XYZ Company is considering the installation of a permanent security alarm system. It currently self-insures losses up to $50,000 and purchases insurance which covers losses in excess of $50,000 for an annual premium of $6000. The cost of the proposed alarm system is $20,000 and has a useful life of ten years. Assume that the loss distributions that XYZ faces for retained losses with or without an alarm system are the same as the distributions that ABC faced with or without a security service in the previous problem. If this new alarm system is installed, it will require annual maintenance expenses of $1000 but will reduce the premium XYZ pays for excess insurance coverage by $3000 per year. Using capital budgeting techniques, determine if the purchase of the permanent alarm system is financially advantageous. Assume an interest rate of 10% and ignore any tax effects not already included in the loss distribution itself.

Distributions from ABC company:

Total Annual After-Tax Dollar Losses from Burglary and Theft

Dollar Loss Probability

Losses No Security With Security

$ 0 0.010 0.050

500 0.030 0.120

1,000 0.080 0.200

2,000 0.150 0.300

3,000 0.200 0.150

4,000 0.280 0.090

5,000 0.180 0.050

10,000 0.050 0.030

15,000 0.014 0.010

25,000 0.005 -

50,000 0.001 -

1.000 1.000