Let's break this down step-by-step: ## **Step 1: Summarize Key Data** - **Purchase price:** $250,000 (includes delivery/installation) - **Loan:** 4 years, 10% interest, fully amortized - **Maintenance:** $20,000/year (end of each year) - **MACRS (5-year):** 0.20, 0.32, 0.19, 0.12 for Years 1-4 - **Tax rate:** 40% - **Salvage value after 4 years:** $42,500 - **Lease:** $70,000 upfront + $70,000/year for 4 years (5 payments total, includes maintenance) - **Timeframe:** 4 years (Tanner-Woods will not use the loom more than 4 years) ## **Step 2: Compute Annual Loan Payments** - **Loan Amount:** $250,000 - **Interest Rate:** 10% - **Years:** 4 The formula for the annual payment (A) on an amortizing loan: \[ A = \frac{P \cdot r}{1 - (1 + r)^{-n}} \] Where \(P = \$250,000\), \(r = 0.10\), \(n = 4\) \[ A = \frac{250,000 \times 0.10}{1 - (1.10)^{-4}} \] \[ (1.10)^{-4} = 0.6830 \] \[ 1 - 0.6830 = 0.3170 \] \[ A = \frac{25,000}{0.3170} = \$78,857 \] ## **Step 3: Calculate Cash Flows for Purchase Option** ### **Year 0:** - Outflow: $250,000 (purchase) ### **Years 1-4:** - Loan payment: $78,857/year (includes principal & interest) - Maintenance: $20,000/year - Tax shield on depreciation & interest ### **Depreciation via 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 ### **Interest Portion of Loan Payments:** We need to calculate interest for each year (declines as principal is repaid). Let's calculate outstanding principal and interest for each year: #### **Amortization Schedule** - Year 0: $250,000 - Year 1: Interest = $250,000 × 10% = $25,000; Principal repaid = $78,857 - $25,000 = $53,857; Remaining principal: $250,000 - $53,857 = $196,143 - Year 2: Interest = $196,143 × 10% = $19,614; Principal repaid = $78,857 - $19,614 = $59,243; Remaining principal: $196,143 - $59,243 = $136,900 - Year 3: Interest = $136,900 × 10% = $13,690; Principal repaid = $78,857 - $13,690 = $65,167; Remaining principal: $136,900 - $65,167 = $71,733 - Year 4: Interest = $71,733 × 10% = $7,173; Principal repaid = $78,857 - $7,173 = $71,684; Remaining principal: $71,733 - $71,684 = $49 ### **Tax Shields:** - Depreciation tax shield: Depreciation × tax rate - Interest tax shield: Interest × tax rate - Maintenance tax shield: Maintenance × tax rate ### **After-Tax Cash Flows (Years 1-4):** #### *Year 1:* - Loan payment: $78,857 (outflow) - Maintenance: $20,000 (outflow) - Depreciation: $50,000 - Interest: $25,000 - Tax shield = (Depreciation + Interest + Maintenance) × 40% = ($50,000 + $25,000 + $20,000) × 0.4 = $95,000 × 0.4 = $38,000 Net outflow = $78,857 + $20,000 - $38,000 = $60,857 #### *Year 2:* - Loan payment: $78,857 - Maintenance: $20,000 - Depreciation: $80,000 - Interest: $19,614 - Tax shield = ($80,000 + $19,614 + $20,000) × 0.4 = $119,614 × 0.4 = $47,846 Net outflow = $78,857 + $20,000 - $47,846 = $51,011 #### *Year 3:* - Loan payment: $78,857 - Maintenance: $20,000 - Depreciation: $47,500 - Interest: $13,690 - Tax shield = ($47,500 + $13,690 + $20,000) × 0.4 = $81,190 × 0.4 = $32,476 Net outflow = $78,857 + $20,000 - $32,476 = $66,381 #### *Year 4:* - Loan payment: $78,857 - Maintenance: $20,000 - Depreciation: $30,000 - Interest: $7,173 - Tax shield = ($30,000 + $7,173 + $20,000) × 0.4 = $57,173 × 0.4 = $22,869 Net outflow = $78,857 + $20,000 - $22,869 = $75,988 #### *Salvage Value:* - After-tax salvage value = $42,500 - [($42,500 - Book value) × 0.4] - Book value after 4 years = $250,000 - (sum of depreciation) = $250,000 - ($50,000 + $80,000 + $47,500 + $30,000) = $42,500 - Gain = $42,500 - $42,500 = $0 → No tax on gain - After-tax salvage = $42,500 (inflow in Year 4) ## **Step 4: Calculate Cash Flows for Lease Option** - Lease payment: $70,000 at t=0, and $70,000 at end of each year for 4 years - Maintenance included - Tax shield: Lease payment × tax rate ### **Years 0-4:** Each year (including Year 0): Lease payment $70,000 Tax shield: $70,000 × 0.4 = $28,000 Net outflow each year = $70,000 - $28,000 = $42,000 per year (Years 1-4) Year 0: $70,000 (no tax shield in Year 0) ## **Step 5: Find Present Value of Cash Flows (at 12% required return)** ### **Purchase Option:** - Year 0: $250,000 (outflow) - Year 1: $60,857 - Year 2: $51,011 - Year 3: $66,381 - Year 4: $75,988 - $42,500 (salvage) = $33,488 PV = $250,000 + $60,857/(1.12)^1 + $51,011/(1.12)^2 + $66,381/(1.12)^3 + $33,488/(1.12)^4 Let's calculate each term: - Year 1: $60,857 / 1.12 = $54,340 - Year 2: $51,011 / (1.12)^2 = $51,011 / 1.2544 = $40,685 - Year 3: $66,381 / (1.12)^3 = $66,381 / 1.4049 = $47,286 - Year 4: $33,488 / (1.12)^4 = $33,488 / 1.5735 = $21,292 Total PV = $250,000 + $54,340 + $40,685 + $47,286 + $21,292 = **$413,603** ### **Lease Option:** - Year 0: $70,000 (outflow) - Years 1-4: $42,000 per year PV = $70,000 + $42,000/(1.12)^1 + $42,000/(1.12)^2 + $42,000/(1.12)^3 + $42,000/(1.12)^4 - Year 1: $42,000 / 1.12 = $37,500 - Year 2: $42,000 / 1.2544 = $33,486 - Year 3: $42,000 / 1.4049 = $29,900 - Year 4: $42,000 / 1.5735 = $26,705 Total PV = $70,000 + $37,500 + $33,486 + $29,900 + $26,705 = **$197,591** --- ## **Step 6: Decision & Conclusion** - **Present Value of Cost of Purchase:** $413,603 - **Present Value of Cost of Lease:** $197,591 ### **Final Answer:** > **Tanner-Woods should lease the loom, as the present value of the lease option ($197,591) is significantly less than the present value of the purchase option ($413,603).** --- **Let me know if you need the calculations shown in Excel or further clarifications!**