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, C₁= (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, C₀ = 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 = -C₀ + C₁ / 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