## 5 Case Study: CV Joint Replacement in Korean Automotive Market
### Relationship between Environmental and Economic Impact  
The increased proportion of remanufactured CV joints consistently has a positive effect on reducing environmental impact. However, it has been identified that companies within the remanufacturing industry incur a loss in profit, as described in Figure 8 (profit vs. environmental impact). In Figure 8, the \(X\)-axis represents environmental impact, while the \(Y\)-axis represents total profit change. Figure 7 was generated by calculating environmental impact and profit reduction based on the assumptions explained in the previous subsections. The replacement preferences for vehicles older than seven years were fixed at 10% for new CV joints and 90% for remanufactured CV joints, respectively. The replacement preference for remanufactured CV joints was varied from 0% to 100%. The calculations were based on accumulated vehicle sales data, resulting in a linear-like relationship between environmental impact and profit. The slope of this relationship depends on the retail price, production cost, and replacement preferences. The figure indicates that environmental impact is inversely proportional to profit change. It is necessary to reduce environmental impact by increasing the proportion of remanufactured CV joints during replacements. This reduction in environmental impact  
Figure 8: Relation between economic and environmental impact. Figure 7: Total profit analysis according to profit difference between new and remanufactured products (profit gap: 0, 8, 16, and 25%). results in a profit loss for companies manufacturing new CV joints. Therefore, accurately determining the slope in Figure 8 is crucial for calculating the profit loss associated with environmental impact savings, and vice versa. The environmental impact savings \(\left(EI_{saving}=\delta X\right)\) and profit drop \(\left(P_{drop}=\delta Y\right)\) are defined in Equations (4) and (5). \[EI_{saving}=X_{now}-X_{target} \tag{4}\]  
\[P_{drop}=Y_{now}-Y_{target} \tag{5}\]  
Since the profit drop is proportional to the environmental impact savings, the slope of this relationship can be easily determined. The amount of profit drop per remanufactured CV joint can be calculated using Equation (6). The coefficient of the slope is determined by the retail price of a remanufactured CV joint. The slope is defined by dividing the profit drop by the environmental impact savings. Therefore, the total profit drop can be obtained by multiplying the slope coefficient by the environmental impact savings. Additionally, the unit profit drop is calculated by dividing the profit drop by the total number of increased remanufactured CV joints \(\left(D_{gap}\right)\). \[P_{drop/unit}=\frac{a\times EI_{saving}}{D_{gap}}\ \ \left(\text{per a remanufactured CV joint}\right) \tag{6}\]  
Once the unit profit drop is estimated, the amount of subsidy for a remanufactured CV joint replacement can be calculated by considering the preservation of the loss rate (9) using Equation (7). The profit drop caused by the increased proportion of remanufactured CV joints can be compensated by governments through tax benefits or direct financial aid for each remanufactured CV joint. If the preservation of the loss rate exceeds 100%, the preference for remanufactured CV joints can be increased by the industry or consumers. The compensated benefit is defined as \(P_{sub/unit}\). This allows governments to use the obtained subsidy as a guideline for determining the amount of subsidy to provide to the remanufacturing industry or vehicle owners to expand the market size. \[P_{sub/unit}=P_{drop/unit}\times\theta\ \ \left(\text{per a remanufactured CV joint}\right) \tag{7}\]  
Table 4 describes the amount of subsidy \(\left(P_{sub}\right)\) per increased number of remanufactured CV joints according to the retail price of remanufactured CV joints. First, all parameters in Tables 2 and 3 must be determined based on the scenario. Except for replacement preference, the parameters are generally fixed.