Rocky Mountain Lumber, Inc., is considering purchasing a new wood saw that costs
ID: 2735549 • Letter: R
Question
Rocky Mountain Lumber, Inc., is considering purchasing a new wood saw that costs $55,000. The saw will generate revenues of $100,000 per year for five years. The cost of materials and labor needed to generate these revenues will total $60,000 per year, and other cash expenses will be $10,000 per year. The machine is expected to sell for $1,100 at the end of its five-year life and will be depreciated on a straight-line basis over five years to zero. Rocky Mountain’s tax rate is 34 percent, and its opportunity cost of capital is 17.90 percent.
What is the project's NPV?
Explanation / Answer
Annual depreciation = $55,000/5 = $11,000
Net income before taxes = Revenues – Material and labor costs – Other expenses – Depreciation = $100,000 - $60,000 - $10,000 - $11,000 = $19,000
Net income after taxes = $19,000 * (1-0.34) = $12,540
Annual free cash inflows = Net income after taxes + Depreciation = $12,540 + $11,000 = $23,540
Present value of annuity = Annuity*{1 – (1+r)-n}/r
Present value of annual free cash inflows = $23,540*(1-1.1790-5)/0.1790 = $73,780.66
Salvage value of machine = $1,100
After tax salvage value = $1,100 * (1-0.34) = $726
Present value of salvage value = $726/1.17905 = $318.69
Net present value = -Purchase price of machine + Present value of annual cash inflows + Present value of salvage value = -$55,000 + $73,780.66 + $318.69 = $19,099.35
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