To calculate the Net Present Value (NPV) of Project X, we'll follow these steps:

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1. Definitions and Components

• Initial Investment: $328,000
• Operating Cash Flows (OCF):
  • Year 1: $171,000
  • Year 2: -$24,000
  • Year 3: $174,000
• Net Working Capital (NWC):
  • Year 0: $14,000
  • Year 1: -$3,000
  • Year 2: -$7,000
  • Year 3: -$4,000
• Equipment Sale (Year 3): $52,000
• Loan Payments:
  • Interest in Year 3: $89,000
  • Principal in Year 3: $328,000
• Cost of Capital: 9.45%

2. Timeline of Cash Flows

We calculate cash flows for each year as follows:

Year 0:

• Net investment = $328,000 - $14,000 (NWC) = $314,000 outflow

Year 1:

• OCF = $171,000
• Change in NWC = -$3,000 (cash inflow)
• Total cash flow = $171,000 + $3,000 = $174,000 inflow

Year 2:

• OCF = -$24,000
• Change in NWC = -$7,000 (cash inflow)
• Total cash flow = -$24,000 + $7,000 = -$17,000 outflow

Year 3:

• OCF = $174,000
• Equipment Sale = $52,000
• Change in NWC = -$4,000 (cash inflow)
• Loan Repayment = $417,000 (outflow)
• Total cash flow = $174,000 + $52,000 + $4,000 - $417,000 = -$187,000 outflow

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3. Present Value Calculation

Using the cost of capital (9.45%) as the discount rate, we calculate the present value (PV) of each cash flow:

• PV Formula:
  $PV = \frac{\text{Cash Flow}}{(1 + r)^t}$

PVs of Each Year:

• Year 0: $-314,000 \cdot (1) = -314,000$
• Year 1: $\frac{174,000}{(1 + 0.0945)^1} = 158,990$
• Year 2: $\frac{-17,000}{(1 + 0.0945)^2} = -14,214$
• Year 3: $\frac{-187,000}{(1 + 0.0945)^3} = -143,835$

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4. Net Present Value (NPV)

$NPV = \text{Sum of PVs for all years}$

$NPV = -314,000 + 158,990 - 14,214 - 143,835 = -312,059$

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Final Answer

The Net Present Value (NPV) of Project X is -$312,059. This means the project is not financially viable under these assumptions.

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Would you like a detailed breakdown of any particular step or an explanation of why the project isn't viable?

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Relative Questions

1. How does the cost of capital influence the viability of a project?
2. What alternative financing methods could improve the project’s NPV?
3. How are changes in net working capital included in cash flow calculations?
4. Why is equipment sale added in Year 3's cash flow?
5. What would happen if operating cash flows were higher in Year 2?

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Tip

Always compare NPV results with alternative projects or investments to ensure you're choosing the most profitable option.