Let's work through your problem step-by-step. --- ## **Given Data** - **Land (original cost):** $260,000 (bought 3 years ago) - **Current market value of land:** $500,000 (can sell now for this) - **Year 0 construction cost (plant):** $600,000 (paid now) - **Construction time:** 2 years (so production starts in year 3) - **Machinery & installation:** $790,000 (paid at start of production, i.e., year 2) - **Life of project:** 4 years (years 3–6) - **Depreciation (straight-line):** Over 4 years for both plant and machinery - **Salvage value at end of project (year 6):** - Plant: $600,000 - Machinery: $150,000 - **Annual sales:** $850,000 (years 3–6) - **Annual variable costs:** $90,000 - **Annual fixed costs:** $25,000 - **Net working capital needed:** $10,000 (recovered at end) - **Discount rate:** 12% - **Tax rate:** 34% - **OPTION 2:** Sell land for $500,000 (now) --- # 1. **What is the proper cash flow amount to use as the initial investment? Show your computation.** ### **Step 1: Opportunity Cost of Land** Even though the land was purchased at $260,000, you could sell it now for $500,000. **The opportunity cost is $500,000, not the historical cost.** ### **Step 2: Initial Cash Outlays** - **Year 0:** - Construction of Plant: $600,000 - Opportunity Cost of Land: $500,000 - Net Working Capital: $10,000 (required at start of production, i.e., at year 2, but some put it at year 0 for simplicity—let’s use year 2 for precision) - Machinery: $790,000 (paid at year 2, at start of production) So, **Year 0 cash outflow:** - Plant construction: $600,000 - Opportunity cost of land: $500,000 - **Total at Year 0:** **$1,100,000** **Year 2 cash outflow:** - Machinery purchase & installation: $790,000 - Net working capital: $10,000 - **Total at Year 2:** **$800,000** --- ### **Summary Table** | Year | Cash Flow Item | Amount | |------|----------------------------|------------| | 0 | Plant Construction | $600,000 | | 0 | Opportunity cost of Land | $500,000 | | 2 | Machinery | $790,000 | | 2 | Net Working Capital | $10,000 | --- # 2. **What are the proper cash flow amounts that will occur over each of the 4 years of production?** Let’s compute the **annual cash flows** for years 3-6 (the 4 years of operation). ## **A. Depreciation Calculation** **Total depreciable base:** - Plant: $600,000 - Machinery: $790,000 - **Total:** $1,390,000 - **Annual depreciation:** $1,390,000 / 4 = **$347,500 per year** --- ## **B. Operating Cash Flows (Years 3–6)** ### **Operating cash flow formula:** \[ \text{OCF} = (\text{Sales} - \text{Variable Costs} - \text{Fixed Costs} - \text{Depreciation}) \times (1 - \text{Tax Rate}) + \text{Depreciation} \] #### **1. Compute EBIT:** - Sales: $850,000 - Variable Costs: $90,000 - Fixed Costs: $25,000 - Depreciation: $347,500 \[ \text{EBIT} = 850,000 - 90,000 - 25,000 - 347,500 = 387,500 \] #### **2. Taxes:** - Tax = $387,500 × 34% = $131,750 #### **3. Net Income:** - Net income = $387,500 - $131,750 = $255,750 #### **4. Add back Depreciation (non-cash):** - Operating Cash Flow = $255,750 + $347,500 = **$603,250 per year** (years 3–6) --- ## **C. Terminal Year Adjustments (Year 6):** 1. **Salvage value:** - Plant: $600,000 - Machinery: $150,000 - **Total salvage: $750,000** 2. **Book value at end of 4 years:** - Both fully depreciated, so book value = $0 3. **Tax on Salvage Value:** - Since book value is $0, the entire amount is taxable as gain. - Tax = $750,000 × 34% = $255,000 - After-tax salvage = $750,000 - $255,000 = **$495,000** 4. **Recovery of Net Working Capital:** +$10,000 --- ### **Summary Table of Cash Flows (Years 3–6):** | Year | OCF | Salvage + NWC | Total Cash Flow | |------|-------------|---------------|-----------------| | 3 | $603,250 | $0 | $603,250 | | 4 | $603,250 | $0 | $603,250 | | 5 | $603,250 | $0 | $603,250 | | 6 | $603,250 | $495,000 + $10,000 = $505,000 | $1,108,250 | --- # 3. **What is the NPV of option 1?** ## **List all cash flows:** | Year | Cash Flow | |------|---------------| | 0 | -1,100,000 | | 2 | -800,000 | | 3 | 603,250 | | 4 | 603,250 | | 5 | 603,250 | | 6 | 1,108,250 | --- ## **NPV Formula:** \[ NPV = \sum_{t=0}^{n} \frac{CF_t}{(1+r)^t} \] Where \( r = 0.12 \) --- ### **Calculate Present Values:** - **Year 0:** -1,100,000 - **Year 2:** -800,000 / (1.12)^2 = -800,000 / 1.2544 = **-638,222** - **Year 3:** 603,250 / (1.12)^3 = 603,250 / 1.404928 = **$429,529** - **Year 4:** 603,250 / (1.12)^4 = 603,250 / 1.573519 = **$383,642** - **Year 5:** 603,250 / (1.12)^5 = 603,250 / 1.762341 = **$342,435** - **Year 6:** 1,108,250 / (1.12)^6 = 1,108,250 / 1.974823 = **$561,526** --- ### **Sum of Present Values:** \[ NPV = -1,100,000 - 638,222 + 429,529 + 383,642 + 342,435 + 561,526 \] \[ NPV = -1,100,000 - 638,222 + 1,717,132 \] \[ NPV = -1,738,222 + 1,717,132 = \boxed{-\$21,090} \] --- # 4. **Which option should the company ultimately choose and why?** - **Option 1:** NPV = **\(-$21,090\)** - **Option 2:** Sell land for $500,000 **now**. (Assume no taxes since basis is $260,000, so gain is $240,000 taxed at 34% = $81,600, so after-tax proceeds = $500,000 - $81,600 = $418,400.) **Option 1** has a negative NPV, meaning it destroys shareholder value compared to the required return. **Option 2** gives an immediate after-tax inflow of $418,400, which is higher than a project with negative NPV. --- ## **Conclusion:** > **The company should choose Option 2 and sell the land.** > > This is because Option 1's NPV is negative, meaning it is not a value-creating investment at the required 12% discount rate, while Option 2 gives an immediate positive after-tax inflow. --- ## **Summary Table** | Option | NPV / Value | |------------------|------------------| | Build facility | -$21,090 | | Sell land (after-tax) | $418,400 | **Choose Option 2: Sell the land.** --- ## **If you need detailed Excel formulas or further breakdowns of calculations, let me know!**