Homework #4 RMI PDF

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Homework #4...

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RMI 2101 Spring 2018 Homework Assignment 4 35 points Due on March 22, 2018 At 5:30 PM EST on BlackBoard/SafeAssign No hard copies will be accepted in class. All homework must be submitted on SafeAssign and time stamped by 5:30 PM EST on the due date. Carefully follow the Instructions – Homework Guidelines and Submitting Homework to SafeAssign located in the Homework Section of BlackBoard. Hint: Read the questions carefully and be sure that you answer the questions asked. Many times students give correct information in an answer but that information is not the answer to the question. **Note these additional guidelines for this assignment: All matrices are to be constructed with the Risk Management Alternatives as the rows and the States of the World as the columns, as was illustrated in lecture. Show ALL of your work, in order to receive full credit for an answer. And, provide your answers using Word docs only In question #1a., 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 $75,000 company car. If there is a loss, it is a total loss. The company’s probability distribution for losses is estimated as follows: Loss ($) 0 $75,000

Probability .9 .1

The risk manager is considering three options to manage this risk:  Retention  Retention plus loss control  Full insurance at an annual premium of $8,300

The loss control measure costs $3,500. Using the loss control measures is expected to result in the following loss distribution: Loss ($) 0 $75,000

Probability (with loss control) .95 .05

a. Construct an after-tax loss matrix. Assume that the firm’s tax rate is 30%. (10 points)

Retention After Tax of 30% Probability Before Tax After Tax RETENTION PLUS LOSS CONTROL

After Tax of 30% Probability Before Tax Cost After Tax Cost

FULL INSURANCE After Tax of 30% Probability Before Tax Cost After Tax Cost

Loss $75,000 $52,000 10% $7,500 $5,250

No Loss $0 $0 90% $0 $0

$75,000 $3,500 = $78,000 $54,950 5% $3,925 $2,747.5 0

$0 $3,500 = $3,500 $2,450 95% $3,325 $2,327.5 0

$8,300 $5,810 N/A $8,300 $5,810

$8,300 $5,810 N/A N/A N/A

Expected Cost

$7,500 $5,250

$7,250 $5,075

$8,300 $5,810

b. Suppose the risk manager’s decision rule it to minimize after-tax expected loss. Which risk management alternative will she choose? (3 points)



If the risk manager’s decision rule to minimize after-tax expected loss, she will choose the Retention Plus Loss Control. It is the lowest expected cost compared to Retention and Full Insurance.

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 all total cost calculations and work and explain why the risk manager selects the option. (3 points) Retention: $5,250 + $2,000 = $7,250 Retention & Safety: $5,075 + $1000 = $6075 Full Insurance: $5,810 + $0 = $5,810 

The best option for the risk manager is to get full insurance. Based off the number with included worry value, full insurance is the cheapest oftion.

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

0 200,000 600,000 1,000,000

.65 .25 .08 .02

The firm would like to purchase insurance for this risk and is considering the following three different insurance alternatives: 

Retention (No Insurance)



Deductible Insurance Face amount of the policy = $1,000,000 Deductible = $100,000 (the maximum amount the client would pay in a loss) Premium = $110,000 Full Insurance Face amount of the policy = $1,000,000 Premium = $150,000



a. Construct a before-tax loss matrix. (8 points)

$0

Probability

65%

$200,00 0 $200,00 0

Expected Cost

$0

$50,000 $48,000 $20,000

$110,0 00 $0 $110,0 00

$110,00 0 $100,00 0 $210,00 0

$110,00 0 $100,00 0 $210,00 0

$110,00 0 $100,00 0 $210,00 0

25%

8%

2%

1) Retention

2) Deductible Insurance

Probability

$0

65%

Expected Cost

3) Full Insurance

Probability

Expected Cost

$600,00 0 $600,00 0

$1,000,0 00 $1,000,0 00

25%

8%

2%

$71,50 0

$52,500 $16,800 $4,200

$150,0 00 $0 $150,0 00

$150,00 0 $0 $150,00 0

$150,00 0 $0 $150,00 0

$150,00 0 $0 $150,00 0

N/A

N/A

N/A

N/A

$150,0 00

N/A

N/A

N/A

Expected Cost 100%

$118,000

100%

$145,000

100%

$150,000

b. If the risk manager decision rule is to minimize EXPECTED Cost, which option will be chosen? And why? (3 points)



In order to minimize expected cost, the risk manager will use Retention.

c. What is the actuarially fair premium for this example? (2 points)



AFP = $118,000, the retention option.

d. If the risk manager makes decisions by minimizing TOTAL COST, show what conditions the WVs would make if: i. What Worry Value for Retention would make the Full Insurance Alternative preferable to Retention? Show all work and explain the numerical answer. (3 points) 

150,000 + WVfi < $118,000 + WVr 32,000 < WVr

If WVr = 32,000, it is indifferent but if WVr < 32,000 then choose retention over full insurance. ii. What Worry Value for Deductible Insurance would make the Full Insurance Alternative preferable to Deductible Insurance? Show all work and explain the numerical answer. (3 points) 

150,000 + WVfi < 145,000 + WVdi 5,000 < WVdi

If WVdi = 5,000, it is indifferent but if WVdi < 5,000 then choose insurance with deductible....