Assignment
1. Manaca Company owns a small office building worth $100,000. Art Vandelay is the risk manager. Manaca faces the risk of fire which would completely destroy their building. The probability of a fire is known to be 5%.
Manaca is considering the following risk management options to address the risk of fire to their building:
[1] Retention
[2] Full Insurance for a premium of $4,000
[3] Safety Program + Retention
[4] Safety Program + Full Insurance [premium falls to $3,000]
The cost of the Safety Program is $600. It has the impact of lowering the probability of a fire from 5% to 3%. However, if a fire does occur it is still a total loss.
a. Construct a loss matrix.
b. What is the actuarially fair premium [AFP] in this case?
c. What is the AFP when safety is introduced?
Assume Art's worry value for retention (WVR) is $2,000 and for retention and safety (WVRS) is $1,200.
d. If Art decides to minimize TOTAL COST, what risk management option does he choose? Make sure that you show all calculations and clearly define TOTAL COST in each case.
e. What is Art's PMAX for full insurance?
f. During a meeting, the Chief Risk Officer (CRO) told Art that the most he would pay for full insurance is $7,500. What is the CRO's WVR?
g. Who is more risk averse, the CRO or Art? Explain.
2. Kramerica Company has a small plant worth $60,000. The plant is subject to physical damages and total destruction as a result of fire.
From over 10,000 industry observations, the firm has derived the following probability distribution of fire losses for its physical plant.
|
Loss Amount ($)
|
Probability of Loss
|
|
0
|
0.4
|
|
20,000
|
0.3
|
|
40,000
|
0.2
|
|
60,000
|
?
|
Kramerica is considering the following risk management options:
[1] Retention
[2] Partial insurance - Face Amount = $50,000; Premium = $1,200
[3] Deductible insurance - Face Amount = $60,000; Deductible per occurrence = $800; Premium = $1,500
[4] Full insurance - Face Amount = $60,000; Premium = $7,000
a. Construct the loss matrix.
b. Assume that the firm decides to choose a risk management alternative without including valuation for subjective risk. What risk management option is chosen? Show all work and calculations.
c. What worry value(s) would make full insurance preferred to partial insurance? Show all work and calculations and explain your numerical answer.
d. What worry value(s) would make deductible insurance preferred to partial insurance? Show all work and calculations and explain your numerical answer.