Question

rust industrial systems company is trying to decide between two different conveyor belt systems. system a costs $320,000, has a four-year life, and requires $117,000 in pretax annual operating costs. system b costs $400,000, has a six-year life, and requires $111,000 in pretax annual operating costs. both systems are to be depreciated straight-line to zero over their lives and will have zero salvage value. whichever project is chosen, it will not be replaced when it wears out. the tax rate is 21 percent and the discount rate is 10 percent. calculate the npv for both conveyor belt systems.

Answer 1

The NPV of both System A and System B are -$559,736.92 and -$720,939.16. The firm choose System A conveyor belt system.

System A

Initial Investment in System A = Cost of System A = $320,000

Life of System A = 4 Years

Annual Depreciation of System A as per SLM = Cost of System A / Life

= $320,000 / 4

= $80,000

Pretax Annual Operating Costs = $117,000

Annual Operating Cash Flow = (-Pre-tax Annual Operating Cost - Annual Depreciation) × (1-Tax rate) + Annual Depreciation

= (-$117,000 - $80,000) × (1-0.21) + $80,000

= (-$197,000 × 0.79) + $80,000

= -$155630 + $80,000

= -$75630

NPV of System A = Present value of Operating Cash Flows - Initial Investment

Calculation of Present Value of Operating cash Flows

Present value of Operating cash Flows = Annual Operating Cash Flow × Present value Annuity factor of 10% for 4 Years

= -$75,630 × PVAF(10%,4)

$PVFA(i,n)=\frac{1-\frac{1}{(1+i)^n} }{n}\\PVFA(10,4)=\frac{1-\frac{1}{(1+0.1)^4} }{0.1}\\\\=3.16986545$

= -$75630 × 3.16986545

= -$239,736.92

NPV of System A = Present value of Operating Cash Flows - Initial Investment

= -$239,736.92 - $320,000

= -$559,736.92

System B

Initial Investment in System B = Cost of System B = $400,000

Life of System B = 6 Years

Annual Depreciation of System B as per SLM = Cost of System B / Life of A

= $400,000 / 6

= $66,666.6667

Pretax Annual Operating Costs = $111,000

Annual Operating Cash Flow = (-Pre-tax Annual Operating Cost - Annual Depreciation) × (1-Tax rate) + Annual Depreciation

= (-$111,000 - $66,666.6667) × (1-0.21) + $66,666.6667

= (-$177,666.667 × 0.79) + $66,666.6667

= -$140,356.6667 + $66,666.6667

= -$73,690.00

NPV of System B = Present value of Operating Cash Flows - Initial Investment

Calculation of Present Value of Operating cash Flows

Present value of Operating cash Flows = Annual Operating Cash Flow × Present value Annuity factor of 10% for 6 Years

= -$73,690 × PVAF(10%,6)

$PVFA(i,n)=\frac{1-\frac{1}{(1+i)^n} }{n}\\PVFA(10,6)=\frac{1-\frac{1}{(1+0.1)^6} }{0.1}\\\\=4.3552607$

= -$73,690 × 4.3552607

= -$320,939.16

NPV of System B = Present value of Operating Cash Flows - Initial Investment

= -$320,939.16 - $400,000

= -$720,939.16

NPV of System A = -$559,736.92

NPV of System B = -$720,939.16

Since System A's NPV is less negative, System A ought to be picked.

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