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Equipment replacement decisions

Jamal Munshi, Sonoma State Univesity, 1992
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Equipment replacement decisions are made on the basis of the NPV of the increase in cash flows caused by the replacement during the life of the new machine. We start by computing the increase in CFO that we can achieve if we make the replacement. The variables are:

Equations for computing the [delta.CFO] vector (subscripts 'o' and 'n' are for 'old' and 'new' respectively):

  • Io = net investment today = price of new equipment - investment tax credit - what we sold the old equipment for + taxes on capital gains on the old equipment + new working capital required.
  • = FAo*(1 - ITC) - Vm + t*(Vm-Vb) + wcs*delta.S
  • (Note: trade-ins do not have capital gains/loss tax consequences)
  • If Vm < Vb then we will have book losses and there will be a corresponding tax savings.
  • delta.Dep = Depn - Depo
  • vcsn = vcso - delta.vcs
  • delta.NOI = delta.S*(1-vcsn) +So*(1-delta.vcs)- delta.Dep (dep is the only change in fixed costs)
  • delta.NIAT = delta.NOI*(1-t)
  • delta.CFO = delta.NIAT + delta.Dep
  • Substituting the expression for delta.NOI,
  • delta.CFO = (delta.S*(1-vcsn) +So*(1-delta.vcs))*(1-t) + t*delta.Dep
  • The net increase in salvage value, delta.SV = SVn - SVo and the future value of the replacement will be given by FV = delta.SV + FV(stream of delta.CFO's)

Example problem:

The Cotati Clarion has sales of $3000 with a vc/s ratio of 70%. An old printing press with a book value of $100 is to be replaced with a new one costing $1000. The salesman has offered us a trade in value or $80 for the old press. The old press would be depreciated to zero book value in its remaining life of 5 years. The new printing press will be depreciated using straight line depreciation to value of $200 in 5 years. It will increase sales by $600 and reduce power consumption by $300/year. Our working capital to sales ratio is 15% and we can take a 10% investment tax credit on this purchase. Our income tax rate is 30%. Our required rate is 16%.

Solution:

  • Io = 1000 *(1-.10) - 80 + 0.15*600 = 910
  • Depnew = (1000 - 200)/5 = 160
  • delta.Dep = 160 - 20 = 140
  • new vc/s = (0.70*3600 - 300)/3600 = 0.6167 delta.vcs = .0833
  • delta.CFO = (600*.3833 + 3000*.0833)*(0.70) + 0.30*140 = 335.29
  • delta.SV = 200-0 = 200
  • now compute pv and make investment decision

You will not be tested on MACRS nor on other computational intense variants of the investment opportunity problem. Your quiz will include a problem such as one of the two examples included in this handout.