Your firm is contemplating the purchase of a new $980,500 computer-based order e

Question

Your firm is contemplating the purchase of a new $980,500 computer-based order entry system. The system will be depreciated straight-line to zero over its 5-year life. It will be worth $95,400 at the end of that time. You will be able to reduce working capital by $132,500 (this is a one-time reduction). The tax rate is 35 percent and your required return on the project is 21 percent and your pretax cost savings are $443,200 per year.

Requirement 1:
What is the NPV of this project?



Requirement 2:
What is the NPV if the pretax cost savings are $319,100 per year?



Requirement 3:
At what level of pretax cost savings would you be indifferent between accepting the project and not accepting it?

Explanation / Answer

P = $980,500 - $132,500 = 848,000
Depreciation = SL = 980,500/5 = 196,100
SV eoy 5 = $95,400
Tax rate = 35% ||| MARR = 21%
Pretax cost savings = $443,200 per year

Requirement 1: What is the NPV of this project?

BTCF = 443,200
Taxable income = BTCF - Depreciation = 443,200 - 196,100 = 247,100
Tax = Taxable income * Tax rate = 247,100 * 35% = 86,485
ATCF = 443,200 - 86,485 = 356,715

NPV = - 848,000 + 356,715 (P/A,i=21%,N=5) + 95,400 (P/F,i=21%,N=5)
NPV = - 848,000 + 356,715 (2.925984) + 95,400 (0.385543)
NPV = - 848,000 + 1,043,742.5 + 36,780.8 = 232,523.3

Requirement 2: What is the NPV if the pretax cost savings are $319,100 per year?
BTCF = 319,100
Taxable income = BTCF - Depreciation = 319,100 - 196,100 = 123,000
Tax = Taxable income * Tax rate = 123,000 * 35% = 43,050
ATCF = 319,100 - 43,050 = 276,050

NPV = - 848,000 + 276,050 (P/A,i=21%,N=5) + 95,400 (P/F,i=21%,N=5)
NPV = - 848,000 + 276,050 (2.925984) + 95,400 (0.385543)
NPV = - 848,000 + 807,717.9 + 36,780.8 = -3,501.3

Requirement 3: At what level of pretax cost savings would you be indifferent between accepting the project and not accepting it?

NPV = - 848,000 + Aftertaxcostsaving (2.925984) + 95,400 (0.385543)
0 = - 848,000 + X (2.925984) + 95,400 (0.385543)
848,000 - 95,400 (0.385543) = X (2.925984)
848,000 - 36,780.8 = X (2.925984)
811,219.2/(2.925984) = X
X = 277,246.6 = ATCF

ATCF = BTCF - [(BTCF - Depreciation)(Tax rate)]
277,246.6 = BTCF - [(BTCF - 196,100)(35%)]
277,246.6 = BTCF - [(35%BTCF - 68,635)]
277,246.6 = BTCF - 35%BTCF + 68,635
277,246.6 - 68,635 = 65%BTCF
208,611.6 = 65%BTCF
208,611.6/65% = BTCF
BTCF = 320,940.9

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