To calculate the Net Present Value (NPV) of the PJX5, we first need to gather the relevant financial information. The NPV will consider the initial costs, any cash flows created by the investment, and the salvage value at the end of its life. However, it seems that some cash flows from operational savings have not been provided. For simplicity, we will assume that the juicer will generate savings that we can analyze.
Step 1: Initial Costs
- Purchase cost of PJX5: $2,360,000
- Research costs: $14,664 (This is a sunk cost and should not be included in NPV calculations)
- Plant redesign costs: $19,542 (This is also a sunk cost and should not be included in NPV calculations)
Thus, the total initial investment is just the cost of the PJX5:
- Total Initial Investment: $2,360,000
Step 2: Cash Flows and Salvage Value
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Since the cash flows resulting from savings are not explicitly provided in the question, we will have to assume a hypothetical annual cash flow generated from the operation of the PJX5.
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The juicer will be sold for its book value of $128,166 at the end of year 10.
Step 3: NPV formula
NPV is calculated using the formula: \[ NPV = \sum \left( \frac{C_t}{(1 + r)^t} \right) - C_0 \] Where:
- \( C_t \) = cash inflow during the year t
- \( r \) = discount rate
- \( t \) = number of time periods
- \( C_0 \) = total initial investment
Example Assumptions
To proceed with the NPV calculation, let's assume:
- Annual cash inflow from savings due to efficiency, \( C_t \) = $400,000 (hypothetically)
- Discount rate \( r \) = 10% (this can be adjusted depending on the company's cost of capital)
Step 4: Calculate NPV
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Calculate the present value of cash flows from year 1 to year 10: \[ \text{PV} = C_t \times \left( \frac{1 - (1 + r)^{-n}}{r} \right) \] Where \( n \) is 10.
Plugging in \( C_t = 400,000, r = 0.10, \text{and } n = 10 \): \[ \text{PV} = 400,000 \times \left( \frac{1 - (1 + 0.10)^{-10}}{0.10} \right) \approx 400,000 \times 5. harvesting = 5.159 = 2,063,611.24 \]
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Present Value of Salvage Value in year 10: \[ PV_{\text{salvage}} = \frac{128,166}{(1 + 0.10)^{10}} \approx \frac{128,166}{2.5937} \approx 49,385.74 \]
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Total PV becomes: \[ \text{Total PV} = 2,063,611.24 + 49,385.74 \approx 2,112,996.98 \]
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Now calculating NPV: \[ NPV = \text{Total PV} - \text{Initial Investment} = 2,112,996.98 - 2,360,000 \approx -247,003.02 \]
Conclusion
Based on these assumptions, the NPV of the PJX5 is approximately -$247,003.02. This indicates the investment may not meet the profitability criteria under the assumed cash inflow.
Note: You must adjust cash flow and discount rate based on your specific scenario for an accurate NPV calculation. If operational cash flows can be provided, insert those to refine this calculation.
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