A firm has the following probability distribution for annual losses due to vanda

Question

A firm has the following probability distribution for annual losses due to vandalism. All amounts are before any tax consideration. The firm has a tax rate of 20%. Annual Losses Probability $0 0.75+ 0.204 $ 4,000 $10,000 0.054 The firm is considering three options: 1. Retention 2. Deductible insurance, Face amount = $10,000, Deductible = $300, Premium = $1300- 3. Full insurance, Face amount = $10,000, Premium = $1500 1. Derive the after-tax loss matrix for the firm. (4 points) = 2. If the risk manager's decision rule is to minimize after-tax expected cost, which option will she choose? Show why? (3 points) 3. What worry value for retention would make the full insurance alternative preferable to retention? Be sure to explain your numerical answer. (2 points) 4. What worry value or values would make deductible insurance preferred to retention? Be sure to explain your numerical answer. (3 points)

Explanation / Answer

1. We assume that firm will receive benefit in tax in case of loss.

The after tax loss matrix for the firm is provided below:

2. if the manager's decision rule is to minimize after tax expected cost, it isrecommended to go ahead with retention option the trade off from the premium of the insurance. The expected loss from all three option is provided below:

hence considering the probability of event occuring, retention provides lowest expected loss at 1040 without considering worry value. however if the manager is conservative in its decision, other two options are preferable.

3. Worry Value is cost associated with decsion making, cost of anxiety concerning a decision. hence such cost is assumed to be incurred while decision making. the worry value of retention which would make full insurance alternative preferable to retention is $200. it is this value if assumed to be incurred in retention decision will make expected loss equal to full insurance option.

4. The worry value of $87.5 in retention decision will make deductible insurance prefered to retention.  it is this value if assumed to be incurred in retention decision will make expected loss equal to deductible insurance option.

After Tax Loss P(0.75) P(0.20) P(0.05) Option retention                 -           -3,200         -8,000 deductible insurance        -1,040         -1,280         -1,280 Full insurance        -1,200         -1,200         -1,200

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