Sure! Let’s break this analysis into **three steps**: --- ## **Step 1: Initial Investment and Depreciation Schedule** ### **a) Initial Outlay:** - **Purchase Price:** $50,000 - **Modification Cost:** $10,000 - **Increase in NWC (Inventory):** $3,000 - **Total Initial Outlay:** = $50,000 + $10,000 + $3,000 = **$63,000** ### **b) Depreciation (MACRS 5-Year Schedule):** MACRS 5-year property rates (for years 1–6): - Year 1: 20.00% - Year 2: 32.00% - Year 3: 19.20% - Year 4: 11.52% - Year 5: 11.52% - Year 6: 5.76% **Depreciable Base:** $60,000 ($50,000 + $10,000; NWC is not depreciable) | Year | MACRS Rate | Depreciation Expense | |------|------------|---------------------| | 1 | 20.00% | $12,000 | | 2 | 32.00% | $19,200 | | 3 | 19.20% | $11,520 | | 4 | 11.52% | $6,912 | | 5 | 11.52% | $6,912 | #### **End of Step 1:** We have established the **initial investment** ($63,000) and the **annual depreciation** schedule. --- ## **Step 2: Annual Cash Flow Calculations** ### **a) Operating Savings:** - **Annual before-tax savings:** $20,000 ### **b) Depreciation Tax Shield:** - **Tax Rate:** 21% - **Formula:** After-tax savings = (Savings - Depreciation) × (1 - Tax Rate) + Depreciation ### **c) Calculate Annual Operating Cash Flows:** | Year | Savings | Depreciation | Taxable Income | Taxes (21%) | Net Income | Add Depreciation | Operating Cash Flow | |------|---------|--------------|---------------|-------------|------------|------------------|--------------------| | 1 | 20,000 | 12,000 | 8,000 | 1,680 | 6,320 | 12,000 | 18,320 | | 2 | 20,000 | 19,200 | 800 | 168 | 632 | 19,200 | 19,832 | | 3 | 20,000 | 11,520 | 8,480 | 1,781 | 6,699 | 11,520 | 18,219 | | 4 | 20,000 | 6,912 | 13,088 | 2,748 | 10,340 | 6,912 | 17,252 | | 5 | 20,000 | 6,912 | 13,088 | 2,748 | 10,340 | 6,912 | 17,252 | #### **End of Step 2:** We have calculated the **annual after-tax cash flows** for each year. --- ## **Step 3: Terminal Year Adjustments and NPV/IRR Calculation** ### **a) Terminal Cash Flows (Year 5):** - **Salvage Value (Sold for):** $15,000 - **Book Value after 5 years:** = $60,000 - (Depreciation over 5 years) Depreciation over 5 years = $12,000 + $19,200 + $11,520 + $6,912 + $6,912 = $56,544 Book Value = $60,000 - $56,544 = $3,456 - **Tax on Salvage Gain:** Salvage gain = $15,000 - $3,456 = $11,544 Tax = 21% × $11,544 = $2,424 - **Net Salvage Value:** = $15,000 - $2,424 = $12,576 - **Recovery of NWC:** + $3,000 - **Total Terminal Cash Flow in Year 5:** = Operating Cash Flow (Year 5) + Net Salvage Value + NWC Recovery = $17,252 + $12,576 + $3,000 = **$32,828** ### **b) Full Cash Flow Timeline:** | Year | Cash Flow | |------|-------------| | 0 | -$63,000 | | 1 | $18,320 | | 2 | $19,832 | | 3 | $18,219 | | 4 | $17,252 | | 5 | $32,828 | ### **c) NPV and IRR Calculation:** #### **NPV Formula:** \[ NPV = \sum \frac{CF_t}{(1 + r)^t} \] Where \( r = 10\% \) \[ NPV = -63,000 + \frac{18,320}{1.1} + \frac{19,832}{1.1^2} + \frac{18,219}{1.1^3} + \frac{17,252}{1.1^4} + \frac{32,828}{1.1^5} \] **Calculate each term:** - Year 1: 18,320 / 1.1 = $16,655 - Year 2: 19,832 / 1.21 = $16,390 - Year 3: 18,219 / 1.331 = $13,691 - Year 4: 17,252 / 1.4641 = $11,782 - Year 5: 32,828 / 1.61051 = $20,390 Sum: $16,655 + $16,390 + $13,691 + $11,782 + $20,390 = $78,908 \[ NPV = -63,000 + 78,908 = \boxed{ \$15,908 } \] #### **IRR Calculation:** The IRR is the discount rate that makes NPV = 0. Using a financial calculator or Excel (`=IRR(range)`): \[ IRR \approx 18.8\% \] --- ## **Summary and Explanation** ### **Final Answers:** - **NPV = $15,908** - **IRR ≈ 18.8%** **Recommendation:** Since NPV > 0 and IRR > cost of capital (10%), **the company should purchase the earth mover**. --- ### **Importance of Cash Flow Analysis:** Cash flow analysis is crucial because it considers all incremental cash inflows and outflows associated with a project, rather than just accounting profits. This helps the company assess the true economic impact of an investment, make informed decisions, and ensure that only value-creating projects are pursued. It also factors in tax effects, depreciation, working capital changes, and terminal values, giving a complete picture of a project's financial viability. --- **In summary:** **The earth mover should be purchased because it has a positive NPV of $15,908 and an IRR of 18.8%, which is well above the company's cost of capital.**