To calculate the Net Present Value (NPV) of the project, we follow these steps:

1. Calculate Cash Flows

• Revenue: $\$64,000$
• Costs: $\$22,000$
• Depreciation: $\$18,000$
• Tax Rate: $50\%$
• Net Working Capital (NWC): Changes across years.

Formula for Operating Cash Flow (OCF):

$OCF = (Revenue - Costs - Depreciation)(1 - Tax\ Rate) + Depreciation$

After-Tax Salvage Value:

$\text{After-tax salvage value} = \text{Sale price} \times (1 - \text{Tax rate})$

Total Cash Flow:

$\text{Total Cash Flow} = OCF + \text{Changes in NWC} + \text{After-Tax Salvage Value (in Year 3)} - \text{Initial Investment}$

---

2. Step-by-Step Calculation

Year 0:

• Initial Investment: $-\$93,000$
• Initial NWC: $-\$11,000$
• Total Cash Flow: $-\$93,000 - \$11,000 = -\$104,000$

Year 1:

$OCF = (\$64,000 - \$22,000 - \$18,000)(1 - 0.5) + \$18,000$ $OCF = (\$24,000)(0.5) + \$18,000 = \$12,000 + \$18,000 = \$30,000$

• Change in NWC: $\$19,000 - \$11,000 = \$8,000$ (outflow)
• Total Cash Flow: $\$30,000 - \$8,000 = \$22,000$

Year 2:

$OCF = (\$64,000 - \$22,000 - \$18,000)(1 - 0.5) + \$18,000$ $OCF = (\$24,000)(0.5) + \$18,000 = \$12,000 + \$18,000 = \$30,000$

• Change in NWC: $\$34,000 - \$19,000 = \$15,000$ (outflow)
• Total Cash Flow: $\$30,000 - \$15,000 = \$15,000$

Year 3:

$OCF = (\$64,000 - \$22,000 - \$18,000)(1 - 0.5) + \$18,000$ $OCF = (\$24,000)(0.5) + \$18,000 = \$12,000 + \$18,000 = \$30,000$

• Change in NWC: $\$0 - \$34,000 = -\$34,000$ (inflow)
• After-Tax Salvage Value: $\$31,000 \times (1 - 0.5) = \$15,500$
• Total Cash Flow: $\$30,000 + \$34,000 + \$15,500 = \$79,500$

---

3. Discount Cash Flows to Present Value

Using the discount rate $r = 8.78\%$: $PV = \frac{CF}{(1 + r)^t}$

Present Value Calculations:

• Year 0: $-\$104,000$ (no discounting)
• Year 1: $\frac{\$22,000}{(1 + 0.0878)^1} = \frac{\$22,000}{1.0878} = \$20,222.89$
• Year 2: $\frac{\$15,000}{(1 + 0.0878)^2} = \frac{\$15,000}{1.1833} = \$12,677.34$
• Year 3: $\frac{\$79,500}{(1 + 0.0878)^3} = \frac{\$79,500}{1.2906} = \$61,594.92$

---

4. Calculate Net Present Value (NPV)

$NPV = \text{Sum of discounted cash flows}$ $NPV = -\$104,000 + \$20,222.89 + \$12,677.34 + \$61,594.92$ $NPV = -\$9,504.85$

---

Conclusion:

The Net Present Value (NPV) of the project is $-\$9,504.85$. Since the NPV is negative, the project should not be undertaken.

---

Do you want further breakdowns or explanations?
Here are 5 related questions to explore:

1. How does the cost of capital impact the NPV?
2. What happens if the tax rate changes?
3. How would changing depreciation methods affect the cash flows?
4. What if the salvage value was higher?
5. How does the timing of cash inflows influence project viability?

Tip: NPV is sensitive to discount rates—always check for variability by conducting sensitivity analysis.