Let's break down the problem step by step. **Given:** - Project life: 6 years - Annual revenue: \$4,300,000 - Variable costs: 36% of revenue each year - Fixed costs: \$2,400,000 per year - Initial capital investment: \$2,390,000 - Additional inventory investment: \$294,101 (current asset) - Increase in A/R: \$638,862 (current asset) - Increase in A/P: \$410,697 (current liability) - Depreciation: Straight-line to zero over 6 years - Salvage value: \$701,387 (capital asset sold at end) - Corporate tax rate: 21% - Required return (discount rate): 10.8% --- ## **Step 1: Calculate Initial Outlay** **Net Working Capital (NWC) Investment:** \[ \text{NWC} = \text{Inventory} + \text{A/R} - \text{A/P} = \$294,101 + \$638,862 - \$410,697 = \$522,266 \] **Total Initial Outlay:** \[ \text{Initial Outlay} = \text{Capital Investment} + \text{NWC Investment} = \$2,390,000 + \$522,266 = \boxed{\$2,912,266} \] --- ## **Step 2: Calculate Annual Cash Flows (Years 1–6)** **Revenue:** \$4,300,000 **Variable Costs:** \(0.36 \times \$4,300,000 = \$1,548,000\) **Fixed Costs:** \$2,400,000 **Total Annual Operating Costs:** \[ \text{Total costs} = \$1,548,000 + \$2,400,000 = \$3,948,000 \] **Annual Depreciation:** \[ \text{Depreciation} = \frac{\$2,390,000}{6} = \$398,333.33 \] **EBIT (Earnings Before Interest and Taxes):** \[ \text{EBIT} = \text{Revenue} - \text{Total Costs} - \text{Depreciation} \] \[ \text{EBIT} = \$4,300,000 - \$3,948,000 - \$398,333.33 = \$4,300,000 - \$4,346,333.33 = -\$46,333.33 \] **Tax Calculation:** If EBIT is negative, tax shield applies (tax savings). \[ \text{Tax} = \text{EBIT} \times \text{Tax Rate} = (-\$46,333.33) \times 0.21 = -\$9,729.99 \] **Net Income:** \[ \text{Net Income} = \text{EBIT} - \text{Tax} = -\$46,333.33 - (-\$9,729.99) = -\$36,603.33 \] **Add back Depreciation (non-cash):** \[ \text{Operating Cash Flow (OCF)} = \text{Net Income} + \text{Depreciation} = -\$36,603.33 + \$398,333.33 = \boxed{\$361,730} \] --- ## **Step 3: Final Year (Year 6) Cash Flows** **a) Salvage Value (After-tax):** \[ \text{Book value at year 6} = 0 \] \[ \text{Tax on Salvage Value} = (\text{Salvage Value} - \text{Book Value}) \times \text{Tax Rate} \] \[ = (\$701,387 - 0) \times 0.21 = \$147,291.27 \] \[ \text{After-tax Salvage Value} = \$701,387 - \$147,291.27 = \boxed{\$554,095.73} \] **b) Return of Net Working Capital:** At project end, NWC is recovered: \(+\$522,266\) **Total Terminal-Year (Year 6) Cash Flow:** \[ \text{Total Year 6 Cash Flow} = \text{OCF} + \text{After-tax Salvage Value} + \text{NWC Recovery} \] \[ = \$361,730 + \$554,095.73 + \$522,266 = \boxed{\$1,438,091.73} \] --- ## **Step 4: NPV Calculation** - **Years 1–5 cash flow:** \$361,730 each year - **Year 6 cash flow:** \$1,438,091.73 - **Year 0 (initial outlay):** \(-\$2,912,266\) - **Discount rate:** 10.8% ### **Find Present Value of Each Cash Flow:** #### **Years 1–5:** \[ \text{PV}_{1-5} = \$361,730 \times \left[ \frac{1 - (1 + r)^{-5}}{r} \right] \] Where \( r = 0.108 \) \[ (1 + r)^{-5} = (1.108)^{-5} \approx 0.5952 \] \[ \frac{1 - 0.5952}{0.108} = \frac{0.4048}{0.108} \approx 3.75 \] \[ \text{PV}_{1-5} = \$361,730 \times 3.75 = \$1,356,487.50 \] Calculating more precisely: \[ \text{PV}_{1-5} = \$361,730 \times \left[ \frac{1 - (1.108)^{-5}}{0.108} \right] \] \[ (1.108)^5 = 1.66913 \] \[ (1.108)^{-5} = 1/1.66913 = 0.5989 \] \[ 1 - 0.5989 = 0.4011 \] \[ 0.4011 / 0.108 = 3.715 \] \[ \text{PV}_{1-5} = \$361,730 \times 3.715 = \$1,344,347 \] #### **Year 6:** \[ \text{PV}_6 = \frac{\$1,438,091.73}{(1.108)^6} \] \[ (1.108)^6 = 1.85265 \] \[ \text{PV}_6 = \frac{\$1,438,091.73}{1.85265} = \$776,443 \] #### **Total PV of all cash inflows:** \[ \text{Total PV} = \$1,344,347 + \$776,443 = \$2,120,790 \] --- ## **Step 5: NPV Calculation** \[ \text{NPV} = \text{Total PV of inflows} - \text{Initial Outlay} \] \[ \text{NPV} = \$2,120,790 - \$2,912,266 = \boxed{-\$791,476} \] --- ## **Final Answer** \[ \boxed{ \text{NPV} = -\$791,476 } \] **Interpretation:** Since the NPV is negative, Lion Industries should **not** undertake this expansion project.