To calculate the Net Present Value (NPV) of this project, we need to consider the following components:

1. Initial Investment (Year 0):

   • The project requires an initial investment of $104,000 for equipment.

   • Net working capital (NWC) changes: inventory decreases by $28,000, accounts receivable increases by $15,000, and accounts payable increases by $6,000. So, the net effect on working capital is:
     $\Delta NWC = -28,000 + 15,000 - 6,000 = -19,000$ This decrease in net working capital means the firm will have $19,000 available at the start of the project (since it's a cash inflow).

   • Thus, the initial cash flow (CF₀) is: $CF₀ = -104,000 + 19,000 = -85,000$

2. Annual Operating Cash Flows (Years 1 to 4):

   • The project produces annual operating cash flows of $57,000 for 4 years.
   • Since the equipment is depreciated straight-line to zero over 4 years, annual depreciation is: $\text{Depreciation} = \frac{104,000}{4} = 26,000 \, \text{per year}$
   • Given that depreciation is a non-cash charge, we do not include it in the operating cash flow, so each year the operating cash flow remains $57,000.

3. Salvage Value and Recovery of Net Working Capital (Year 4):

   • At the end of the project, the equipment is sold, generating an after-tax salvage value of $22,000.
   • Also, the net working capital will return to its normal level, implying a cash inflow of $19,000 at the end of Year 4.
   • Thus, the total cash flow at Year 4 will include the annual operating cash flow, salvage value, and recovery of net working capital: $CF_4 = 57,000 + 22,000 + 19,000 = 98,000$

4. Required Return (Discount Rate):
   The required return or discount rate is given as 16%.

NPV Calculation

The NPV is calculated using the formula: $NPV = CF₀ + \frac{CF_1}{(1 + r)} + \frac{CF_2}{(1 + r)^2} + \frac{CF_3}{(1 + r)^3} + \frac{CF_4}{(1 + r)^4}$ Where:

• $CF_1 = CF_2 = CF_3 = 57,000$
• $CF_4 = 98,000$
• $r = 16\% = 0.16$

Now, we calculate the NPV:

$NPV = -85,000 + \frac{57,000}{(1 + 0.16)} + \frac{57,000}{(1 + 0.16)^2} + \frac{57,000}{(1 + 0.16)^3} + \frac{98,000}{(1 + 0.16)^4}$

Breaking it down:

• $\frac{57,000}{1.16} \approx 49,138.79$
• $\frac{57,000}{1.16^2} \approx 42,332.58$
• $\frac{57,000}{1.16^3} \approx 36,484.29$
• $\frac{98,000}{1.16^4} \approx 54,487.09$

Adding them together:

$NPV = -85,000 + 49,138.79 + 42,332.58 + 36,484.29 + 54,487.09$

$NPV \approx -85,000 + 182,442.75$

$NPV \approx 97,442.75$

Final Answer:

The net present value (NPV) of the project is approximately $97,443.

---

Would you like more details or have any other questions? Here are some related questions to expand your understanding:

1. How does straight-line depreciation affect cash flows?
2. What are the advantages of using NPV as a decision-making tool?
3. How would the NPV change if the required return was higher or lower?
4. What impact does the recovery of working capital have on the NPV?
5. What is the significance of after-tax salvage value in NPV calculations?

Tip: NPV is a crucial tool in capital budgeting because it accounts for both the magnitude and timing of cash flows, unlike other metrics like payback period.