To enhance security in River side Park, a city is considering whether it should install a high-tech security system. The system would not only reduce the cost of police patrols but would also deter crime.
The city has received offers from two contractors who have proposed competing systems. System A would cost $4 million; System B would cost $6million. The city estimates that by reducing the cost of police patrols, System A would save $150,000 per year and System B $260,000 per year.
The city uses a discount rate of 10 percent to evaluate all capital outlays. It determines that each of the systems would have an economic life of ﬁve years.
1. Considering the cost as the initial investment and the beneﬁts as the present value of the cash savings from reduced police patrols, which of the two systems would cost the least in relation to beneﬁts? Based only on this criterion, should that system be acquired?
2. Suppose that the city estimates that System A is likely to deter 40 violent crimes per year and that System B is likely to deter 50 violent crimes per year. Which of the two would cost the least (considering cost as the initial investment less the present value of savings from reduced police patrols) in relation to beneﬁts?
3. Suppose further that consultants engaged by the city have placed a dollar cost upon violent crime. Taking into account victims' medical bills and lost wages, they estimate the present value of net outﬂows owing to violent crime to be $90,000 per victim. Considering the costs as the initial investment and the beneﬁts as the present value of the cash savings (including those from both reduced police patrols and crimes deterred), which of the two systems would cost the least in relation to beneﬁts? Based only on this criterion, should that system be acquired?