You have two mutually exclusive alternatives as detailed below. If your MARR is 20% which option would you choose?

You have two mutually exclusive alternatives as detailed below. If your MARR is 20% which option would you choose

 

 

answer:

The present worth of Alternative A

Net cash flow of Alternative A = $ 10,000 – $ 1,000

Net cash flow of Alternative A = $ 9,000

Terminal cash flow = $ 9,000 + salvage value

Terminal cash flow = $ 14,000

PW = – $ 50,000 + $ 9,000 / 1.201 + $ 9,000 / 1.202 + $ 9,000 / 1.203+ $ 9,000 / 1.204+ $ 9,000 / 1.205+ $ 9,000 / 1.206+ $ 9,000 / 1.207+ $ 9,000 / 1.208+ $ 9,000 / 1.209+ $ 14,000 / 1.2010

PW = – $ 11,460.22

To find the annual worth of Alternative A

EUAW = EUAB – EUAC

EUAB = $ 9,000 + $ 5000 ( A/F , 20% , 10 years )

EUAB = $ 9000 + $ 5000 X 0.038523

EUAB = $ 9,192.62

EUAC = $ 50,000 ( A/P , 20% , 10 years ) + $ 1,000

EUAC = $ 50,000 x 0.238523 + $ 1,000

EUAC = $ 12,926.20

EUAW = $ 9,192.62 – $ 12,926.20

EUAW = – $ 3,733.58

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The present worth of Alternative B

PW = – $ 20,000 + $ 5000 / 1.201 + $ 5000 / 1.20 2 +$ 5000 / 1.20 3 + $ 5000 / 1.20 4 + $ 5000 / 1.205 + $ 5000 / 1.206 + $ 5000 / 1.207 + $ 5000 / 1.208 + $ 5000 / 1.209 + $ 5000 / 1.2010 + $ 5000 / 1.2011 + $ 5000 / 1.2012 + $ 5000 / 1.2013 + $ 5000 / 1.2014 + $ 5000 / 1.2015 + $ 5000 / 1.2016 + $ 5000 / 1.2017 + $ 5000 / 1.2018 + $ 5000 / 1.2019 + $ 5000 / 1.2020

PW = $ 4347.90

To find the Annual worth

EUAW = EUAB – EUAC

EUAB = $ 5000

EUAC = $ 20,000 (A/P , 20% , 20 years )

EUAC = $ 20,000 x 0.205357

EUAC = $ 4,107.14

EUAW = $ 5000 – $ 4,107.14

EUAW = $ 892.86

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Alternative B is preferred .

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