A 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 aftertax considerations to give the correct answer.
Example 95
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 7year life depreciation with the half year convention (Table A1 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 aftertax 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: 


Year  0  1  2  3  4 
R1  R2  R3  R4  
OC=$320,000  OC=$330,000  OC=$340,000  OC=$350,000  
Existing Machine 


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  


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 


Saving (Income)  240,000  240,000  240,000  240,000  
Depreciation 
71,450

122,450

87,450

62,450

156,200



Taxable income 
71,450

117,550

152,550

177,550

83,800

 Income tax 40% 
+28,580

47,020

61,020

71,020

33,520



Net Income 
42,870

70,530

91,530

106,530

50,280

+Depreciation  71,450  122,450  87,450  62,450  156,200 
 Capital Cost  500,000  


ATCF 
471,420

192,980

178,980

168,980

206,480

Depreciation rate based on method MACRS 7year 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: $1\text{}\left(0.1429+0.2449+0.1749+0.1249\right)=0.3124$
Year 0 depreciation: $0.1429\xb7500,000=\$71,450$
Year 1 depreciation: $0.2449\xb7500,000=\$122,450$
Year 2 depreciation: $0.1749\xb7500,000=\$87,450$
Year 3 depreciation: $0.1249\xb7500,000=\$62,450$
Year 4 depreciation: $0.3124\xb7500,000=\$156,200$
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 96
Consider Example 95 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 


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 


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 


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  


ATCF  471,420  6,000X + 980  6,000X  19,020  6,000X  35,020  6,000X  3,520 
$NPV=471,420+(6,000X+980)\xb7(P/F18\%,1)+(6,000X19,020)\xb7(P/F18\%,2)+$
$(6,000X35,020)\xb7(P/F18\%,3)+(6,000X3,520)\xb7(P/F18\%,4)$
$\text{NPV}=471,420+\left(6,000X+980\right)/\left(1+0.18\right)+\left(6,000X19,020\right)/{\left(1+0.18\right)}^{2}+$
$\left(6,000X35,020\right)/{\left(1+0.18\right)}^{3}+\left(6,000X3,520\right)/\left(1+0.18\right)4$
$\text{NPV}=16140.37X507379.19$
Now we have to find the X that makes the NPV equal to zero.
NPV = 0
$\text{16,140.37X507,379.19=0}$
X = 31.44 dollar per unit
n analysis for price per unit of production for existing machine:
Year  0  1  2  3  4 


Revenue  10,000X  10,000X  10,000X  10,000X  
 Operating cost  320,000  330,000  340,000  350,000  


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  


Net Income  6,000X  192,000  6,000X  198,000  6,000X  204,000  6,000X  210,000  


ATCF  6,000X  192,000  6,000X  198,000  6,000X  204,000  6,000X  210,000 
$\text{NPV}=\left(6,000X192,000\right)\xb7\left(P/{F}_{18\%,1}\right)+\left(6,000X198,000\right)\xb7\left(P/{F}_{18\%,2}\right)+\left(6,000X204,000\right)\xb7\left(P/{F}_{18\%,3}\right)+\left(6,000X210,000\right)\xb7\left(P/{F}_{18\%,4}\right)$
$\text{NPV}=\left(6,000X192,000\right)/\left(1+0.18\right)+\left(6,000X198,000\right)/{\left(1+0.18\right)}^{2}+\left(6,000X204,000\right)/{\left(1+0.18\right)}^{3}+\left(6,000X210,000\right)/{\left(1+0.18\right)}^{4}$
$\text{NPV}=5,084.75X162,711.86+4,309.12X142,200.52+3,651.79X124,160.7+\text{}3,094.73X108,315.66$
$\text{NPV}=16,140.37X537,388.74$
$\text{NPV=0}$
$\text{16,140.37X537,388.74=0}$
$\text{X=33.3}$ 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.