risk
bybdh
risk_hw_exmple.docx
Kruger 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 $15,000
[3] Safety Program + Retention
[4] Safety Program + Full Insurance [premium falls to $10,000]
The cost of the Safety Program is $2,000. It has the impact of lowering the probability of a fire from 3% to 2%. However, if a fire does occur it is still a total loss.
For this problem, we will NOT be considering tax rates.
a. Construct a loss matrix. [4 point]
|
|
Loss $400,000 |
No loss $0 |
|
Retention |
400,000 |
0 |
|
Full Insurance |
15,000 |
15,000 |
|
Safety+ Retention |
402,000 |
2,000 |
|
F.I + Safety |
12,000 |
12,000 |
b. What is the actuarially fair premium [AFP] in this case? [1 point]
400,000*.03+0*.97= 12,000
c. What is the AFP when safety is introduced? [2 points]
400,000*.02+0*.98=8,000
Assume Art’s worry value for retention (WVR) is $4,600 and for retention and safety (WVRS) is $2,500.
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. [4 points]
Total cost retention: 12,000+46,000=16,600
Total cost retention+safety program: 10,000+2500=12,500
Total cost full insurance: 15,000
Total cost full insurance + safety program: 12,000
If he choose full insurance +Safety program: 12,000
Total cost of retention: 400,000*.03+0*.97=12,000 (EC)
Total cost of retention+safety program: 402,000*.02+2000*.98=10,000 (EC)
10,000+2,500(wvrs)=12,500
Total cost of full insurance: 15,000
Total cost of full insurance+safety program: 10,000(premium)+2,000(sp)=12,000
From the calculation we can tell that the total cost of full insurance and safety program has the lowest cost. Therefore, I think Art should choose the full insurance + safety program to minimize total cost.
e. What is Art’s PMAX for full insurance? [1 point]
12,000+4600=16,600
f. During a meeting, the Chief Risk Officer (CRO) told Art that the most he would pay for full insurance is $8,500. What is the CRO’s WVR? [1 point]
8,500-12,000= -3,500
g. Who is more risk averse, the CRO or Art? Explain. [2 points]
The Art’s risk manager’s worry value is 3500, which indicates that he has a greater worry value.
2. Kramerica Company has a small building worth $60,000. The building is subject to physical damage and total destruction as a result of fire. The firm has a 30% tax rate.
Kramerica has derived the following probability distribution of fire losses for its building.
Kramerica is considering the following risk management options:
[1] Retention
[2] Partial insurance - Face Amount = $55,000; Premium = $1,000
[3] Deductible insurance - Face Amount = $60,000; Deductible per occurrence = $1,000; Premium = $2,000
[4] Full insurance - Face Amount = $60,000; Premium = $8,000
a. Construct the after-tax loss matrix. [4 points] For all remaining questions (b-d), please use after-tax numbers.
|
|
No loss |
Partial loss |
Total loss |
|
|
|
0 |
20,000 |
40,000 |
60,000 |
|
Retention |
0 (0) (0)(1-.3)=0 |
1,000 (700) |
1,000 (700) |
6,000 (4,200) |
|
Partial Insurance |
1,000 (700) (1,000) (1-.3)=700 |
1,000 (700) |
1,000 (700) |
6,000 (4,200) |
|
Deductible Insurance |
2,000 (1,400) (2,000) (1-.3)+1,400 |
3,000 (2,100) (2000+1000) (1-.3)=2,100 |
3,000 (2,100) |
3,000 (2,100)
|
|
Full Insurance |
8,000 (5,600) (8,000) (1-.3)=5,600 |
8,000 (5,600) |
8,000 (5,600) |
8,000 (5,600) |
After tax=($amount)*(1-tax rate)
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. [4 points]
Retention: (0*.4)+(14,000*.3)+(28,000*.2)+(42,000*.1)=14,000
Partial insurance:(700*.4)+(700*.3)+(700*.2)+(42,000*.1)=1,050
Deductible insurance:(1400*.4)+(2100*.3)+(2100*.2)+(2100*.1)=1820
Full insurance:(5600*.4)+(5600*.3)+(5600*.2)+(5600*.1)=5600
Kramerica should choose partial insurance.
The firm would like to add worry value to their analysis. For the following questions, when using worry values, use the following abbreviations. WVR (retention); WVP (partial insurance); WVD (deductible insurance); WVF (full insurance).
c. What worry value(s) would make full insurance preferred to partial insurance? Show all work and calculations and explain your numerical answer. [2 points]
Total cost of full insurance < Total cost of partial insurance
5600+wvf < 1050+wvp
4550<wvp-wvf
If the worry value for partial insurance is greather than 4550 then choose full insurance
d. What worry value(s) would make deductible insurance preferred to partial insurance? Show all work and calculations and explain your numerical answer. [3 points]
Total cost of deductible insurance < Total cost of partial insurance
1820+wvd < 1050+wvp
770<WVP-WVD
Choose deductible insurance if WVP-WVD<770
