RightPrice Investors, Inc., is considering the purchase of a $365,000 computer w
ID: 2808338 • Letter: R
Question
RightPrice Investors, Inc., is considering the purchase of a $365,000 computer with an economic life of five years. The computer will be fully depreciated over five years using the straight-line method. The market value of the computer will be $65,000 in five years. The computer will replace 5 office employees whose combined annual salaries are $110,000. The machine will also immediately lower the firm’s required net working capital by $85,000. This amount of net working capital will need to be replaced once the machine is sold. The corporate tax rate is 34 percent. The appropriate discount rate is 14 percent. Calculate the NPV of this project.
Explanation / Answer
Annual depreciation = Cost of computer/Useful life = $365,000/5 years = $73,000
Annual savings in salaries cost due to computer = $110,000
Incremental income before tax due to computer = Annual savings in salary cost – Annual depreciation = $110,000 - $73,000 = $37,000
Tax on the incremental income = $37,000 * 34% = $12,580
Net incremental income = $37,000 - $12,580 = $24,420
Annual cash inflows = Net incremental income + Depreciation expense = $24,420 + $73,000 = $97,420
Present value of annuity = Annuity*{1-(1+r)-n}/r
Present value of annual cash inflows = $97,420*(1-1.14-5)/0.14 = $334,450.75
Sale value of computer at the end of five years = $65,000
Book value of computer at the end of five years = $0 (Since full value is depreciated)
Gain on sale of computer = Sale value – Book value = $65,000 - $0 = $65,000
Tax payable on gain on sale = $65,000 * 0.34 = $22,100
Net cash inflow on sale of computer = Sale value – Tax payable on gain on sale = $65,000 - $22,100 = $42,900
Present value of cash flow on sale = $42,900/1.145 = $22,280.92
Net cash outflow at year 0 = Cost of computer – Savings in net working capital = $365,000 - $85,000 = $280,000
Cash outflow at the end of five year due to replacement of net working capital = $85,000
Present value of net working capital investment = $85,000/1.145 = $44,146.34
NPV of this project = - Net cash flow at year 0 + Present value of annual cash inflows + Present value of cash flow on sale of computer – Present value of net working capital investment
NPV of this project = -$280,000 + $334,450.75 + $22,280.92 - $44,146.34 = $32,585.33
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