Let's analyze and calculate each part step by step: --- ## Given Data- **Unit price ofware:** \$40 - **Unit cost \$20 **Sales forecast:** | Year | Unit Sales | |--------|--------------| | 1 | 37,000 | | 2 | 45,000 | | 3 | 14,000 | | 4 | 8,000 | - **Net working capital requirement:** 20% of sales - **Initial investment:** 20 × \$37,000 × \$40 = \$296,000 - **Additional investment after 3 years:** \$215,000 - **Depreciation period:** 3 years (straight-line) - **Tax rate:** 30% - **Discount rate:** 15% --- ## Part a: Net Present Value (NPV) ### Step 1: Calculate annual cash flows - **Sales revenue** = units sold × \$40 - **Variable costs** = units sold × \$20 - **Annual profit before tax** = (Sales revenue - Variable costs - Depreciation) - **Depreciation** = (Initial equipment cost) / 3 = \$215,000 / 3 ≈ \$71,667 per year - **Tax** = 30% of profit before tax - **Net profit after tax** = profit before tax × (1 - .30) ### Step 2: Calculate cash flows for years 1-3 | Year | Units Sold | Sales Revenue | Variable Costs | Depreciation | Profit before tax | Tax | Net Profit | Cash Flow | |--------|--------------|-----------------|------------------|--------------|-------------------|-----|------------|------------| | 1 | 37,000 | \$1,480,000 | \$740,000 | \$71,667 | (1,480,000 - 740,000 - 71,667) | 30% | Profit after tax | Add back depreciation | | 2 | 45,000 | \$1,800,000 | \$900,000 | \$71,667 | (1,800,000 - 900,000 - 71,667) | 30% | Profit after tax | Add back depreciation | | 3 | 14,000 | \$560,000 | \$280,000 | \$71,667 | (560,000 - 280,000 - 71,667) | 30% | Profit after tax | Add back depreciation | ### Step 3: Calculate for each year **Year 1:** - Profit before tax = 1,480,000 - 740,000 - 71,667 = 668,333 - Tax = 668,333 × .30 = 200,500 - Net profit after tax = 668,333 - 200,500 = 467,833 - Cash flow = Net profit + Depreciation = 467,833 + 71,667 = **539,500** **Year 2:** - Profit before tax = 1,800,000 - 900,000 - 71,667 = 828,333 - Tax = 828,333 × .30 = 248,500 - Net profit after tax = 828,333 - 248,500 = 579,833 - Cash flow = 579,833 + 71,667 = **651,500** **Year 3:** - Profit before tax = 560,000 - 280,000 - 71,667 = 208,333 - Tax = 208,333 × .30 = 62,500 - Net profit after tax = 208,333 - 62,500 = 145,833 - Cash flow = 145,833 + 71,667 = **217,500** ### Step 4: Calculate terminal cash flow at Year 3 - Recover net working capital = 20% of Year 3 sales - Year 3 sales = 14,000 × \$40 = \$560,000 - NWC recovered = .20 × 560,000 = \$112,000 - Sale of equipment = \$ (assuming fully depreciated) - Total cash inflow at year 3 = cash flow + NWC recovered = 217,500 + 112,000 = **329,500** ### Step 5: Calculate the initial investment and additional investment - Initial investment in equipment = \$296,000 - Additional investment after 3 years = \$215,000 ### Step 6: Discount the cash flows Using a discount rate of 15%, the present value (PV) of cash flows: | Year | Cash Flow | Discount Factor | Present Value | |--------|--------------|-------------------|----------------| | | -\$296,000 | 1.000 | -\$296,000 | | 1 | \$539,500 | 1 / (1 + .15)^1 ≈ .87 | \$469,305 | | 2 | \$651,500 | 1 / (1 + .15)^2 ≈ .76 | \$493,940 | | 3 | \$329,500 | 1 / (1 + .15)^3 ≈ .66 | \$217,470 | Additionally, at Year 3, account for the additional investment: - Present value of additional investment = \$215,000 / (1.15)^3 ≈ \$138,341 --- ## **Net Present Value (NPV):** \[ \boxed{ NPV = \text{Sum of PV of cash flows} - \text{Initial investment} } \] \[ NPV = (-\$296,000) + \$469,305 + \$493,940 + \$217,470 - \$138,341 \] \[ NPV = \$746,374 \] --- ## **Answer for part a:** **Net present value (NPV) ≈ \$746,000** --- ## Part b: Increase in NPV with 100% bonus depreciation ### **Effect of bonus depreciation:** - Bonus depreciation allows full immediate depreciation of \$215,000 in year 1. - This increases the tax shield, reducing taxes paid in year 1 and increasing after-tax cash flow in year 1. ### Step 1: Calculate tax savings - Tax shield = \$215,000 × 30% = \$64,500 ### Step 2: Adjust year 1 cash flow - Increase in cash flow in Year 1 = \$64,500 (additional cash flow due to tax shield) ### **Increase in NPV:** \[ \text{NPV increase} = \$64,500 / (1.15)^1 ≈ \$56,087 \] --- ## **Final answers:** | Part | Answer | |--------|---------| | a | **\$746,000** | | b | **\$56,000** (rounded to nearest dollar) | --- Let me know if you'd like the detailed calculations or any clarification!