A) $-2500 B) $-5000 C) $-9500 A machine has a first cost of $10,000 and estimate

Question

A) $-2500 B) $-5000 C) $-9500 A machine has a first cost of $10,000 and estimated operating costs and year-end salvage values as shown. The annual equivalent cost if you operate the machine for 4 years is closest to which value? Year Salvage Value,$ 7,000 5,000 4,200 3,000 2,000 2 3 4 The annual worth of the operating costs are determined below. Annual Worth of Operating Costs, s/year -1,000 Period 1 year 2 years 3 years 4 years 5 years At i = 10% per year, the annual equivalent cost if you operate the machine for 4 years is closest to which 1,500 -2,000 -2,500 -3,000 value?

Explanation / Answer

Present value of annual cost =[PVF10%,1*C1]+[PVF10%,2*CF2]+....+[PVF10%,4*CF4]

=[.90909*1000]+[.82645*1500]+[.75131*2000]+[.68301*2500]

= 909.09+ 1239.68+ 1502.62+ 1707.53

   = 5358.91

present value of salvage :PVF10%,4*salvage

           = .68301*3000

         = 2049.04

Net cost =initial cost+Present value of annual cost -Present value of salvage

      = 10000+5358.91-2049.04

= 13309.87

PVA10%,4 =3.16987

Equivalent cost =Total cost /PVA10%,4

     = 13309.87 /3.16987

     = 4198.87

correct option is "B" -5000 [equivalent cost is nearest to 5000 ]

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