Question

Gateway Communications is considering a project with an initial fixed assets cost of $1.63 million that will be depreciated straight-line to a zero book value over the 10-year life of the project. At the end of the project the equipment will be sold for an estimated $233,000. The project will not change sales but will reduce operating costs by $384,000 per year. The tax rate is 40 percent and the required return is 10.8 percent. The project will require $48,500 in net working capital, which will be recouped when the project ends. What is the project's NPV?

           
            A)    $138,291
            B)    $175,685
            C)    $182,712
            D)    $144,577
            E)    $188,803
           

Please show work - we are not allowed to use excel on exam

Answer 1

Depreciation = Cost of the Project / Useful life years = $1,630,000 / 10 = $163,000

Cash flow at year 0 = Cost of Project + Investment in NWC = $1,630,000 + $48,500 = $1,678,500

Annual Cash Flow(Year 1 - 10) = [Savings in Costs * (1 - t)] + [Depreciation * t]

= [$384,000 * (1 - 0.40)] + [$163,000 * 0.40]

= $230,400 + $65,200 = $295,600

Additional Cash Flow at year 10 = After-tax Salvage Value + Recovery of NWC

= [$233,000 * (1 - 0.40)] + $48,500 = $139,800 + $48,500 = $188,300

NPV = PV of Cash Inflows - PV of Cash Outflows

= [$295,600 * {1 - (1 + 0.108)^-10} / 0.108] + [$188,300 / (1 + 0.108)¹⁰] - $1,678,500

= [$295,600 * 5.9389] + [$188,300 / 2.7887] - $1,678,500

= $1,755,553.39 + $67,523.15 - $1,678,500 = $144,576.54, or $144,577

So, Option "D" is correct.