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Answered: - Your name Homework # Due date Your seat number RMI 2101 Spring
Please I need help with assignment.....This assignment is consist of probability
Your name
Homework #
Due date
Your seat number
RMI 2101
Spring 2016
Homework Assignment 6
24 points
1) Nakatomi Plaza is an office building in Los Angeles. In a vault in the basement, they keep bearer bonds
worth $100 million. These bonds, of course, are subject to the risk of theft. The risk manager (John
McClane) has identified three possible theft scenarios. First, an opportunistic employee might steal a
few bonds while cleaning the vault, resulting in a small loss. A more unscrupulous employee may
develop a sophisticated embezzlement plan, stealing 10% of the bonds. Finally, a German terrorist
(Hans Gruber) may fake a terrorist attack during the Nakatomi Christmas party, using the attack as a
distraction while his group steals all the bonds in the vault. Based on these scenarios, McClane has
determined the following ?status quo? probability distribution of losses:
Status Quo
Loss
Probabilit
y
$0
0.85
$10,000
0.09
$10,000,00
0
$100,000,0
00
0.04
0.02
McClane has discussed these risks with his insurance broker, Al Powell. Al goes to the insurance
markets to solicit quotes for partial and full insurance. The risk financing options are as follows:
Retention alone.
Partial insurance with a limit of $10,000,000 and a premium of $500,000.
Full insurance with a premium of $3,000,000.
In addition, McClane can install security cameras in the vault for $50,000. While this won?t deter Hans
Gruber, it will eliminate the possibility that an employee can steal the bonds and also reduces the
chance of a sophisticated embezzlement scheme. With the security system, the distribution of losses is
as follows:
With Security
Loss
$0
Probabilit
y
0.95
$10,000
$10,000,00
0
$100,000,0
00
0.00
0.03
0.02
If he chooses to install these cameras, the insurers will give him a premium discount. With the
cameras, the options for risk financing are as follows:
Retention with cameras.
Partial insurance with a limit of $10,000,000 and a premium of $400,000 with cameras.
Full insurance with a premium of $2,800,000.
The tax rate for Nakatomi Industries is 40%.
a) Construct an after-tax loss matrix of these six RM options and four states of the world. This should
follow the exact same format as we used in class ? the RM alternatives as the rows, the states of
the world as columns, and after-tax numbers in brackets . This should be typed. You do not have
to show calculations for the numbers in this loss matrix, but you must show calculations for the
other quantitative problems in this homework (b-f). [5 points]
b) Assume that McClane is risk neutral and chooses a risk management option based on the after-tax
expected loss. What does he choose? Justify your answer and show your work. [3 points]
Al Powell, the broker, recommends that McClane think more deeply about the risk of these bonds being
stolen. Not only will the bonds be stolen, but McClane may have to fight the thieves himself on
Christmas! McClane considers this possibility and decides that some of these states of the world may
cause him anxiety. His worry values are as follows:
Retention alone: WVR = $1,000,000
Retention with security cameras: WVR+S = $800,000
Partial insurance alone: WVPI = $600,000
Partial insurance with security cameras: WVPI+S = $500,000
c) If McClane chooses a risk management option based on the after-tax total cost of each option, what
risk management option should he choose? Justify your answer and show your work. [4 points]
d) What is McClane?s Pmax for full insurance without the security cameras? Since this is the largest
premium he would pay, you should use pre-tax expected values. (Hint: Imagine he?s choosing
between buying full insurance or nothing. What inequality represents choosing full insurance?) [2
points]
e) What is McClane?s Pmax for full insurance with the security cameras? Since this is the largest
premium he would pay, you should use pre-tax expected values. Remember that the cost of the
cameras is not part of the insurance premium. (Hint: Use the same inequality as in ?d? above.) [3
points]
f)
Assume that John McClane chooses to install the security cameras. Under what conditions would
McClane choose retention over full insurance? Give an intuitive explanation of what these
conditions mean. WVs are not tax-deductible, so you should use pre-tax numbers for this
calculation. [3 points]
g) McClane just received information that Hans Gruber?s brother Simon is also targeting the vault in
Nakatomi Plaza for a similar heist of the full $100 million. How would this information affect John?s
worry values? Explain. [2 points]
h) McClane recently found out that the insurer offering full insurance is on the verge of bankruptcy.
How might this information affect John?s worry values for full insurance? Explain. [2 points]
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