Let's analyze which option (Gasoline or Electric) is more economical using **annual cash flow analysis** at an **% interest rate**. ## **Step 1: List All Costs and Cash Flows** | | Gasoline | Electric | |-----------------|----------|----------| | First cost | $2,400 | $9,000 | | Annual operating| $1,200 | $250 | | Annual maintenance | $300 | $50 | | Salvage value | $300 | $600 | | Life (years) | 5 | 10 | - Analysis period: **10 years** (the pump is needed for 10 years). ## **Step 2: Handle Different Lives (Repeatability Assumption)** - **Gasoline pump** will need to be replaced after 5 years (so, two pumps needed in 10 years). - **Electric** lasts the full 10 years. --- ## **Step 3: Calculate Annual Worth (AW) for Each Option** We'll use the **Annual Worth (AW)** method: \[ AW = (P \cdot A/P, i, n) + (A) - (F \cdot A/F, i, n) \] Where: - \(P\) = Present (first) cost - \(A\) = Annual operating + annual maintenance cost - \(F\) = Salvage value - \(i\) = Interest rate (8%) - \(n\) = Life of pump ### **A. Electric Pump** - \(P = 900\) - \(A = 250 + 50 = 300\) - \(F = 600\) - \(n = 10\) - \(i = 8\%\) #### Find Factors \[ (A/P, 8\%, 10) = \frac{.08(1+.08)^{10}}{(1+.08)^{10} - 1} = .14903 \] \[ (A/F, 8\%, 10) = \frac{.08}{(1+.08)^{10} - 1} = .069 \] #### Plug Values \[ AW_{electric} = (900 \times .14903) + 300 - (600 \times .069) \] \[ = 1341.27 + 300 - 41.40 \] \[ = 160.87 \] --- ### **B. Gasoline Pump** - \(P = 240\) - \(A = 120 + 300 = 150\) - \(F = 300\) - \(n = 5\) - \(i = 8\%\) #### Find Factors \[ (A/P, 8\%, 5) = .25046 \] \[ (A/F, 8\%, 5) = .17046 \] #### First 5-Year Cycle \[ AW_{gasoline, 5yr} = (240 \times .25046) + 150 - (300 \times .17046) \] \[ = 601.10 + 150 - 51.14 \] \[ = 2049.96 \] #### Adjust for 10-Year Analysis (Repeatability) Since the gasoline pump is replaced after 5 years, the same AW applies for the second 5 years. So, **use the same annual worth for the full 10-year period**. --- ## **Step 4: Compare Annual Worths** - **Electric:** \$1,600.87 per year - **Gasoline:** \$2,049.96 per year --- ## **Final Answer** ### **The pump should be powered by the electric motor, as its annual worth (cost) is less than that of the gasoline pump.** --- ### **Summary Table** | Option | Annual Worth (\$/year) | |-----------|-----------------------| | Electric | 1,600.87 | | Gasoline | 2,049.96 | **Electric is the more economical choice.**