# 20k at time zero and 15 of sales the after year nwc

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(20k at time zero and 15% of sales the after)YearNWCChange NWCChange capital Spending0.20K20k800k1.54K34k2.90K36k3.108K18k4.107.25K-.75k5.99K-8.25k6.82.5K-16.5k7.66K-16.5k8.49.5k-16.5k-49.5release of working capital6
Salvage: .2*\$800k=\$160k(1-T)=\$160k(1-.34)=105.6k.Note we pay tax on the whole amountbecause we have depreciated the asset to zero, so to the IRS the \$160k is a pure profit.Cash flows from project:YearsOCF- Change NWC-Change Cap Spend =0.020k800k-820,0001.141,16934k107,1692.248,11336k212,1133.268,67318k250,6734.231,973-.75k232,7235.205,790-8.25k214,0406.172,790-16.5k189,2907.139,790-16.5k156,2908.94,604-16.5+-49.5k-105,600266,204[email protected]%= 65,488.8 =>Accept;IRR=17.236%, again Accept.OCF can obviously increase for two reasons:1.Sales increase from new project.OCF = (S-C)(1-T) + Dep.*T2.Cost decreases.Cost Reduction Example:\$100,000 machine with 12-year depreciable life, use straight line.The discount rate is 11%.Themachine will reduce cost by \$11,000/year and increases current expenditures by \$1000/yr.Thetax rate is 25%.Also there is one other machine that has depreciation of \$20,000/yr, no salvagevalue.DEP= 100,000/12=8,333.33OCF= (Rev.-Cost)(1-T) + DEP(T)= (11,000-1000)(1-.25)+ 8,333.33(.25)= 7500+2083.33= 9583.33CF0 -\$100k, CF1-12: \$9583.33Required return= 11%, NPV= -\$37,781.61, IRR= 2.219 or2.22%, so REJECT.CF
Let’s change this problem:Assume that you have the same cash flows described above, but now unexpectedly the projectends you must sell the machine in the 6thyear for \$70,000.How does this change the problemand what is the salvage value?
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sell the machine in year 6, you now will no longer receive cash flows from year 7-12, but you doget the salvage value in the 6thyear.So in year 6 we have accumulated depreciation of 6*8,333.33= 49,999.98 or \$50k, so this meansthat we have told the IRS that the machine is worth \$100k-\$50k= \$50k. So salvage is 70k-(70k-50k)(.25)= 65k because we have to pay taxes in the 20k profit. This means our cash flows are:CF0: -\$100k, CF1-CF5: \$9583.33+\$65,000. Find NPV now: -\$24,705.71.Let’s Change this again:\$100,000 machine with 6-year life and 5 year MACRS depreciable life, use MACRS.Thediscount rate is 6%.The machine will reduce cost by \$11,000/year and increases currentexpenditures by \$1000/yr.The tax rate is 25%.Also there is one other machine that hasdepreciation of \$20,000/yr, no salvage value.DepreciationYrCost*Schedule=DEP1\$100,000.2\$20,0002\$100,000.32\$32,0003\$100,000.192\$19,2004\$100,000.1152\$11,5205\$100,000.1152\$11,5206\$100,000.0576\$5,760Now putting together the OCFs:OCF0==-\$100,000OCF1= (11000-1000)*(1-.25) + 20000*.25=\$12,500OCF2= (11000-1000)*(1-.25) + 32000*.25=\$15,500OCF3= (11000-1000)*(1-.25) + 19200*.25=\$12,300OCF4= (11000-1000)*(1-.25) + 11520*.25=\$10,380OCF5= (11000-1000)*(1-.25) + 11520*.25=\$10,380OCF6= (11000-1000)*(1-.25) +5760*.25=\$8,940Then entering all these in the cash flow keys and i=6% we get:NPV=-\$41,804, REJECT; IRR= -9.97, again REJECTUnequal Lives of ProjectsSo far we have considered projects with equal lives.Now let’s look at unequal lives.NPVdepends on the length of the life of the project.This doesn't matter for independent projects butfor mutually exclusive projects it does.Say we have 2 mutually exclusive projects of 2 machines with the same function.Machine 1 hasa 5yr life, machine 2 has a 10yr life.If we used the same discount rate (which we should) thenwe could calculate the NPV's of both projects.Let’s say NPV1<NPV2.

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