Respuesta :
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)
[tex]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[/tex]
= -$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)
[tex]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[/tex]
= -$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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