quivalent Annual Cost (EAC) Problem
ACE Corporation is looking at buying three machines. Machine 1 will cost $20,000, have a useful life of 6 years, and will have costs of $4,500 annually. Machine 2 will cost $25,000, have a useful life of 8 years, and will have costs of $4,250 annually. Machine 3 will cost $18,000, have a useful life of 5 years, and will have costs of $4,600 annually. Which machine should ACE purchase if the discount rate is 10%
ACE Corporation is looking at buying three machines.
Machine 1 will cost $20,000, have a useful life of 6 years, and will have costs of $4,500 annually.
Machine 2 will cost $25,000, have a useful life of 8 years, and will have costs of $4,250 annually.
Machine 3 will cost $18,000, have a useful life of 5 years, and will have costs of $4,600 annually.
Calculation for the Equivalent Annual Cost (EAC) is as fllow
Machine 1
Machine 1 will cost $20,000, have a useful life of 6 years, and will have costs of $4,500 annually.
| Year | Cost | PV Factor @10% | Pv of cost |
| 0 | 20,000 | 1 | 20000 |
| 1 | 4500 | 0.909090909 | 4090.909 |
| 2 | 4500 | 0.826446281 | 3719.008 |
| 3 | 4500 | 0.751314801 | 3380.917 |
| 4 | 4500 | 0.683013455 | 3073.561 |
| 5 | 4500 | 0.620921323 | 2794.146 |
| 6 | 4500 | 0.56447393 | 2540.133 |
| 39598.67 |
EAC = $39598.67/4.3553 = $9,092.066 per year
Machine 2 will cost $25,000, have a useful life of 8 years, and will have costs of $4,250 annually.
| Year | Cost | PV Factor @10% | Pv of cost |
| 0 | 25,000 | 1 | 25000 |
| 1 | 4250 | 0.909090909 | 3863.636 |
| 2 | 4250 | 0.826446281 | 3512.397 |
| 3 | 4250 | 0.751314801 | 3193.088 |
| 4 | 4250 | 0.683013455 | 2902.807 |
| 5 | 4250 | 0.620921323 | 2638.916 |
| 6 | 4250 | 0.56447393 | 2399.014 |
| 7 | 4250 | 0.513158118 | 2180.922 |
| 8 | 4250 | 0.46650738 | 1982.656 |
| 47673.44 | |||
EAC = $ 47673.44 /5.3349 = $ 8936.14 per year
Machine 3 will cost $18,000, have a useful life of 5 years, and will have costs of $4,600 annually.
| Year | Cost | PV Factor @10% | Pv of cost |
| 0 | 18,000 | 1 | 18000 |
| 1 | 4600 | 0.909090909 | 4181.818 |
| 2 | 4600 | 0.826446281 | 3801.653 |
| 3 | 4600 | 0.751314801 | 3456.048 |
| 4 | 4600 | 0.683013455 | 3141.862 |
| 5 | 4600 | 0.620921323 | 2856.238 |
| 35437.62 | |||
| 3.7908 | |||
| 9348.322 |
EAC = $ 35437.62 / 3.7908 = $ 9348. 32 per year
The decision:
As the calculated equivalent annual costs of three machines, they can be compared to come to a decision.
Hence, as an annual cost of machine 2 $ 8936.144 is less than an annual cost ofmachine 1 and machine 3 cost so it is said to be the optimal to chose machine 2
