1. Kimberly-Clark Company owns a warehouse worth $75,000. Ray Van Eperen is the risk manager. Kimberly-Clark faces the risk of fire which would completely destroy their warehouse. The probability of a fire is known to be 4%.
Kimberly-Clark is considering the following risk management options to address the risk of fire to their warehouse:
[1] Retention
[2] Full Insurance for a premium of $3,600
[3] Safety Program + Retention
[4] Safety Program + Full Insurance [premium falls to $1,250]
The cost of the Safety Program is $2,500. It has the impact of lowering the probability of a fire from 4% to 1%. However, if a fire does occur it is still a total loss.
a. Construct the loss matrix from Kimberly-Clarks perspective. Make sure you show loss in the top row and out-of-pocket cost in the bottom row in each cell of the loss matrix.
[2 points]
b. Construct the payout matrix from an insurers perspective. [1 point]
c. What is the actuarially fair premium [AFP] for full insurance without safety program? What is the AFP for full insurance with safety program? [2 points]
Assume Rays worry value for retention without safety program (WVR) is $850 and his worry value for retention with safety program (WVRS) is $400.
d. If Rays decision rule is to pick the option that minimizes TOTAL EXPECTED COST, what risk management option does he choose? Make sure that you show all calculations and clearly define TOTAL EXPECTED COST in each case. [2 points]
e. What is Rays PMAX for full insurance without safety program as opposed to retention without safety? [1 point]
f. During a meeting, the Chief Risk Officer (CRO) told Ray that the most he would pay for full insurance without safety program (as opposed to retention without safety) is $4,000. What is the CROs worry value for retention without safety program (WVR)? [1 point]
g. Who is more risk averse, the CRO or Ray? Explain. [1 point]
2. Kramerica Company has a small plant worth $10,000. The plant is subject to physical damages and total destruction as a result of fire.
From over 6,000 industry observations, the firm has derived the following probability distribution of fire losses for its physical plant.
Loss Amount ($)
Probability of Loss
0
0.89
1,500
?
6,000
0.065
10,000
0.005
Kramerica is considering the following risk management options:
[1] Retention
[2] Partial insurance Face Amount = $8,000; Premium = $580
[3] Deductible insurance Face Amount = $10,000; Premium = $470;
Deductible per occurrence = $1,000
[4] Full insurance Face Amount = $10,000; Premium = $600
a. Construct the loss matrix from Kramericas perspective. Make sure you show loss in the top row and out-of-pocket cost in the bottom row in each cell of the loss matrixEx. [2 points]
b. Construct the payout matrix from an insurers perspective. [2 points]
c. What is the AFP for deductible insurance in this case? [2 points]
d. Assume that the companys decision rule is to pick the option that minimizes TOTAL EXPECTED COST. Can you identify what risk management option is chosen? Why or why not? Make sure that you show all calculations and clearly define TOTAL EXPCTED COST in each case. [2 points]
e. Assume that the companys decision rule is to pick the option that minimizes TOTAL EXPECTED COST, what worry value(s) would make deductible insurance preferred to full insurance? Show all work and calculations and explain your numerical answer. [1 point]
f. What worry value(s) would make retention preferred to partial insurance? Show all work and calculations and explain your answer. [1 point]
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