rmi2101 homework


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 ($) Probability

0 .9

$75,000 .1

The risk manager is considering three options to manage this risk:


Retention plus loss control

Full insurance at an annual premium of $8,300

The loss control measure costs $3,500. Using the loss control measures is expected

to result in the following loss distribution:

Loss ($) Probability (with loss control)

0 .95

$75,000 .05

a. Construct an after-tax loss matrix. Assume that the firm’s tax rate is 30%. (6


b. Suppose the risk manager’s decision rule it to minimize after-tax expected

loss. Which risk management alternative will she choose? (2 points)


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 all total cost calculations

and work and explain why the risk manager selects the option. (2 points)

2. Assume a firm owns a $1,000,000 office building with the following probability

distribution related to property losses:

Loss ($) Probability of the loss

0 .65

200,000 .25

600,000 .08

1,000,000 .02

The firm would like to purchase insurance for this risk and is considering the

following three different insurance alternatives:

Partial Insurance

Face amount of the policy = $200,000

Premium = $75,000

Deductible Insurance

Face amount of the policy = $1,000,000

Deductible = $100,000

Premium = $110,000

Full Insurance

Face amount of the policy = $1,000,000

Premium = $150,000