Question

3.) A theme park manager, in order to improve security at a theme park, can invest in a new security intrusion detection system that has a first cost of $250,000 (System A). System A will produce annual savings (benefits - maintenance costs) of $79,000 per year. There is no salvage value. Or the theme parh manager can have the existing security system (System B) upgraded at a cost of $150,000 and this will produce annual savings (benefits - maintenance costs) of $53,100 per year. There is no salvage value. The CEO of the theme park wants a benefit/cost ratio comparison of the two systems (Present Worth of the Benefits / Present Worth of the Costs or PWbenefits/PWcosts). The CEO directs that an interest rate of 12% be used for these comparisons. What is the B/C ratio then for each System? What System should therefore be chosen?

Answer 1

The benefit-cost ratio for System A is 2.63 and for System B is 2.95. Since System B has a higher B/C ratio, it is the preferred security system to be chosen for cost-effectiveness at the theme park.

Step-by-step explanation:

The student has asked for a calculation of the benefit-cost ratio for two different security systems under consideration at a theme park. To find the benefit-cost (B/C) ratio for each system, you compare the present worth of the benefits (PWbenefits) to the present worth of the costs (PWcosts) using the formula B/C = PWbenefits/PWcosts. Since neither system has a salvage value, the present worth of the benefits is equal to the annual savings for each, discounted at the given interest rate of 12%. For System A the calculation is $79,000 per year for a cost of $250,000, and for System B it is $53,100 per year for a cost of $150,000.

To calculate the present worth of the annual savings for each system, we use the formula PW = A × (P/A, i%, n), where 'A' is the annual savings, 'i' is the interest rate, and 'n' is the number of years. As the number of years is not specified and we assume an infinite time horizon, the formula simplifies to PW = A/i. Therefore, for System A the present worth is $79,000/0.12 = $658,333.33, and for System B it is $53,100/0.12 = $442,500.

Now we calculate the B/C ratio for each system. For System A, the B/C ratio is $658,333.33/$250,000 = 2.63, and for System B, the B/C ratio is $442,500/$150,000 = 2.95. Since System B has a higher B/C ratio, it is the more cost-effective security option and should be chosen according to the criteria provided by the CEO.