Let's break down the NPV calculation step by step for Lion Industries' project: ## **Given Data** - **Project life:** 6 years - **Annual revenue:** \$4,300,000 - **Variable costs:** 36% of revenue - **Fixed costs:** \$2,400,000 per year - **Initial capital investment:** \$2,390,000 - **Additional inventory investment:** \$294,101 (year 0) - **Increase in accounts receivable:** \$638,862 (year 0) - **Increase in accounts payable:** \$410,697 (year 0) - **Depreciation:** Straight-line to zero over 6 years (\$2,390,000 / 6 = \$398,333.33 per year) - **Salvage value:** \$701,387 at end of year 6 - **Corporate tax rate:** 21% - **Discount rate (required return):** 10.8% ## **Step 1: Initial Outlay (Year 0)** ### Net Working Capital (NWC) Investment: \[ \text{NWC} = (\text{Inventory} + \text{A/R}) - \text{A/P} = (294,101 + 638,862) - 410,697 = 932,963 - 410,697 = \$522,266 \] ### Total Initial Outlay: \[ \text{Total Initial Outlay} = \text{Capital Investment} + \text{NWC Investment} = 2,390,000 + 522,266 = \$2,912,266 \] (This is a cash outflow at Year 0.) --- ## **Step 2: Annual Operating Cash Flows (Years 1-6)** ### **Revenues & Costs** - **Revenue:** \$4,300,000 - **Variable Costs:** 36% of \$4,300,000 = \$1,548,000 - **Fixed Costs:** \$2,400,000 - **Depreciation:** \$398,333.33/year ### **Earnings Before Tax (EBT)** \[ \text{EBT} = \text{Revenue} - \text{Variable Costs} - \text{Fixed Costs} - \text{Depreciation} \] \[ = 4,300,000 - 1,548,000 - 2,400,000 - 398,333.33 \] \[ = 4,300,000 - 4,346,333.33 = -46,333.33 \] ### **Taxes** \[ \text{Taxes} = \text{EBT} \times \text{Tax Rate} = -46,333.33 \times 0.21 = -\$9,729.999 \] (Negative taxes mean a tax shield.) ### **Net Income** \[ \text{Net Income} = \text{EBT} - \text{Taxes} = -46,333.33 - (-9,729.999) = -46,333.33 + 9,729.999 = -\$36,603.33 \] ### **Add Back Depreciation (Non-cash)** \[ \text{Operating Cash Flow} = \text{Net Income} + \text{Depreciation} = -36,603.33 + 398,333.33 = \$361,730 \] --- ## **Step 3: Terminal Year Cash Flows (Year 6)** ### **Salvage Value (After-Tax)** - Book value at end = 0 (depreciated to zero) - Gain on sale = \$701,387 (full amount is taxable) \[ \text{Tax on Salvage} = \text{Salvage Value} \times \text{Tax Rate} = 701,387 \times 0.21 = 147,291.27 \] \[ \text{After-tax Salvage Value} = 701,387 - 147,291.27 = \$554,095.73 \] ### **Return of NWC** - The full NWC (\$522,266) is recovered in Year 6. ### **Total Year 6 Cash Flow** \[ \text{Year 6 CF} = \text{Operating Cash Flow} + \text{After-tax Salvage} + \text{NWC Recovery} \] \[ = 361,730 + 554,095.73 + 522,266 = \$1,438,091.73 \] --- ## **Step 4: Cash Flow Timeline** | Year | Cash Flow | |------|------------------| | 0 | -2,912,266 | | 1-5 | 361,730 each | | 6 | 1,438,091.73 | --- ## **Step 5: NPV Calculation** \[ \text{NPV} = \sum_{t=1}^{6} \frac{\text{CF}_t}{(1 + r)^t} - \text{Initial Outlay} \] Let's compute each term: ### **Years 1-5:** \[ \text{PV (Years 1-5)} = 361,730 \times \left[ \frac{1 - (1 + 0.108)^{-5}}{0.108} \right] \] First, find the annuity factor: \[ (1 + 0.108)^{-5} = (1.108)^{-5} \approx 0.5972 \] \[ \text{Annuity factor} = \frac{1 - 0.5972}{0.108} = \frac{0.4028}{0.108} \approx 3.731 \] \[ \text{PV (1-5)} = 361,730 \times 3.731 = \$1,349,253 \] ### **Year 6:** \[ \text{PV (Year 6)} = \frac{1,438,091.73}{(1.108)^6} \] \[ (1.108)^6 \approx 1.769 \] \[ \text{PV (Year 6)} = \frac{1,438,091.73}{1.769} \approx \$813,168 \] ### **Total PV of Cash Inflows:** \[ \text{Total PV} = 1,349,253 + 813,168 = \$2,162,421 \] ### **NPV:** \[ \text{NPV} = \text{Total PV} - \text{Initial Outlay} = 2,162,421 - 2,912,266 = -\$749,845 \] --- ## **Final Answer** ### **The NPV of the project is:** \[ \boxed{-\$749,845} \] **The project has a negative NPV and should not be undertaken.** --- **If you need an Excel formula or more details on the calculations, let me know!**