Core Corp. is considering the purchase of a new machine for $85,000. The machine would generate an annual cash flow of $25,500 per year for six years. At the end of five years, the machine would have no salvage value. The company's cost of capital is 10 percent. The company uses straight-line depreciation with no mid-year convention. What is the net present value of the machine, assuming no taxes are paid? (Round your answers to two decimal places.)

Question

Quizplus · Accepted Answer

The net present value (NPV) of the machine can be calculated using the formula for NPV, which involves discounting the future cash flows back to their present value and subtracting the initial investment. Given the annual cash flow of $25,500 for six years, a discount rate of 10%, and an initial investment of $85,000, the NPV can be calculated as follows:NPV = (Cash Flow / (1 + r)^n) - Initial Investment, where r is the discount rate and n is the year.The cash flows are the same for each of the six years, so we can use the formula for the present value of an annuity to find the present value of the cash flows:PV = Cash Flow * [(1 - (1 + r)^-n) / r]Plugging in the values:PV = $25,500 * [(1 - (1 + 0.10)^-6) / 0.10] = $25,500 * 4.35526 = $111,059.13Subtracting the initial investment:NPV = $111,059.13 - $85,000 = $26,059.13However, this calculation does not match any of the provided options, suggesting a mistake in the calculation or interpretation of the options. The correct approach to calculate the NPV involves discounting each of the annual cash flows individually and then subtracting the initial investment. Without the specific calculations leading to the options provided, it's important to note that the correct NPV calculation must consider the time value of money for each of the cash flows and then subtract the initial cost of the machine. Given the discrepancy, let's correct the approach based on the options provided:The correct NPV calculation should closely align with the methodology of discounting each cash flow at the 10% rate over the six years and then subtracting the initial investment. However, without the exact calculations shown here, the correct answer based on the options provided and assuming no taxes and straight-line depreciation (which does not affect the cash flow since there are no taxes) would be an approximation based on the given options.Given the mistake in the initial explanation and calculation, the correct answer should be derived from recalculating the NPV correctly with the provided information. Since the detailed calculation leading directly to one of the options was not provided correctly, the intention was to guide on how to approach the NPV calculation. The correct NPV would indeed involve discounting the cash flows at the 10% rate and subtracting the initial investment, but without the precise calculation here, the selection from the provided options (A, B, C, D) based on the initial incorrect explanation cannot be accurately determined. The correct approach involves applying the NPV formula accurately with the given data.

Core Corp Is Considering the Purchase of a New Machine for for $85,000