Your firm is contemplating the purchase of a new $943,500 computer-based order e

Question

Your firm is contemplating the purchase of a new $943,500 computer-based order entry system. The system will be depreciated straight-line to zero over its 5-year life. It will be worth $91,800 at the end of that time. You will be able to reduce working capital by $127,500 (this is a one-time reduction). The tax rate is 31 percent and your required return on the project is 19 percent and your pretax cost savings are $393,400 per year.

What is the NPV?

At what level of pretax cost savings would you be indifferent between accepting the project and not accepting it?

At what level of pretax cost savings would you be indifferent between accepting the project and not accepting it?

Explanation / Answer

Here investment = $943500, change in working capital = -$127500, Tax=31%,
Depreciation on straight line for 5 years to 0 = 943500/5 = 188700 and thus book value at the end of 5 years will be zero
Pretax cost saving 393400 per year, Salvage value=91800

Thus Initial outlay of the project = fixed cost of investment + change in working capital
= 943500-127500
=816000

After tax operating cash flow = (pretax cost saving)(1-T) + (T*Depreciation)
=393400(1-0.31)+(0.31*188700)
=271446+58479
=329925

Terminal year after tax non operating Cash flow = Salvage value+change in working capital - Tax(salvage - book value)
=91800-127500 - 0.31(91800-0)
=-35700 - 28458
=-64158

Thus CFs are
Year 0= -816000
Year1=329925
Year2=329925
Year3=329925
Year4=329925
Year5=329925-64158=265767

Solving it with discount rate of 19% in BA II plus calculator or on excel file using NPV formula you get NPV = $139415.82, Its NPV is positive and thus with Pretax cost savings are $393400, we will accept the project.


If the Pretax cost savings are 283250 and rest all remaining same
Initial outlay = 816000
Terminal year after tax non operating Cash flow = -64158

Only After tax operating cash flow will change and it is = (pretax cost saving)(1-T) + (T*Depreciation)
=283250(1-0.31)+(0.31*188700)
=195443+58479
=253922

Thus Cash flows would be
Year 0= -816000
Year1=253922
Year2=253922
Year3=253922
Year4=253922
Year5=253922-64158=189764

Solving it with discount rate of 19% in BA II plus calculator or on excel file using NPV formula you get NPV = $-55869.41. Its NPV is negative and thus with Pretax cost savings are $283250, we wont accept the project.


I would be indifferent between accepting and not accepting a project when the NPV of the project is Zero and thus at the after tax cost savings of $275670 the NPV of the project is zero
Thus pretax cost savings i.e. x will be
275670=x(1-0.31)+(0.31*188700)
275670=0.69x+58479
275670-58479=0.69x
217191=0.69x
x=217191/0.69
thus x=314770
Hence at pretax cost saving of $314770, it would be indifferent between accepting the project and not accepting the project

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