Let's break down the solution step by step: ### Given Data **Hydraulic Press (HP):** - First cost (\(P_{HP}\)) = \$680,000 - Annual cost (\(A_{HP}\)) = \$200,000 - Salvage value (\(S_{HP}\)) = \$70,000 - Life = 5 years **Electric Machine Technology (EMT):** - First cost (\(P_{EMT}\)) = \$800,000 - Annual cost (\(A_{EMT}\)) = \$152,000 - Salvage value (\(S_{EMT}\)) = \$130,000 - Life = 5 years --- ### Step 1: Identify the "extra investment" and "savings" - **Extra initial investment:** \( P_{EMT} - P_{HP} = \$800,000 - \$680,000 = \$120,000 \) - **Annual savings:** \( A_{HP} - A_{EMT} = \$200,000 - \$152,000 = \$48,000 \) (savings per year if choosing EMT) - **Extra salvage value:** \( S_{EMT} - S_{HP} = \$130,000 - \$70,000 = \$60,000 \) (additional salvage value at end) --- ### Step 2: AW-based Equation for Incremental Analysis Set up the equation for the incremental investment using the **Annual Worth (AW) method**. The incremental cash flows are: - Initial cost: \(-\$120,000\) (at year 0) - Annual savings: \(+\$48,000\) (years 1-5) - Extra salvage value: \(+\$60,000\) (at year 5) We want to solve for the ROR (\(i\)) that makes the net present worth of these cash flows zero: \[ 0 = -120,000 + 48,000(P/A, i, 5) + 60,000(P/F, i, 5) \] --- ### Step 3: Substitute Present Worth Factors \[ 0 = -120,000 + 48,000 \left( \frac{1-(1+i)^{-5}}{i} \right) + 60,000 \left((1+i)^{-5}\right) \] --- ### Step 4: Rearranged Equation \[ 120,000 = 48,000 \left( \frac{1-(1+i)^{-5}}{i} \right) + 60,000 \left((1+i)^{-5}\right) \] --- ### Step 5: Solve for \(i\) (Trial and Error or Financial Calculator) Let's use trial and error (or Excel/financial calculator) to solve for \(i\): #### Guess \(i = 20\%\): - \( (1+i)^{-5} = (1.20)^{-5} = 0.4013 \) - \( \frac{1 - 0.4013}{0.20} = 2.993 \) - Compute: \[ 120,000 = 48,000 \times 2.993 + 60,000 \times 0.4013 = 143,664 + 24,078 = 167,742 \] This is **too high** (we get more than \$120,000), so try a **higher rate**. #### Guess \(i = 30\%\): - \( (1.3)^{-5} = 0.2374 \) - \( \frac{1 - 0.2374}{0.30} = 2.5419 \) - Compute: \[ 48,000 \times 2.5419 = 122,011 \] \[ 60,000 \times 0.2374 = 14,244 \] \[ \text{Sum} = 122,011 + 14,244 = 136,255 \] Still **too high**. Try **40%**. #### Guess \(i = 40\%\): - \( (1.4)^{-5} = 0.186 \) - \( \frac{1 - 0.186}{0.40} = 2.035 \) - Compute: \[ 48,000 \times 2.035 = 97,680 \] \[ 60,000 \times 0.186 = 11,160 \] \[ \text{Sum} = 97,680 + 11,160 = 108,840 \] Now, **too low** (\$108,840 < \$120,000). --- #### Interpolate between 30% (\$136,255) and 40% (\$108,840): \[ i = 30\% + \frac{136,255 - 120,000}{136,255 - 108,840} \times 10\% \] \[ = 30\% + \frac{16,255}{27,415} \times 10\% \] \[ = 30\% + 0.593 \times 10\% = 30\% + 5.93\% = 35.9\% \] --- ### **Final Answer** **The ROR on the extra investment for the EMT alternative is approximately:** \[ \boxed{36\%} \] --- **If you need this to two decimal places, enter:** \[ \boxed{35.9\%} \] --- **Summary of Steps:** 1. Set up the incremental cash flows. 2. Write the AW-based ROR equation. 3. Plug in numbers and solve for \(i\) by trial and error or interpolation. --- **If you need more decimal places or want to see the calculation in Excel, let me know!**