Answer :
The NPV for this project is approximately $326,939.29
To calculate the payback period for this project, we need to determine the number of years it takes for the cumulative cash inflows to recover the initial investment. Here are the calculations:
Year 1:
Cash inflow = Sales - Variable costs - Fixed costs = $840,000 - (0.18 * $840,000) - $206,000 = $492,000
Cumulative cash inflow at the end of Year 1 = $492,000
Year 2:
Cash inflow = $840,000 - (0.18 * $840,000) - $206,000 = $492,000
Cumulative cash inflow at the end of Year 2 = $492,000 + $492,000 = $984,000
Year 3:
Cash inflow = $840,000 - (0.18 * $840,000) - $206,000 = $492,000
Cumulative cash inflow at the end of Year 3 = $984,000 + $492,000 = $1,476,000
Year 4:
Cash inflow = $840,000 - (0.18 * $840,000) - $206,000 = $492,000
Cumulative cash inflow at the end of Year 4 = $1,476,000 + $492,000 = $1,968,000
Since the cumulative cash inflows reach $1,968,000 at the end of Year 4, which is greater than the initial investment of $125,000, the payback period is less than 4 years.
To calculate the NPV for this project, we need to discount the cash flows at the required return rate of 13%. Here are the calculations:
NPV = -Initial Investment + (Cash inflow Year 1 / (1 + Required Return)¹ + (Cash inflow Year 2 / (1 + Required Return)² + (Cash inflow Year 3 / (1 + Required Return)³ + (Cash inflow Year 4 / (1 + Required Return)⁴)
NPV = -$125,000 + ($492,000 / (1 + 0.13)¹ + ($492,000 / (1 + 0.13)² + ($492,000 / (1 + 0.13)³ + ($492,000 / (1 + 0.13)⁴
NPV ≈ -$125,000 + $434,513.27 + $382,949.92 + $337,469.01 + $297,007.09
NPV ≈ $326,939.29
Therefore, the NPV for this project is approximately $326,939.29.
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