Clemente Company is considering the purchase of a new machine for $160,000. The machine would generate an annual cash flow before depreciation and taxes of $62,588 for four years. At the end of four 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 and has a 40 percent tax rate. What is the net present value for the machine?

Question

Quizplus · Accepted Answer

The net present value (NPV) of the machine can be calculated by first determining the annual cash flows after taxes and then discounting these cash flows back to their present value at the company's cost of capital. 1. Calculate annual depreciation: $160,000 / 4 years = $40,000 per year.2. Calculate annual cash flow before taxes: $62,588 - $40,000 (depreciation) = $22,588.3. Calculate taxes: $22,588 * 40% = $9,035.2.4. Calculate annual cash flow after taxes: $22,588 - $9,035.2 = $13,552.8.5. Add back depreciation (since it's a non-cash expense) to get the total annual cash flow: $13,552.8 + $40,000 = $53,552.8.Now, discount these cash flows back to their present value using the cost of capital (12%):$$ NPV = \sum \frac{CF_t}{(1 + r)^t} - Initial\ Investment $$Where $ CF_t $ is the cash flow in year $ t $, $ r $ is the discount rate (12%), and $ t $ is the year.$$ NPV = \frac{53,552.8}{1.12} + \frac{53,552.8}{1.12^2} + \frac{53,552.8}{1.12^3} + \frac{53,552.8}{1.12^4} - 160,000 $$$$ NPV \approx 47,812.86 + 42,688.98 + 38,116.41 + 34,021.79 - 160,000 $$$$ NPV \approx 162,640.04 - 160,000 = 2,640.04 $$Therefore, the NPV is approximately $2,640, which is closest to choice D.

Clemente Company Is Considering the Purchase of a New Machine