Let's analyze the problem step-by-step: ### Given Data: - Initial outlay for Design A: **\$437,000** - Annual operating & maintenance costs for Design A: **\$45,000** - Investment for Design B: **\$343,000** - Annual operating & maintenance costs for Design B: **\$92,000** - Revenue from collections: **\$95,000/year** - Duration: **17 years** - Interest rate (i): **5% per year** --- ### Step 1: Determine the benefit-cost ratio (BC) for each system The benefit-cost ratio is given by: \[ BC(i) = \frac{\text{Present Value of Benefits}}{\text{Present Value of Costs}} \] Since the benefits are the fee collections of \$95,000 annually, and costs include initial outlay and annual maintenance, the present values are calculated using the **annuity formula**: \[ PV = \text{Annual benefit} \times \frac{1 - (1 + i)^{-n}}{i} \] --- ### Step 2: Compute the present value of benefits \[ PV_{benefits} = 95,000 \times \frac{1 - (1 + .05)^{-17}}{.05} \] Calculating: \[ (1 + .05)^{17} \approx 2.292 \] \[ (1 + .05)^{-17} = \frac{1}{2.292} \approx .436 \] \[ PV_{benefits} = 95,000 \times \frac{1 - .436}{.05} = 95,000 \times \frac{.564}{.05} \] \[ PV_{benefits} \approx 95,000 \times 11.28 \approx 1,072,200 \] --- ### Step 3: Compute the present value of costs for each system **Design A:** \[ PV_{costA} = 437,000 + 45,000 \times \frac{1 - (1 + .05)^{-17}}{.05} \] \[ PV_{costA} = 437,000 + 45,000 \times 11.28 \approx 437,000 + 507,600 = 944,600 \] **Design B:** \[ PV_{costB} = 343,000 + 92,000 \times 11.28 \approx 343,000 + 1,038,000 = 1,381,000 \] --- ### Step 4: Calculate benefit-cost ratios \[ BC_A = \frac{1,072,200}{944,600} \approx 1.14 \] \[ BC_B = \frac{1,072,200}{1,381,000} \approx .78 \] --- ### **Answer:** **System A** should be selected based on the benefit-cost ratio as it has a higher ratio. **The benefit-cost ratio for System A is approximately 1.14** (rounded to two decimal places).