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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.

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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

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

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