In question #1 a., show how you calculated one of the after tax numbers in the m

Question

In question #1 a., show how you calculated one of the after tax numbers in the matrix. Then you do not have to show the work for all of the after tax numbers in the matrix. Note that question #2 asks for before-tax values. You do NOT need to calculate after tax numbers for question #2. 1. A small company owns a $75,000 company car. If there is a loss, it is a total loss. The company's probability distribution for losses is estimated as follows: Loss (S) $75,000 The risk manager is considering three options to manage this risk Retention Retention plus loss control Full insurance at an annual premium of S8,300 The loss control measure costs S3,500. Using the loss control measures is expected to result in the following loss distribution: obability (with loss control 0 $75,000 95 05 a. Construct an after-tax loss matrix. Assume that the firm's tax rate is 30%. (8 points) b. Suppose the risk manager's decision rule it to minimize after-tax expected loss. Which risk management alternative will she choose? (2 points) c. Assume that the risk manager has a worry value (WV) equal to $2,000 for retention. Assume also that the WV for retention with loss control is $1,000 If the risk manager decides to minimize TOTAL COST what risk management alternative does she choose? Show manager selects the option. (2 points)

Explanation / Answer

The Above table is the after-tax loss marix

B) After Tax Expected Loss for each RM Option

Assume the following probabilities:

Retention

Probability of loss = 10%

Probability of No loss = 90%

Retention with Loss control

Probability of Loss = 5%

Probability of No loss = 95%

Insurance

Probability = 1 . KNOWN COST

Case Study 1: Calculation of Expected Losses

Retention = ($52500) * (0.1) + ($0) * (0.90) = $5250

Retention with loss control = ($54950) * (0.05) + ($2450) * (0.95) = $5075

Full Insurance = $5810 with P[Loss] = 1.00 = $5810 Known Loss

He will choose retention with loss control.

C) WV = $2000

WV for retention with loss control = $1000

Retention = 52500 + 2000 = 54500

Full Insurance = 5810 + 0 = 5810

Retention + Loss Control = 2450 + 2000 = 4450

He would choose Retention + loss control = $4450

Loss No Loss Retention $75000*(1-0.3) = $52500 0*0.7= $0 Full insurance $8,300*(0.7) = $5810 $8300*0.7=$5810 Retention+Loss Control $(75000+3500)*0.7=$54950 $3500*0.7= $2450

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