Let's break down your problem step by step. --- ### **Given Data Recap** - **Land**: bought for **$260,000** three years ago, can now be sold for **$500,000** - **Facility Cost**: $600,000 (upfront, construction takes 2 yrs) - **Machinery/Installation**: $790,000 (paid at start of production, i.e., end of Year 2) - **Depreciation**: straight-line over 4 years (plant + machinery), salvage values: plant $600,000; machinery $150,000 - **Sales (per year)**: $850,000 - **Variable cost**: $90,000 per year - **Fixed cost**: $25,000 per year - **Net Working Capital**: $10,000 (invested at start of production, recovered at end) - **Discount rate**: 12% - **Corporate tax rate**: 34% - **Option 2**: Sell land now for $500,000 (immediate cash inflow, but pay capital gains tax) --- ## **1. Initial Investment for Option 1** #### **Step A: Opportunity Cost of Land** - If land is used, the company forgoes selling it for $500,000 and must pay capital gains tax on the gain. - **Capital Gain** = Sale price - Original cost = $500,000 - $260,000 = **$240,000** - **Tax on gain** = $240,000 × 34% = **$81,600** - **Net proceeds if sold** = $500,000 - $81,600 = **$418,400** **Therefore, the opportunity cost (relevant cash outflow) is $418,400.** #### **Step B: Facility Construction Cost** - $600,000 paid upfront (Year 0), but construction takes 2 years. For NPV, treat as paid at Year 0. #### **Step C: Machinery/Installation** - $790,000 paid at start of production (end of Year 2). #### **Step D: Net Working Capital** - $10,000 invested at start of production (end of Year 2), recovered at end of project (Year 6). --- #### **Summary Table: Timing of Cash Flows** | Year | Cash Flow Item | Outflow | |------|-------------------------------|--------------| | 0 | Opportunity cost of land | $418,400 | | 0 | Facility construction | $600,000 | | 2 | Machinery/installation | $790,000 | | 2 | Net working capital | $10,000 | **Total initial investment at Year 0 is $418,400 (opportunity cost) + $600,000 (facility) = $1,018,400.** However, the $790,000 for machinery and the $10,000 for working capital are spent at Year 2, not Year 0, so they must be discounted to Year 0 for NPV. But when asked for "initial investment," typically this refers to the **Year 0 outflow**. ### **Answer to Q1:** > **The proper cash flow amount to use as the initial investment is:** > > - **Opportunity cost of land:** $418,400 > - **Facility construction:** $600,000 > **Total initial investment at Year 0:** $1,018,400 --- ## **2. Annual Operating Cash Flows (Years 3-6)** #### **A. Depreciation Calculation** - **Total depreciable base:** $600,000 (facility) + $790,000 (machinery) = $1,390,000 - **Salvage values:** $600,000 (facility at end), $150,000 (machinery at end) - **Annual depreciation:** Straight-line over 4 years, no salvage value considered in depreciation (for U.S. GAAP/tax, salvage value is not subtracted until asset is sold). - **Depreciation per year:** $1,390,000 / 4 = $347,500 per year #### **B. Operating Cash Flows (per year, Years 3–6)** - **Sales:** $850,000 - **Variable costs:** $90,000 - **Fixed costs:** $25,000 - **Depreciation:** $347,500 ##### **EBIT Calculation:** \[ EBIT = Sales - Variable Costs - Fixed Costs - Depreciation \\ = 850,000 - 90,000 - 25,000 - 347,500 = 387,500 \] ##### **Tax:** \[ Tax = EBIT \times 34\% = 387,500 \times 0.34 = 131,750 \] ##### **Net Income:** \[ Net Income = EBIT - Tax = 387,500 - 131,750 = 255,750 \] ##### **Add back Depreciation (non-cash):** \[ Operating\ Cash\ Flow = Net\ Income + Depreciation = 255,750 + 347,500 = 603,250 \] ##### **Summary:** - **Annual after-tax cash flow (Years 3–6):** $603,250 --- #### **C. Terminal Cash Flow (Year 6):** - **Salvage value of facility:** $600,000 - **Salvage value of machinery:** $150,000 - **Net working capital recovery:** $10,000 ##### **Tax on Salvage Value:** Book value at end of Year 6 for both assets is $0 (fully depreciated). - **Total salvage value received:** $750,000 - **Tax on gain:** $750,000 × 34% = $255,000 - **Net cash from salvage:** $750,000 - $255,000 = $495,000 ##### **Total terminal cash flow (Year 6):** \[ 495,000\ (salvage\ after\ tax) + 10,000\ (NWC\ recovery) = 505,000 \] --- #### **Summary Table of Cash Flows** | Year | Cash Flow Item | Amount | |------|-------------------------------|-----------------| | 0 | Land opp. cost + facility | -1,018,400 | | 2 | Machinery/installation | -790,000 | | 2 | Net working capital | -10,000 | | 3-6 | Operating CF | +603,250 (each) | | 6 | Terminal (salvage + NWC) | +505,000 | --- ## **3. Net Present Value (NPV) of Option 1** Let's discount all cash flows to Year 0 using the 12% discount rate. ### **Step 1:** Discount the Year 2 outflows to Year 0 \[ PV_{Y2\ Outflows} = (790,000 + 10,000) / (1.12)^2 = 800,000 / 1.2544 = 638,212 \] ### **Step 2:** Discount the annual operating inflows (Years 3-6) For Years 3–6, each inflow is $603,250. \[ PV = \sum_{t=3}^6 \frac{603,250}{(1.12)^t} \] Calculate each term: - Year 3: \( 603,250 / 1.404928 = 429,567 \) - Year 4: \( 603,250 / 1.573519 = 383,635 \) - Year 5: \( 603,250 / 1.762341 = 342,349 \) - Year 6: \( 603,250 / 1.974821 = 305,663 \) Sum: \( 429,567 + 383,635 + 342,349 + 305,663 = 1,461,214 \) ### **Step 3:** Discount the terminal cash flow (Year 6) \[ PV_{terminal} = 505,000 / 1.974821 = 255,830 \] ### **Step 4:** Add all together \[ NPV = -1,018,400\ (Y0) - 638,212\ (Y2\ outflows) + 1,461,214\ (Y3-6\ inflows) + 255,830\ (terminal) \] \[ NPV = -1,018,400 - 638,212 + 1,461,214 + 255,830 \] \[ NPV = -1,656,612 + 1,717,044 = 60,432 \] --- ## **4. Which Option Should the Company Choose?** **Option 1:** NPV ≈ $60,432 (positive, so value-adding) **Option 2:** Sell land now for $500,000, pay $81,600 tax, net $418,400. This is a one-time inflow; if you want to compare as NPV, it's just $418,400 at Year 0. **Therefore, Option 1 creates more value for the company by $60,432 in NPV terms, in addition to the opportunity cost already considered.** --- ## **Final Answers (Summary Table)** ### **1. Initial Investment (Year 0):** > **$1,018,400** (opportunity cost of land plus facility construction cost) ### **2. Cash Flows During Each Year of Production (Years 3–6):** - **Annual after-tax operating cash flow:** $603,250 (Years 3–6) - **Terminal cash flow at Year 6:** $505,000 (salvage after tax + NWC recovery) ### **3. NPV of Option 1:** > **NPV = $60,432** ### **4. Which Option Should the Company Choose?** > **The company should build the facility (Option 1) because it yields a higher net present value ($60,432) compared to selling the land now for $418,400.** --- **Let me know if you want a breakdown of Option 2's NPV or a spreadsheet-ready version!**