Homework 6 Risk Control Decision (15 points)

The purpose of this assignment is to make sure you are able to use Excel to help you make risk control decisions. You will need to turn in the excel spreadsheet along with your answer.

The owner of the Illinois Bakery Company, Lisa, must decide how to handle all kinds of potential property losses facing the firm. Currently the company retains all the risk (i.e. no insurance is in place). You have been asked to assist Lisa in making a decision regarding whether she should install a sprinkler system and whether she should purchase insurance. She has provided you access with the following information:

• Sprinkler System

• The automatic sprinkler will cost $4,000 to install.
• Annual depreciation on the sprinkler, assuming a 10-year life span, is $400.
• The sprinkler will cost $100 annually to maintain and such cost is payable for the first 9 years.

• Taxes: The firm is in a 40% tax bracket. It can deduct from its taxable income all

• Costs for loss control (like the depreciation of the sprinkler and maintenance expenses).
• Costs for loss financing (like insurance premiums), and
• Costs for losses not reimbursed by insurance.

• Probability distribution of losses table (for any given year)

Losses	Probability without Sprinkler			Probability with Sprinkler
$0		0.70	0.70
$500		0.15	0.17
$2,000		0.10	0.11
$20,000		0.04	0.013
$75,000		0.007	0.006
$150,000		0.002	0.001
$250,000		0.001	0.000

Assuming there are only three choices (see below) and also there will be at most one loss at any given year. Further assuming that the opportunity cost of capital (i.e. market interest rate) for this decision is 8%. What would be your suggestion to Lisa? Support your answer by calculating the net present value of each alternative (and compare with the default option: no insurance and no sprinkler system). Hint: youll need to calculate the expected retained loss for each alternative using the above distribution first.

1. Install an automatic sprinkler system for $4,000 but buy no insurance. (5 points)
2. Purchase insurance coverage of $75,000 with no deductible for an annual premium of $2,000. (5 points)
3. Install the automatic sprinkler for $4,000 and purchase $75,000 of insurance with no deductible for an annual premium of $900. (5 points)

x Office Update To keep up-to-date with security updates, fixes, and improvements, choose Check for Updates. B2 4 x vfx Retained Loss D H J K L o Q E F G Alternative 1 (only sprinkler) Probability Retained Loss E(Retained loss) Alternative 2 (only insurance) Probability Retained Loss E(Retained loss) M N Alternative 3 (both) Probability Retained Loss E(Retained loss) Expected Value Expected Value Expected Value Savings in Retained Loss Savings in Retained Loss Savings in Retained Loss B 1 No sprinker and no insurance: 2 Probability Retained Loss E(Retained loss) 3 0.7 SO $0 4 0.15 $500 $75 5 0.1 $2,000 $200 6 0.04 $20.000 $800 7 0.007 $75,000 $525 8 0.002 $150,000 $300 9 0.001 $250,000 $250 10 11 Expected Value $2,150 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 32 x Office Update To keep up-to-date with security updates, fixes, and improvements, choose Check for Updates. B2 4 x vfx Retained Loss D H J K L o Q E F G Alternative 1 (only sprinkler) Probability Retained Loss E(Retained loss) Alternative 2 (only insurance) Probability Retained Loss E(Retained loss) M N Alternative 3 (both) Probability Retained Loss E(Retained loss) Expected Value Expected Value Expected Value Savings in Retained Loss Savings in Retained Loss Savings in Retained Loss B 1 No sprinker and no insurance: 2 Probability Retained Loss E(Retained loss) 3 0.7 SO $0 4 0.15 $500 $75 5 0.1 $2,000 $200 6 0.04 $20.000 $800 7 0.007 $75,000 $525 8 0.002 $150,000 $300 9 0.001 $250,000 $250 10 11 Expected Value $2,150 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 32