Final answer:
For Frank's sausage system, the annual depreciation charge is $74,000, the annual operating cash flow is $89,540, the initial year cash flow is a negative $398,000, and subsequent years vary ending with $117,540 in year 5. The NPV must be calculated using these cash flows and if positive, the project is worth accepting.
Step-by-step explanation:
The annual depreciation charge for the sausage system is calculated by dividing the installed cost by its useful life. With a cost of $370,000 and a life of 5 years, the annual depreciation is:
370,000 / 5 = $74,000.
To determine the annual operating cash flow (OCF), we need to account for the savings in operating costs, the depreciation, and the taxes. The OCF is calculated using the formula: OCF = (Savings in operating costs - Depreciation) * (1 - Tax rate) + Depreciation. Plugging in the values:
OCF = ($105,000 - $74,000) * (1 - 0.34) + $74,000 = $89,540.
The project's total cash flow at Year 0 is the sum of the installed cost and the initial investment in net working capital, which is a cash outflow:
Year 0 Cash Flow = Installed cost + Initial investment in net working capital
Year 0 Cash Flow = -$370,000 - $28,000 = -$398,000.
For Year 1 through Year 4, the cash flow is simply the OCF since there's no further investment:
Year 1 to Year 4 Cash Flow = OCF = $89,540.
In Year 5, there is no additional depreciation charge, but the initial investment in net working capital is recovered:
Year 5 Cash Flow = OCF + Recovery of net working capital
Year 5 Cash Flow = $89,540 + $28,000 = $117,540.
The net present value (NPV) of the project can be calculated by discounting the cash flows at the project's discount rate and summing them up. The formula to calculate NPV is:
NPV = ∏_{t=0}^{N} Π t / (1+r)^t
where Π t is the cash flow in year t, N is the number of years, and r is the discount rate.
Using a financial calculator or spreadsheet, the NPV can be determined, and if it is positive, the project should be accepted.