Question 10.4: This extended example illustrates what happens to the EAC wh...
This extended example illustrates what happens to the EAC when we consider taxes. You are evaluating two different pollution control options. A filtration system will cost $1.1 million to install and $60,000 annually, before taxes, to operate. It will have to be completely replaced every five years. A precipitation system will cost $1.9 million to install, but only $10,000 per year to operate. The precipitation equipment has an effective operating life of eight years.
Straight-line depreciation is used throughout, and neither system has any salvage value. Which option should we select if we use a 12 percent discount rate? The tax rate is 34 percent.
We need to consider the EACs for the two systems because they have different service lives and they will be replaced as they wear out. The relevant information can be summarized as follows:
| Filtration System | Precipitation System | |
| Aftertax operating cost | – $ 39,600 | – $ 6,600 |
| Depreciation tax shield | \underline{74,800} | \underline{80,750} |
| Operating cash flow | $ \underline{35,200} | $ \underline{74,150} |
| Economic life | 5 years | 8 years |
| Annuity factor (12%) | 3.6048 | 4.9676 |
| Present value of operating cash flow | $ 126,888 | $ 368,350 |
| Capital spending | – \underline{1,100,000} | – \underline{1,900,000} |
| Total PV of costs | – $ \underline{\underline{973,112}} | – $\underline{\underline{1,531,650}} |
Notice that the operating cash flow is actually positive in both cases because of the large depreciation tax shields. This can occur whenever the operating cost is small relative to the purchase price.
To decide which system to purchase, we compute the EACs for both using the appropriate annuity factors:
Filtration system: – $973,112 = EAC × 3.6048
EAC = – $269,951
Precipitation system: – $1,531,650 = EAC × 4.9676
EAC = – $308,328
The filtration system is the cheaper of the two, so we select it. In this case, the longer life and smaller operating cost of the precipitation system are not sufficient to offset its higher initial cost.