IRM4030: Risk Management Solutions 1. The marginal tax rate of ABC Corp is specified as below:...

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IRM4030: Risk Management Solutions 1. The marginal tax rate of ABC Corp is specified as below: Taxable Income Tax rate $0-$5 10% $5 - $10 20% $10- 30% A firm has its taxable income as the following: Probability 0.1 0.9 Pre-tax income $20m $50m (1) Assume the company could purchase a zero-loading insurance policy. What is the premium of the insurance policy? (2) Continue to assume the policy to have a zero loading. How much tax saving will ABC Corp have by purchasing the insurance policy? (3) Answer (1) and (2) assuming the insurance policy has a 25% loading. Solution: (1) With a full insurance, ABC Corp's pre-tax income is 50 million when its pre-tax income is 20 million -- the insurer pays (50 million -20 million) when its pre-tax income is 20 million. As a result, the actuarially fair premium is the payment ABC receives from the insurer multiplied by the probability of receiving the payment, which is 10%. Therefore, Actuarially fair premium = (50-20)*0.1 = 3million (2) Question: Tax saving by buying a zero-loading insurance policy IRM4030: Risk Management Solutions 1. The marginal tax rate of ABC Corp is specified as below: Taxable Income Tax rate $0-$5 10% $5 - $10 20% $10- 30% A firm has its taxable income as the following: Probability 0.1 0.9 Pre-tax income $20m $50m (1) Assume the company could purchase a zero-loading insurance policy. What is the premium of the insurance policy? (2) Continue to assume the policy to have a zero loading. How much tax saving will ABC Corp have by purchasing the insurance policy? (3) Answer (1) and (2) assuming the insurance policy has a 25% loading. Solution: (1) With a full insurance, ABC Corp's pre-tax income is 50 million when its pre-tax income is 20 million -- the insurer pays (50 million -20 million) when its pre-tax income is 20 million. As a result, the actuarially fair premium is the payment ABC receives from the insurer multiplied by the probability of receiving the payment, which is 10%. Therefore, Actuarially fair premium = (50-20)*0.1 = 3million (2) Question: Tax saving by buying a zero-loading insurance policy