Let's break down the problem into **step-by-step calculations** to determine whether the loom should be **leased or purchased**. --- ## **Step 1: Collect Data** ### **Purchase Option** - **Invoice price (Cost of loom)**: $250,000 - **Loan interest rate**: 10% (amortized over 4 years) - **Maintenance cost**: $20,000 per year - **Tax rate**: 40% - **Useful life (for depreciation)**: 5 years (MACRS rates provided) - **Salvage value after 4 years**: $42,500 - **MACRS depreciation rates for Years 1-4**: 0.20, 0.32, 0.19, 0.12 - **Amortization period**: 4 years ### **Lease Option** - **Lease payment**: $70,000 per year (Years 1-4) + $70,000 at t = 0 (installation & delivery) - **Maintenance included** - **No ownership at end (no salvage value)** ### **Discount Rate (for NPV)**: 12% --- ## **Step 2: Calculate Cash Flows for PURCHASE Option** ### **A. Depreciation (MACRS)** - **Year 1**: $250,000 × 0.20 = $50,000 - **Year 2**: $250,000 × 0.32 = $80,000 - **Year 3**: $250,000 × 0.19 = $47,500 - **Year 4**: $250,000 × 0.12 = $30,000 ### **B. Loan Payment Calculation** Loan amount: $250,000; Rate: 10%; Period: 4 years Use the formula for an amortizing loan: \[ \text{Annual Payment} = \frac{P \cdot r}{1 - (1 + r)^{-n}} \] Where \(P = 250,000\), \(r = 0.10\), \(n = 4\). \[ \text{Annual Payment} = \frac{250,000 \cdot 0.10}{1 - (1 + 0.10)^{-4}} = \frac{25,000}{1 - (1.1)^{-4}} = \frac{25,000}{1 - 0.6830} = \frac{25,000}{0.3170} \approx \$78,862 \] ### **C. After-tax Cash Flows Calculation** #### **Yearly cash outflows:** - **Loan Payment**: $78,862 - **Maintenance**: $20,000 - **Tax Shield from Depreciation**: Depreciation × 40% - **Tax Shield from Interest**: Only interest portion of loan is tax-deductible. Let's break down each year: #### **Step 1: Loan Amortization Schedule** Let’s calculate interest and principal for each year. | Year | Beg. Balance | Payment | Interest (10%) | Principal Paid | Ending Balance | |------|--------------|---------|----------------|---------------|---------------| | 1 | 250,000 | 78,862 | 25,000 | 53,862 | 196,138 | | 2 | 196,138 | 78,862 | 19,614 | 59,248 | 136,890 | | 3 | 136,890 | 78,862 | 13,689 | 65,173 | 71,717 | | 4 | 71,717 | 78,862 | 7,172 | 71,690 | 27 | #### **Step 2: Tax Shield per Year** - **Interest Tax Shield** = Interest × 40% - **Depreciation Tax Shield** = Depreciation × 40% - **Maintenance Tax Shield** = Maintenance × 40% = $8,000 per year #### **Step 3: Net Cash Outflow per Year** \[ \text{Net Outflow} = (\text{Loan Payment} + \text{Maintenance}) - (\text{Interest Tax Shield} + \text{Depreciation Tax Shield} + \text{Maintenance Tax Shield}) \] #### **Year 1** - Loan Payment: $78,862 - Maintenance: $20,000 - Interest: $25,000 - Depreciation: $50,000 - Interest Tax Shield: $10,000 - Depreciation Tax Shield: $20,000 - Maintenance Tax Shield: $8,000 \[ \text{Net Outflow} = (78,862 + 20,000) - (10,000 + 20,000 + 8,000) = 98,862 - 38,000 = \$60,862 \] #### **Year 2** - Interest: $19,614 - Depreciation: $80,000 - Interest Tax Shield: $7,846 - Depreciation Tax Shield: $32,000 \[ \text{Net Outflow} = 98,862 - (7,846 + 32,000 + 8,000) = 98,862 - 47,846 = \$51,016 \] #### **Year 3** - Interest: $13,689 - Depreciation: $47,500 - Interest Tax Shield: $5,476 - Depreciation Tax Shield: $19,000 \[ \text{Net Outflow} = 98,862 - (5,476 + 19,000 + 8,000) = 98,862 - 32,476 = \$66,386 \] #### **Year 4** - Interest: $7,172 - Depreciation: $30,000 - Interest Tax Shield: $2,869 - Depreciation Tax Shield: $12,000 \[ \text{Net Outflow} = 98,862 - (2,869 + 12,000 + 8,000) = 98,862 - 22,869 = \$75,993 \] #### **Year 4: Add After-tax Salvage Value** - Salvage value: $42,500 - Book value after 4 years: $250,000 - (50,000+80,000+47,500+30,000) = $42,500 - Gain on sale = Salvage - Book = 0 - Thus, no tax on salvage. So, in **Year 4**, reduce net outflow by $42,500. \[ \text{Year 4 Net Outflow} = 75,993 - 42,500 = \$33,493 \] --- ### **Step 3: Calculate NPV (PURCHASE Option)** Discount all flows at 12%: \[ \text{NPV} = \sum_{t=1}^{4} \frac{\text{Net Outflow}_t}{(1.12)^t} \] - Year 1: $60,862 / 1.12 = \$54,339$ - Year 2: $51,016 / (1.12)^2 = \$40,676$ - Year 3: $66,386 / (1.12)^3 = \$47,268$ - Year 4: $33,493 / (1.12)^4 = \$21,281$ \[ \text{Total NPV (Purchase Option)} = 54,339 + 40,676 + 47,268 + 21,281 = \$163,564 \] --- ## **Step 4: Calculate Cash Flows for LEASE Option** - Lease payment: $70,000 per year (t=0 to 4, i.e., 5 payments) - Tax shield on lease: $70,000 × 40% = $28,000 per year - Net lease outflow: $70,000 - $28,000 = $42,000 per year ### **NPV of Lease Payments** \[ \text{NPV} = \frac{42,000}{1.12^0} + \frac{42,000}{1.12^1} + \frac{42,000}{1.12^2} + \frac{42,000}{1.12^3} + \frac{42,000}{1.12^4} \] Calculate each term: - Year 0: $42,000 - Year 1: $42,000/1.12 = $37,500 - Year 2: $42,000/(1.12)^2 = $33,482 - Year 3: $42,000/(1.12)^3 = $29,902 - Year 4: $42,000/(1.12)^4 = $26,697 \[ \text{Total NPV (Lease Option)} = 42,000 + 37,500 + 33,482 + 29,902 + 26,697 = \$169,581 \] --- ## **Step 5: Decision** - **Purchase Option NPV (cost): $163,564** - **Lease Option NPV (cost): $169,581** **Lower NPV (cost) is better.** --- ## **Final Answer** **Tanner-Woods should PURCHASE the loom, as the NPV of after-tax cash outflows is lower ($163,564) compared to leasing ($169,581).** --- ### **Summary Table** | Option | NPV of After-Tax Outflows | |----------|--------------------------| | Purchase | $163,564 | | Lease | $169,581 | **→ Recommend Purchasing the loom.** --- **Let me know if you want to see the full amortization table or breakdowns!**