Russell Corp.is considering the purchase of a new machine for $76,000.The machine would generate an annual cash flow of $23,214 per year for five years.At the end of five years, the machine would have no salvage value.The company's cost of capital is 12 percent.The company uses straight-line depreciation with no mid-year convention. What is the net present value for the machine, assuming no taxes are paid?

Question

Quizplus · Accepted Answer

To calculate the net present value (NPV), we need to discount the cash flows generated by the machine to their present value and subtract the initial cost of the machine.

The annual cash flow generated by the machine is $23,214, and this cash flow is expected to continue for 5 years. Therefore, the total cash flow generated over 5 years would be:

Total cash flow = $23,214 × 5 = $116,070

The salvage value of the machine is zero, so we only need to consider the initial cost of $76,000.

We know that the company's cost of capital is 12%, so we can use this rate to discount the cash flows. Using a financial calculator, we can calculate the present value of the cash flows:

PV of cash flows = $23,214 × [1 - 1/(1+0.12)^5]/0.12
PV of cash flows = $82,648.50

Now we can calculate the NPV as follows:

NPV = PV of cash flows - Initial cost
NPV = $82,648.50 - $76,000
NPV = $7,648.50

Therefore, the net present value for the machine is $7,648.50. Option A is the correct answer.