Question

MC algo 9-33 Cash Flows And NPV Gateway Communications is considering a project with an initial fixed assets cost of $1.50 million that will be depreciated straight-line to a zero book value over the 9-year life of the project. At the end of the project the equipment will be sold for an estimated $245,000. The project will not change sales but will reduce operating costs by $409,000 per year. The tax rate is 40 percent and the required return is 12.7 percent. The project will require $54,500 in net working capital, which will be recouped when the project ends. What is the project's NPV?

Multiple Choice

$133,641

$127,831

$169,560

$182,220

$176,342

Answer 1

Initial investment = Cost + increase in NWC

Initial investment = 1,500,000 + 54,500

Initial investment = 1,554,500

Annual depreciation = 1,500,000 / 9 = 166,666.6667

Operating cash flows from year 1 to year 9 = (savings - depreciation)(1 - tax) + depreciation

Operating cash flows from year 1 to year 9 = (409,000 - 166,666.6667)(1 - 0.4) + 166,666.6667

Operating cash flows from year 1 to year 9 = 145,400 + 166,666.6667

Operating cash flows from year 1 to year 9 = 312,066.6667

Year 9 non operating cash flow = Market value + recover in NWC - tax(market value - book value)

Year 9 non operating cash flow = 245,000 + 54,500 - 0.4(245,000 - 0)

Year 9 non operating cash flow = 245,000 + 54,500 - 98,000

Year 9 non operating cash flow = 201,500

NPV = Presnet value of cash inflows - present value of cash outflows

NPV = Annuity * [1 - 1 / (1 + r)^n] / r + FV / (1 + r)^n - Initial investment

NPV = 312,066.6667 * [1 - 1 / (1 + 0.127)^9] / 0.127 + 201,500 / (1 + 0.127)^9 - 1,554,500

NPV = 312,066.6667 * [1 - 0.340945] / 0.127 + 68,700.48548 - 1,554,500

NPV = 312,066.6667 * 5.19409 + 68,700.48548 - 1,554,500

NPV = $133,641