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    Equivalent Annual Cost and Minimum Attractive Rate of Return

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    Compare the equivalent annual costs for 2 pumps. The minimum attractive rate of return is 12%.

    First cost of PUMP A is $8000
    First cost of PUMP B is $6000

    Salvage of PUMP A is zero
    Salvage of PUMP B is zero

    Life span of PUMP A is 8 years
    Life span of PUMP B is 8 years

    Annual repair costs of PUMP A is $500
    Annual repair costs of PUMP B is $800

    Annual operating costs of PUMP A is $1500
    Annual operating costs of PUMP B is $1800

    Use equivalent annual cost method.

    © BrainMass Inc. brainmass.com December 24, 2021, 7:55 pm ad1c9bdddf
    https://brainmass.com/business/equivalent-annual-annuity/equivalent-annual-cost-minimum-attractive-rate-return-230535

    SOLUTION This solution is FREE courtesy of BrainMass!

    Compare the equivalent annual costs for 2 pumps. The minimum attractive rate of return is 12%.

    First cost of PUMP A is $8000
    First cost of PUMP B is $6000

    Salvage of PUMP A is zero
    Salvage of PUMP B is zero

    Life span of PUMP A is 8 years
    Life span of PUMP B is 8 years

    Annual repair costs of PUMP A is $500
    Annual repair costs of PUMP B is $800

    Annual operating costs of PUMP A is $1500
    Annual operating costs of PUMP B is $1800

    Use equivalent annual cost method

    Answer:
    Note: To compare the two systems we calculate the Net Present Value of the costs of the two systems and then divide by PVIFA to get the equivalent annual cost. The system with a lower equivalent unit cost gets selected.
    PVIFA= Present Value Interest Factor for an Annuity
    It can be read from tables or calculated using the following equations
    PVIFA( n, r%)= =[1-1/(1+r%)^n]/r%

    Pump A:
    Initial cost (time t=0)= $8,000
    Annual operating+ repair cost= $2,000 =500+1500
    Life= 8 years
    MARR= 12%

    n= 8
    r= 12.00%
    PVIFA (8 periods, 12.% rate ) = 4.96764

    Annuity (Annual cost)= $2,000
    Therefore, present value= $9,935.28 =2000x4.96764

    Initial investment= $8,000
    Therefore NPV= $17,935.28 =9935.28+8000

    Thus the Net Present Value of the costs= $17,935.28

    Equivalent Annual cost = NPV/ PVIFA= $3,610.42 =17935.28/4.96764

    Pump B:
    Initial cost (time t=0)= $6,000
    Annual operating+ repair cost= $2,600 =800+1800
    Life= 8 years
    MARR= 12%

    n= 8
    r= 12.00%
    PVIFA (8 periods, 12.% rate ) = 4.96764

    Annuity (Annual cost)= $2,600
    Therefore, present value= $12,915.86 =2600x4.96764

    Initial investment= $6,000
    Therefore NPV= $18,915.86 =12915.86+6000

    Thus the Net Present Value of the costs= $18,915.86

    Equivalent Annual cost = NPV/ PVIFA= $3,807.82 =18915.86/4.96764

    Equivalent Annual Cost
    Pump A= $3,610.42
    Pump B= $3,807.82

    Therefore, Pump A is better as it has a lower Equivalent Annual Cost

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 7:55 pm ad1c9bdddf>
    https://brainmass.com/business/equivalent-annual-annuity/equivalent-annual-cost-minimum-attractive-rate-return-230535

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