PrintA common economic decision is whether to replace an existing asset with a new costly asset that can help enhance the economics of the project. This decision is made: to increase the capacity, to improve the quality of products, to reduce the costs, to increase the production efficiency, or to make a product that can meet the market demands better. The old asset usually has lower capital and higher operating cost than the new asset.
In such decision making processes, the old and new assets are also called “defender” and “challenger.” The economics of the project is the key to making replacement decisions. An asset should be replaced if to do so improves the economics, and this decision shouldn’t depend on physical deterioration of the asset. Financial and intangible considerations should be taken into consideration for the final decision. Also, risk and uncertainty can be included in the evaluation. The old asset, already in place, usually has lower risk than the new one. Methods explained in previous lessons such as present worth cost, annual cost, incremental NPV or ROR analysis can be applied for replacement decisions. Please note that since tax deductions for two alternatives are different, evaluations should be based on after-tax considerations to give the correct answer.
Example 9-5
Assume, as a manager, you have two alternatives: to keep the existing machine or replace it with a new one. The capital cost required for the new machine is $500,000 that needs to be paid at time zero and is depreciable from time 0 to year 4 (over five years) based on MACRS 7-year life depreciation with the half year convention (Table A-1 at IRS). The new machine produces similar products with the same rate as the existing machine, so the revenue of selling product would be the same. But the new machine operates at lower operating costs of 80,000, $90,000, 100,000, and 110,000 dollars years 1, 2, 3 and 4. The operating cost of the existing machine is 320,000, $330,000, $340,000, and 350,000 dollars for year 1, 2, 3 and 4. Salvage value of both machines would be zero at the end of the 4th year. Consider the income tax of 40% and minimum after-tax ROR is 18%. Evaluate the project using Incremental ROR Analysis and conclude which alternative would be more economically satisfactory.
The following table displays the cost and revenue as it occurred for each decision alternative.
| R1 | R2 | R3 | R4 | |||
| C=$500,000 | OC=$80,000 | OC=$90,000 | OC=$100,000 | OC=$110,000 | ||
| New Machine: |
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| Year | 0 | 1 | 2 | 3 | 4 | |
| R1 | R2 | R3 | R4 | |||
| OC=$320,000 | OC=$330,000 | OC=$340,000 | OC=$350,000 | |||
| Existing Machine |
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| Year | 0 | 1 | 2 | 3 | 4 | |
The following table displays the incremental cost and revenue for New Machine - Existing Machine. Since questions assume similar production rate for new and old machines, they cancel out from incremental analysis. So, we can deduct the operating costs.
| New Machine - Existing Machine | C=$500,000 | S=$240,000 | S=$240,000 | S=$240,000 | S=$240,000 | |
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| Year | 0 | 1 | 2 | 3 | 4 | |
R: Revenue, C: Capital Cost, OC: Operating cost, S: Saving
Note that since operating costs for the new machine are less than for the old one, the difference between the operating costs for the old and new machines is the savings due to installing the new machine. This saving implies that more income will be generated by installing the new machine.
| Year | 0 | 1 | 2 | 3 | 4 |
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| Saving (Income) | 240,000 | 240,000 | 240,000 | 240,000 | |
| -Depreciation |
-71,450
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-122,450
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-87,450
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-62,450
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-156,200
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| Taxable income |
-71,450
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117,550
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152,550
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177,550
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83,800
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| - Income tax 40% |
+28,580
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-47,020
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-61,020
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-71,020
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-33,520
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| Net Income |
-42,870
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70,530
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91,530
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106,530
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50,280
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| +Depreciation | 71,450 | 122,450 | 87,450 | 62,450 | 156,200 |
| - Capital Cost | -500,000 | ||||
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| ATCF |
-471,420
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192,980
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178,980
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168,980
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206,480
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Depreciation rate based on method MACRS 7-year life with the half year convention for year 0, 1, 2, and 3 will be 0.1429, 0.2449, 0.1749, and 0.1249. And, for year 4, we apply the remaining:
Year 0 depreciation:
Year 1 depreciation:
Year 2 depreciation:
Year 3 depreciation:
Year 4 depreciation:
The incremental NPV at 18% minimum ROR for this ATCF equals 30,010. And with the trial and error method, incremental ROR will be 21.2%. These results indicate that replacing the existing machine with the new one is economically satisfactory.
Example 9-6
Consider Example 9-5 and assume each machine produces 10,000 units per year. Calculate the cost per unit of the product and conclude which decision is more economically satisfactory.
Here we assume price of each unit of product equals X, then revenue in each year equals number of goods produced multiplied by the price. New machine break even analysis for price per unit of production will be:
| Year | 0 | 1 | 2 | 3 | 4 |
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| Revenue | 10,000X | 10,000X | 10,000X | 10,000X | |
| - Operating cost | -80,000 | -90,000 | -100,000 | -110,000 | |
| -Depreciation | -71,450 | -122,450 | -87,450 | -62,450 | -156,200 |
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| Taxable income | -71,450 | 10,000X - 202,450 | 10,000X - 177,450 | 10,000X - 162,450 | 10,000X - 266,200 |
| - Income tax 40% | +28,580 | -4,000X+80,980 | -4,000X + 70,980 | -4,000X+64,980 | -4,000X+106,480 |
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| Net Income | -42,870 | 6,000X - 121,470 | 6,000X - 106,470 | 6,000X - 97,470 | 6,000X - 159,720 |
| +Depreciation | 71,450 | 122,450 | 87,450 | 62,450 | 156,200 |
| - Capital Cost | -500,000 | ||||
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| ATCF | -471,420 | 6,000X + 980 | 6,000X - 19,020 | 6,000X - 35,020 | 6,000X - 3,520 |
Now we have to find the X that makes the NPV equal to zero.
NPV = 0
X = 31.44 dollar per unit
n analysis for price per unit of production for existing machine:
| Year | 0 | 1 | 2 | 3 | 4 |
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| Revenue | 10,000X | 10,000X | 10,000X | 10,000X | |
| - Operating cost | -320,000 | -330,000 | -340,000 | -350,000 | |
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| Taxable income | 10,000X - 320,000 | 10,000X - 330,000 | 10,000X - 340,000 | 10,000X - 350,000 | |
| - Income tax 40% | -4,000X+128,000 | -4,000X +132,000 | -4,000X+136,000 | -4,000X+140,000 | |
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| Net Income | 6,000X - 192,000 | 6,000X - 198,000 | 6,000X - 204,000 | 6,000X - 210,000 | |
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| ATCF | 6,000X - 192,000 | 6,000X - 198,000 | 6,000X - 204,000 | 6,000X - 210,000 | |
dollar per unit
Since the new machine breaks even at a lower unit price, we can conclude that replacing the existing machine with the new one is a better economic decision.