Final answer:
The NPV of the project is $657,789.26.
Step-by-step explanation:
To calculate the NPV of the project, we need to discount the cash flows to the present value. The initial investment of $740,000 and the net working capital investment of $69,000 are both cash outflows, so we need to discount them. The annual savings of $217,000 in pretax operating costs is a cash inflow, so we also need to discount it. The salvage value of $102,000 at the end of the project's life is a cash inflow, but it is not discounted.
To calculate the NPV, we calculate the present value of each cash flow and sum them all up. The present value of the initial investment and the net working capital investment can be calculated using the discount rate and the number of years. The present value of the annual savings can be calculated using the discount rate and the number of years. The NPV is the sum of the present values minus the initial investment.
Using the given information:
Initial Investment = $740,000
Net Working Capital Investment = $69,000
Annual Savings = $217,000
Salvage Value = $102,000
Tax Rate = 22%
Discount Rate = 9%
Project Life = 7 years
Step 1: Calculate the present value of the initial investment and the net working capital investment:
PV of Initial Investment = Initial Investment / (1 + Discount Rate)^Project Life = $740,000 / (1 + 0.09)^7 = $740,000 / 1.71701 = $430,395.99
PV of Net Working Capital Investment = Net Working Capital Investment / (1 + Discount Rate)^Project Life = $69,000 / (1 + 0.09)^7 = $69,000 / 1.71701 = $40,172.40
Step 2: Calculate the present value of the annual savings:
PV of Annual Savings = Annual Savings * (1 - Tax Rate) * ((1 - (1 + Discount Rate)^(-Project Life)) / Discount Rate) = $217,000 * (1 - 0.22) * ((1 - (1 + 0.09)^(-7)) / 0.09) = $217,000 * 0.78 * (1 - (1 + 0.09)^(-7)) / 0.09 = $217,000 * 0.78 * 0.487605 = $85,221.87
Step 3: Calculate the NPV:
NPV = PV of Initial Investment + PV of Net Working Capital Investment + PV of Annual Savings + Salvage Value = $430,395.99 + $40,172.40 + $85,221.87 + $102,000 = $657,789.26
Therefore, the NPV of this project is $657,789.26.