Question

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 park 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 (B/C) ratio for System A is approximately 1.16, and for System B, it is approximately 1.14. Based on these calculations, System A is the more favorable choice as it has a higher B/C ratio, indicating a better return on investment at the specified 12% interest rate.

Step-by-step explanation:

To determine the benefit/cost ratio for each system, we first calculate the present worth of the benefits and costs for both System A and System B. For System A, the present worth of benefits over the system's life is found by subtracting the first cost from the present worth of the annual savings. Using the formula PWbenefits_A =
`\( (S_A)/(i) \),` where
`\(S_A\)` is the annual savings of $79,000 and
`\(i\)`is the interest rate of 12%, we get PWbenefits_A ≈ $607,142.86. Similarly, for System B, the present worth of benefits is calculated as PWbenefits_
`B ≈ \( (S_B)/(i) \),`where
`\(S_B\)` is the annual savings of $53,100, resulting in PWbenefits_
`B ≈ $470,833.33.`

Next, the present worth of costs for System A is the first cost, which is $250,000. For System B, it is the upgrade cost of $150,000. Therefore, PWcosts_A = $250,000 and PWcosts_B = $150,000.

Finally, the benefit/cost ratio is determined by dividing the present worth of benefits by the present worth of costs for each system. The B/C ratio for System A is
`\( (PWbenefits_A)/(PWcosts_A) \),` resulting in approximately 1.16, and for System B, it is
`\( (PWbenefits_B)/(PWcosts_B) \)`, resulting in approximately 1.14.

In conclusion, since System A has a higher benefit/cost ratio (1.16) compared to System B (1.14), the theme park manager should choose System A for better cost-effectiveness and a higher return on investment at the specified 12% interest rate.