Question

Kemp Copy Co. is considering to purchase a new high speed copy machine. The machine costs $500,000 and can be depreciated to zero on a straight-line basis over its life of 5 years. Thus, annual depreciation will be $100,000. The machine is expected to have salvage value of $10,000. Revenues are expected to be $450,000 per year (in real terms), and operating expenses are estimated 60 percent of revenues. Operating cash flows are expected to rise with inflation, forecasted at 3% per year.The working capital needed for the machine is $100,000. The discount rate for the machine is 8% in real terms. The firm pays corporate income tax at 30%. What is the NPV?

Answer #1

All financials below are in $.

Operating annual cash flows in year 1, C_{1}= (Revenue -
operating expenses - annual depreciation) x (1 - Tax rate) +
Depreciation = (450,000 - 60% x 450,000 - 100,000) x (1 - 30%) +
100,000 = 156,000

growth rate in OCF = g = inflation = 3%

Initial investment, C_{0} = Machine cost + working
capital = 500,000 + 100,000 = 600,000

Terminal cash flows = C_{T} = Release of working capital
+ Post tax salvage value = 100,000 + 10,000 x (1 - 30%) =
107,000

Real discount rate = 8%

Nominal discount rate, R = (1 + real rate) x (1 + inflation) - 1= (1 + 8%) x (1 + 3%) - 1 = 11.24%

N = life = 5 years

Hence, NPV = -C_{0} + C_{1} / R x [1 - (1 +
R)^{-N}] + C_{T} x (1 + R)^{-N} = - 600,000
+ 156,000 / 11.24% x [1 - (1 + 11.24%)^{-5}] + 107,000 x (1
+ 11.24%)^{-5} = $ 35,913.16

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