**Let's break down the problem step by step, following a standard Chegg-style format:** --- ### Given Data - **Initial Investment in Mini Golf Course:** $138,000 - **Depreciation:** Straight-line over 5 years, zero salvage value - **Annual Golfing Fees Revenue:** $72,000 - **Variable Costs:** $24,000 per year - **Fixed Costs:** $11,600 per year - **Additional Revenue from Existing Facilities:** $14,000 per year - **Net Working Capital Required (NWC):** $3,000 (fully recovered at end) - **Project Life:** 5 years - **Discount Rate:** 12% - **Tax Rate:** 34% --- ## Step 1: Calculate Annual Depreciation \[ \text{Annual Depreciation} = \frac{\text{Initial Cost}}{\text{Life}} = \frac{138,000}{5} = \$27,600 \] --- ## Step 2: Calculate Incremental Annual Revenues and Costs **Total Revenue per year:** \[ \text{Golfing Fees} + \text{Additional Revenue} = 72,000 + 14,000 = \$86,000 \] **Total Costs per year:** \[ \text{Variable Cost} + \text{Fixed Cost} = 24,000 + 11,600 = \$35,600 \] --- ## Step 3: Calculate Annual Operating Cash Flows ### 3.1. **Earnings Before Depreciation and Taxes (EBDT)** \[ \text{EBDT} = \text{Total Revenue} - \text{Total Costs} \] \[ = 86,000 - 35,600 = \$50,400 \] ### 3.2. **Earnings Before Taxes (EBT)** \[ \text{EBT} = \text{EBDT} - \text{Depreciation} = 50,400 - 27,600 = \$22,800 \] ### 3.3. **Taxes** \[ \text{Taxes} = \text{EBT} \times \text{Tax Rate} = 22,800 \times 0.34 = \$7,752 \] ### 3.4. **Net Income** \[ \text{Net Income} = \text{EBT} - \text{Taxes} = 22,800 - 7,752 = \$15,048 \] ### 3.5. **Operating Cash Flow (OCF)** \[ \text{OCF} = \text{Net Income} + \text{Depreciation} \] \[ = 15,048 + 27,600 = \$42,648 \] --- ## Step 4: Cash Flow Timeline - **Year 0:** - Initial Investment: \(-\$138,000\) - Net Working Capital Outflow: \(-\$3,000\) - **Total Year 0 Cash Outflow:** \(-\$141,000\) - **Years 1-5:** - Annual OCF: \(+\$42,648\) - **Year 5:** - Recovery of NWC: \(+\$3,000\) - **Total Year 5 Cash Inflow:** \(42,648 + 3,000 = \$45,648\) --- ## Step 5: Calculate NPV \[ \text{NPV} = -141,000 + \sum_{t=1}^{4} \frac{42,648}{(1.12)^t} + \frac{45,648}{(1.12)^5} \] ### Calculate each year's PV: #### Years 1-4: \[ \text{PV of OCF (Years 1-4)} = 42,648 \times \left[ \frac{1 - (1 + r)^{-n}}{r} \right] \] Where \( r = 0.12, n = 4 \): \[ \left[ \frac{1 - (1 + 0.12)^{-4}}{0.12} \right] = \left[ \frac{1 - (1.12)^{-4}}{0.12} \right] \] \[ (1.12)^{-4} = 0.6355 \] \[ 1 - 0.6355 = 0.3645 \] \[ 0.3645 / 0.12 = 3.0375 \] \[ \text{PV (Years 1-4)} = 42,648 \times 3.0375 = \$129,540 \] #### Year 5: \[ \text{PV (Year 5)} = \frac{45,648}{(1.12)^5} \] \[ (1.12)^5 = 1.7623 \] \[ 45,648 / 1.7623 = \$25,918 \] --- ### Total PV of Cash Inflows \[ \text{Total PV} = 129,540 + 25,918 = \$155,458 \] --- ## Step 6: Calculate NPV \[ \text{NPV} = \text{Total PV} - \text{Initial Outflow} \] \[ \text{NPV} = 155,458 - 141,000 = \$14,458 \] --- ## **Final Summary** - **Net Present Value (NPV) of the project at 12% discount rate is \$14,458.** - Since the NPV is positive, **the project is financially acceptable and should be undertaken.** --- ### **Summary Table** | Year | Cash Flow | PV Factor (12%) | Present Value | |--------|----------------|-----------------|-----------------| | 0 | -141,000 | 1.0000 | -141,000 | | 1-4 | 42,648 | 3.0375* | 129,540 | | 5 | 45,648 | 0.5674 | 25,918 | | | | | **\$14,458** | (*PV factor for annuity for 4 years at 12%.) --- ### **Conclusion** - The NPV of the proposed miniature golf course is **\$14,458** at a 12% discount rate. - The project is **financially viable** and should be accepted. --- **If you need the detailed stepwise calculation or have doubt in any step, please let me know!**

**Let's break down the problem step by step, following a standard Chegg-style format:** --- ### Given Data - **Initial Investment in Mini Golf Course:** \$138,000 - **Depreciation:** Straight-line over 5 years, zero salvage value - **Annual Golfing Fees Revenue:** \$72,000 - **Variable Costs:** \$24,000 per year - **Fixed Costs:** \$11,600 per year - **Additional Revenue from Existing Facilities:** \$14,000 per year - **Net Working Capital (NWC):** \$3,000 (recovered at end) - **Project Life:** 5 years - **Discount Rate:** 12% - **Tax Rate:** 34% --- ### Step 1: Calculate Annual Depreciation \[ \text{Depreciation} = \frac{\text{Initial Cost}}{\text{Life}} = \frac{\$138,000}{5} = \$27,600 \] --- ### Step 2: Calculate Incremental Revenues and Operating Expenses **Total Revenue per year:** \[ \$72,000 + \$14,000 = \$86,000 \] **Total Operating Costs per year:** \[ \$24,000 + \$11,600 = \$35,600 \] --- ### Step 3: Compute Earnings Before Depreciation and Taxes (EBDT) \[ \text{EBDT} = \text{Total Revenue} - \text{Operating Costs} = \$86,000 - \$35,600 = \$50,400 \] ### Step 4: Calculate Earnings Before Taxes (EBT) \[ \text{EBT} = \text{EBDT} - \text{Depreciation} = \$50,400 - \$27,600 = \$22,800 \] ### Step 5: Calculate Taxes \[ \text{Taxes} = \text{EBT} \times \text{Tax Rate} = \$22,800 \times 0.34 = \$7,752 \] ### Step 6: Calculate Net Income \[ \text{Net Income} = \text{EBT} - \text{Taxes} = \$22,800 - \$7,752 = \$15,048 \] ### Step 7: Compute Operating Cash Flow (OCF) \[ \text{OCF} = \text{Net Income} + \text{Depreciation} = \$15,048 + \$27,600 = \$42,648 \] --- ### Step 8: Cash Flows Over the Project Duration - **Year 0:** - Initial Investment: \(-\$138,000\) - NWC Outflow: \(-\$3,000\) - **Total Year 0 Outflow:** \(-\$141,000\) - **Years 1-5:** - Annual Operating Cash Flow: \$42,648 - **Year 5 (end):** - Recovery of NWC: \$3,000 - Total cash inflow in Year 5: \[ \$42,648 + \$3,000 = \$45,648 \] --- ### Step 9: Calculate Present Value of Cash Flows Using the discount rate of 12%, we find the present value (PV) of cash flows: **PV of Years 1-4:** \[ PV_{1-4} = \$42,648 \times \left( \frac{1 - (1 + r)^{-4}}{r} \right) \] Calculate the annuity factor: \[ (1 + 0.12)^4 = 1.5748 \] \[ (1 + 0.12)^{-4} = \frac{1}{1.5748} \approx 0.6355 \] \[ \text{Annuity factor} = \frac{1 - 0.6355}{0.12} = \frac{0.3645}{0.12} \approx 3.0375 \] PV of Years 1-4: \[ \$42,648 \times 3.0375 \approx \$129,300 \] **PV of Year 5 cash flow:** \[ PV_{Year 5} = \frac{\$45,648}{(1 + 0.12)^5} \] Calculate: \[ (1 + 0.12)^5 = 1.7623 \] \[ PV_{Year 5} = \frac{\$45,648}{1.7623} \approx \$25,927 \] --- ### Step 10: Total Present Value and NPV \[ \text{Total PV} = \$129,300 + \$25,927 = \$155,227 \] \[ \text{NPV} = \text{Total PV} - \text{Initial Investment} = \$155,227 - \$141,000 = \boxed{\$14,227} \] --- ### **Final Summary** - **The net present value (NPV) of the project at a 12% discount rate is approximately \$14,227.** - **Since NPV is positive, the project is financially viable and should be accepted.** --- **If you need further clarification or detailed calculations, feel free to ask!**