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Your firm is thinking about investing ​$200 comma 000200,000 in the overhaul of a manufacturing cell in a lean environment. Revenues are expected to be ​$33 comma 00033,000 in year one and then increasing by ​$11 comma 00011,000 more each year thereafter. Relevant expenses will be ​$20 comma 00020,000 in year one and will increase by ​$10 comma 00010,000 per year until the end of the​ cell's ninenine​-year life. Salvage recovery at the end of year ninenine is estimated to be ​$11 comma 00011,000. What is the annual equivalent worth of the manufacturing cell if the MARR is 1010​% per​ year?

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jepessoa

Answer:

EAW = -$17,545.71

Explanation:

initial investment = $200,000

cash inflows;

  • Year 1 = $33,000
  • Year 2 = $44,000
  • Year 3 = $55,000
  • Year 4 = $66,000
  • Year 5 = $77,000
  • Year 6 = $88,000
  • Year 7 = $99,000
  • Year 8 = $110,000
  • Year 9 = $132,000

cash outflows:

  • Year 1 = $20,000
  • Year 2 = $30,000
  • Year 3 = $40,000
  • Year 4 = $50,000
  • Year 5 = $60,000
  • Year 6 = $70,000
  • Year 7 = $80,000
  • Year 8 = $90,000
  • Year 9 = $100,000

EAW = equivalent annual worth = equivalent annual benefits - equivalent annual costs

to determine the EAB we must first find the PV of the cash inflows using a financial calculator = $408,348.84

EAB = (PV x r) / [1 - (1 + r)⁻ⁿ] = ($408,348.84 x 10%) / [1 - (1 + 10%)⁻⁹] = $70,905.91

to determine the EAC we must first find the PV of the cash outflows (including initial outlay) using a financial calculator = $509,395

EAC = (PV x r) / [1 - (1 + r)⁻ⁿ] = ($509,395 x 10%) / [1 - (1 + 10%)⁻⁹] = $88,451.62

EAW = $70,905.91 - $88,451.62 = -$17,545.71

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