Let's solve the problem step by step: --- ### **Step 1: Calculate Initial Outlay** - **Cost of the course:** $138,000 (capital expenditure) - **Net working capital:** $3,000 (outflow at t=0, recovered at t=5) - **Total Initial Outlay:** $138,000 + $3,000 = **$141,000** --- ### **Step 2: Calculate Annual Incremental Cash Flows** #### **A. Annual Revenues** - Golfing fees: $72,000 - Additional revenue from existing facilities: $14,000 - **Total Revenue:** $72,000 + $14,000 = **$86,000** #### **B. Annual Costs** - Variable cost: $24,000 - Fixed cost: $11,600 - **Total Costs:** $24,000 + $11,600 = **$35,600** #### **C. Depreciation** - Straight-line: $138,000 / 5 = **$27,600 per year** #### **D. EBIT (Earnings Before Interest and Taxes)** \[ \text{EBIT} = \text{Total Revenue} - \text{Total Costs} - \text{Depreciation} \] \[ \text{EBIT} = 86,000 - 35,600 - 27,600 = 22,800 \] #### **E. Taxes** - Tax rate = 34% - Taxes = $22,800 \times 0.34 = **$7,752** #### **F. Net Income** - Net Income = EBIT - Taxes = $22,800 - $7,752 = **$15,048** #### **G. Add Back Depreciation (Non-cash Expense)** - Annual Operating Cash Flow = Net Income + Depreciation - $15,048 + $27,600 = **$42,648** --- ### **Step 3: Terminal Year Cash Flow (Year 5)** - **Add back working capital:** $3,000 (recovered) - **No salvage value** So, **Year 5 Cash Flow** = $42,648 (operating) + $3,000 (working capital) = **$45,648** --- ### **Step 4: Calculate the NPV** - Initial outlay (t=0): **-$141,000** - Year 1-4 cash flows: **$42,648** per year - Year 5 cash flow: **$45,648** (includes working capital recovery) - Discount rate: **12%** #### **A. Present Value of Operating Cash Flows (Years 1-4)** PV (Years 1-4) = $42,648 × [1 - (1+0.12)^-4] / 0.12 First, calculate the 4-year annuity factor at 12%: \[ \text{Annuity Factor} = \frac{1 - (1+0.12)^{-4}}{0.12} \] \[ (1+0.12)^{-4} = (1.12)^{-4} \approx 0.6355 \] \[ \text{Annuity Factor} = \frac{1 - 0.6355}{0.12} = \frac{0.3645}{0.12} = 3.0375 \] \[ \text{PV (Years 1-4)} = 42,648 \times 3.0375 = \$129,505 \] #### **B. Present Value of Year 5 Cash Flow** \[ \text{PV (Year 5)} = \frac{45,648}{(1.12)^5} \] \[ (1.12)^5 = 1.7623 \] \[ \text{PV (Year 5)} = \frac{45,648}{1.7623} = \$25,902 \] #### **C. Add Together and Subtract Initial Outlay** \[ \text{NPV} = PV(\text{Years 1-4}) + PV(\text{Year 5}) - \text{Initial Outlay} \] \[ \text{NPV} = 129,505 + 25,902 - 141,000 = \$14,407 \] --- ## **Final Summary** - **Initial Outlay:** $141,000 - **Annual Operating Cash Flow (after-tax):** $42,648 (Years 1-4), $45,648 (Year 5) - **Discount Rate:** 12% - **NPV:** **$14,407** ### **Interpretation:** Since the NPV is **positive ($14,407)**, **Outdoor Sports should proceed with the investment** in the miniature golf course, as it is expected to increase the firm's value.

Let's carefully analyze and calculate the Net Present Value (NPV) of the proposed miniature golf course project step by step. --- ### **1. Initial Investment and Working Capital** - **Cost of the golf course:** $138,000 - **Net working capital (NWC):** $3,000 (recovered at end) - **Total initial outlay:** $138,000 + $3,000 = **$141,000** --- ### **2. Estimating Annual Operating Cash Flows** **a. Additional Revenues and Costs** - **Incremental golf fees:** $72,000/year - **Additional revenue from existing facilities:** $14,000/year - **Total incremental revenue:** $86,000/year **b. Variable and Fixed Costs** - **Variable costs:** $24,000/year - **Fixed costs:** $11,600/year - **Total operating costs:** $24,000 + $11,600 = **$35,600/year** **c. Earnings Before Depreciation and Taxes (EBITDA)** \[ \text{EBITDA} = \text{Total Revenue} - \text{Total Operating Costs} = 86,000 - 35,600 = \$50,400 \] **d. Depreciation** - Straight-line over 5 years: \[ \frac{\$138,000}{5} = \$27,600 \text{ per year} \] **e. Earnings Before Taxes (EBIT)** \[ \text{EBIT} = \text{EBITDA} - \text{Depreciation} = 50,400 - 27,600 = \$22,800 \] **f. Taxes (34%)** \[ \text{Taxes} = 22,800 \times 0.34 = \$7,752 \] **g. Net Income** \[ \text{Net Income} = 22,800 - 7,752 = \$15,048 \] **h. Operating Cash Flow (OCF)** Add back depreciation (a non-cash expense): \[ \text{OCF} = \text{Net Income} + \text{Depreciation} = 15,048 + 27,600 = \boxed{\$42,648} \] *Note:* This cash flow is after taxes and includes the effects of depreciation. --- ### **3. Year 5 Cash Flow (Including Working Capital Recovery)** At the end of Year 5, recover the net working capital: \[ \text{Total Year 5 cash flow} = \text{OCF} + \text{NWC recovered} = 42,648 + 3,000 = \boxed{\$45,648} \] --- ### **4. Discounting Cash Flows to Present Value** **a. Present value of Years 1-4 cash flows** Using the annuity formula with a 12% discount rate: \[ PV_{\text{Years 1-4}} = \text{OCF} \times \frac{1 - (1 + r)^{-4}}{r} \] Calculate the annuity factor: \[ (1 + 0.12)^{-4} = 1.12^{-4} \approx 0.6355 \] \[ \text{Annuity factor} = \frac{1 - 0.6355}{0.12} = \frac{0.3645}{0.12} \approx 3.0375 \] \[ PV_{\text{Years 1-4}} = 42,648 \times 3.0375 \approx \$129,505 \] **b. Present value of Year 5 cash flow** \[ PV_{\text{Year 5}} = \frac{\$45,648}{(1.12)^5} \] Calculate denominator: \[ (1.12)^5 \approx 1.7623 \] \[ PV_{\text{Year 5}} \approx \frac{45,648}{1.7623} \approx \$25,902 \] --- ### **5. Calculate Total NPV** \[ NPV = PV_{\text{Years 1-4}} + PV_{\text{Year 5}} - \text{Initial Outlay} \] \[ NPV = 129,505 + 25,902 - 141,000 = \boxed{\$14,407} \] --- ### **Final Summary:** - **Initial investment:** \$141,000 - **Annual operating cash flows (Years 1-4):** \$42,648 - **Year 5 cash flow (including working capital recovery):** \$45,648 - **Discount rate:** 12% - **NPV:** **\$14,407** **Conclusion:** Since the NPV is positive ($14,407), adding the miniature golf course is expected to increase the firm's value. Therefore, **Outdoor Sports should proceed with the project**.