## Answered: - Your name Homework # Due date Your seat number RMI 2101 Spring

Please I need help with assignment.....This assignment is consist of probability

Homework #

Due date

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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