To calculate the Net Present Value (NPV) of the project, we need to determine the cash flows for each year, discount them back to present value, and then sum them up. Here's the step-by-step process:

Step 1: Calculate Annual Cash Flows

1. Year 0: Initial Investment

   • Equipment: $-93,000$
   • Net Working Capital (NWC): $-11,000$
   • Total Year 0 Cash Flow: $-104,000$

2. Year 1 Cash Flow:

   • Revenue: $68,000$
   • Costs: $-22,000$
   • Depreciation: $-18,000$ (non-cash expense)
   • Taxable Income = Revenue - Costs - Depreciation $\text{Taxable Income} = 68,000 - 22,000 - 18,000 = 28,000$
   • Taxes = Taxable Income × Tax Rate $\text{Taxes} = 28,000 \times 0.50 = 14,000$
   • Net Income = Taxable Income - Taxes $\text{Net Income} = 28,000 - 14,000 = 14,000$
   • Cash Flow = Net Income + Depreciation $\text{Cash Flow} = 14,000 + 18,000 = 32,000$
   • Adjust for NWC: NWC increases by $8,000$ (from $11,000$ to $19,000$), so the cash flow will be $-8,000$ (outflow).
   • Total Year 1 Cash Flow: $32,000 - 8,000 = 24,000$

3. Year 2 Cash Flow:

   • Revenue: $68,000$
   • Costs: $-22,000$
   • Depreciation: $-18,000$
   • Taxable Income = $28,000$ (same as above)
   • Taxes = $14,000$ (same as above)
   • Net Income = $14,000$
   • Cash Flow = $14,000 + 18,000 = 32,000$
   • Adjust for NWC: NWC increases by $15,000$ (from $19,000$ to $34,000$), so the cash flow will be $-15,000$ (outflow).
   • Total Year 2 Cash Flow: $32,000 - 15,000 = 17,000$

4. Year 3 Cash Flow:

   • Revenue: $68,000$
   • Costs: $-22,000$
   • Depreciation: $-18,000$
   • Taxable Income = $28,000$ (same as above)
   • Taxes = $14,000$ (same as above)
   • Net Income = $14,000$
   • Cash Flow = $14,000 + 18,000 = 32,000$
   • NWC is recovered (inflow) of $34,000$ and equipment sold for $31,000$.
   • Total Year 3 Cash Flow: $32,000 + 34,000 + 31,000 = 97,000$

Step 2: Calculate NPV

Using the cash flows:

• Year 0: $-104,000$
• Year 1: $24,000$
• Year 2: $17,000$
• Year 3: $97,000$

Discount these cash flows back to present value using the cost of capital (8.78%).

$\text{NPV} = \sum \left( \frac{\text{Cash Flow}_t}{(1 + r)^t} \right)$

Where $r = 0.0878$.

Calculating each term:

1. Year 0: $\text{PV}_0 = -104,000$

2. Year 1: $\text{PV}_1 = \frac{24,000}{(1 + 0.0878)^1} = \frac{24,000}{1.0878} \approx 22,065$

3. Year 2: $\text{PV}_2 = \frac{17,000}{(1 + 0.0878)^2} = \frac{17,000}{1.1820} \approx 14,392$

4. Year 3: $\text{PV}_3 = \frac{97,000}{(1 + 0.0878)^3} = \frac{97,000}{1.2836} \approx 75,682$

Step 3: Summing the Present Values

$\text{NPV} = -104,000 + 22,065 + 14,392 + 75,682 \approx 7,139$

Final Result

The Net Present Value (NPV) of the project is approximately $7,139.

Would you like further details or have any questions? Here are some related topics you might find interesting:

1. How to calculate internal rate of return (IRR)?
2. What factors affect the cost of capital?
3. How does depreciation impact cash flow calculations?
4. What are the risks associated with capital budgeting?
5. How to assess the profitability of multiple projects simultaneously?

Tip: Always consider different scenarios (best case, worst case) in cash flow projections to understand potential risks and returns better.