# Equivalent Annual Cost and Minimum Attractive Rate of Return

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.

Â© BrainMass Inc. brainmass.com December 24, 2021, 7:55 pm ad1c9bdddfhttps://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

Â© 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