The net present value of the alternative of overhauling the present system is closest to $(1,119,316).
Note: See the attached photo for the rearrangement of the data in the question on a table.
The net present value (PV) of the alternative of overhauling the present system can therefore be calculated as follows:
PV of present system annual cash operating cost = Present system annual cash operating cost * ((1 - (1 + Discount rate)^-number of years) / discount rate) = $180,000 * ((1 - (1 + 0.1)^-8) / 0.1) = $960,286.72
PV of present system salvage value at the end of 8 years = Salvage value at the end of 8 years / (1 + discount rate)^number of years = $152,000 / (1 + 0.1)^8 = $70,909.12
Therefore, we have:
PV of the alternative of overhauling the present system = PV of present system salvage value at the end of 8 years - Overhaul costs needed now - PV of present system annual cash operating cost = $70,909.12 - $230,000 - $960,286.72 = –1,119,378, or $(1,119,378)
From the question, the closest option is $(1,119,316).
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