Question

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

Answer 1

In this question we need to compare two options which are:

1. Not setting up a security alarm system.

2. Setting up a security alarm system.

To compare these two we need to find the PV of cost associated with both. Whichever has a lesser present value is a better option:

The answer is as:

As shown in solution above the cost in PV terms for

with security system is : 60,831$

with security system is : 59,141 $

Thus, it is advisable to buy security system.