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Suppose a company had an initial investment of $45,000. The cash flow for the next five years are $14,000, $20,000, $14,000, $19,000, and $14,000, respectively. The interest rate is 6%. What is the NPV of the project?

User Nikhil S
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Final answer:

NPV is calculated by discounting the future cash flows to present value and subtracting the initial investment. For the given case with an initial investment of $45,000 and cash flows over five years at a 6% interest rate, each annual cash flow is discounted to its present value and summed to obtain the NPV.

Step-by-step explanation:

To calculate the Net Present Value (NPV) of a project, you need to discount future cash flows back to their present value and then subtract the initial investment. This is done using the formula:

NPV = ∑(CFt / (1 + r)^t) - initial investment,

where CFt represents the cash flows in each period t, r is the discount rate (interest rate), and t is the number of time periods.

For the given case, we have the initial investment of $45,000 and cash flows of $14,000, $20,000, $14,000, $19,000, and $14,000 for the next five years, with a discount rate of 6%. The calculation of the present value (PV) for each cash flow is as follows:

  • PV year 1 = $14,000 / (1 + 0.06)^1
  • PV year 2 = $20,000 / (1 + 0.06)^2
  • PV year 3 = $14,000 / (1 + 0.06)^3
  • PV year 4 = $19,000 / (1 + 0.06)^4
  • PV year 5 = $14,000 / (1 + 0.06)^5

After calculating each PV, you sum them up and subtract the initial investment to find the NPV:

NPV = Sum of PVs - initial investment.

This provides the managerial decision-makers with a clear financial indicator of the project's profitability considering the time value of money.

User Gabriel Ferrer
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