

therefore incremental cost will be $39000 - $ 13000 = $26000

and loss of probalility to firm is 2% therefore $ 10 million * 2% = $20000 which has to be get covered

therefore $ 5 million policy should be taken since its cost is less then $10 million policy.

NPV FOR THE SAME WOULD BE

PV OF INCREMENTAL CASH OUTFLOW = $26000

PV OF INCREMENTAL CASH INFLOW = $20000*102% = $20400

NPV = $20400 - $ 26000 = ( $5600).

SINCE NPV IS NEGEATIVE WE SHOULD SELECT $5 MILLION POLICY.

II) WHEN PROBALILTY OF LOSS IS 3% IE $10 MILLION *3% = $ 30000

SAME MANNER WE SHOULD SELECT $ 10 MILLION POLICY.

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