ASSESSMENT OF ECONOMIC LIFE OF FIREFIGHTING AND RESCUE APPLIANCES BASED ON CHASSIS RENAULT MIDLUM IN THE ZLIN REGION ASSESSMENT OF ECONOMIC LIFE OF FIREFIGHTING AND RESCUE APPLIANCES BASED ON CHASSIS RENAULT MIDLUM IN THE ZLIN REGION

This paper is focused on the evaluation of economic data obtained from operational records of fire-fighting equipment with a focus on Firefighting and Rescue Appliance type of vehicles, especially on exit vehicles based on the chassis Renault Midlum, during the period 2006 - 2013. These vehicles were operated by professional units of the Fire and Rescue Service of the Zlin Region. The paper’s aim is to specify the optimum lifetime of the fire-fighting vehicles by the marginal analysis of fire-fighting vehicles’ economical operation. Theoretic calculations of the optimum lifetime have been processed with implementing both the method of exponential trends, and Brown method. The residual value of vehicles has been calculated both according to the current Czech tax law, and to the Expert Standard Valuation of motor vehicles in force in the Czech Republic. Basic characteristics of referred vehicles during


Introduction
This paper follows on previous publications of the author focused on the functional reliability assessment of Firefighting and Rescue Appliances based on the chassis Renault Midlum [1, 2 and 3]. These vehicles were deployed at professional units of the Fire and Rescue Service of the Zlin Region during the reporting period. Results of alternative calculations of theoretical economic lifetime are presented in this paper. * 1 Ladislav Janosik, 2 Ivana Janosikova, 1  Similarly, we can define by using an upward sloping exponential curve the trend of costs for maintenance and repairs N u (t) according to the equation: The total value of firefighting appliances N c (t) is a sum of equations (1) a (2): Further, we can count the local extreme of the function (3) by derivation. The local extreme (N c (t) minimum in this case) represents the optimal time T opt for replacing the appliance: After reaching the minimum point the function N c (t) rises, due to declining price of the firefighting vehicle N c (t) and increasing maintenance and repair costs N u (t). The constants A, C and exponent coefficients α, β are obtained after processing the input of economic data, building charts and drawing or exponential curve of these charts by using appropriate software, e.g. MS Excel.

Brown method
This method was first published over 55 years ago in the journal Railway Age, in Brown's paper "What's the Life of a Diesel?" Theoretical foundations were then summarized and published in 1963 [15]. The method was used for the preliminary determination lifetime of rail vehicles [11]. The optimum lifetime T opt is given by: Here, H 0 is the vehicles' acquisition value given as a percentage = 100 % and B is the linear incremental trend coefficient of the maintenance and repair costs. This coefficient is obtained likewise from the charts using linear regression of data. Application of this method is connected with some weaknesses, as discussed below in the results.

Vehicle's residual value calculations
Calculations of the vehicle's residual value according to the Act on Income Tax [13] consider the depreciation period of 5 years in Article 30 within motor vehicles for special purposes, according to the classification in Appendix No. 1 of the Act. Depreciation percentages are fixed for the first year at the level

Methods
Primary operating data [5] for the years 2010-2013 received from the information system IKIS II, were exported to Excel file format and used for failure rate of monitored vehicles evaluating. Data for the years 2005 to 2009 were investigated by the author personally from machinery service records at individual Regional Departments of the Zlin region.
Service life is the ability of the technical system to perform desired functions in order to achieve the ultimate state [6]. Economic life of the vehicle can be generally characterized as reaching the limit state when further operation is economically unsustainable [7].
The economic efficiency of the investment is calculated to assess the economic life of the technical system in the business environment. This procedure would be relatively difficult to apply for the evaluation of firefighting appliances. The methodology of these calculations is based on the input data extremely difficult to define in the sphere of public service [8 and 9]. Expected annual returns and/or annual operating costs in dealing with accidental incidents are representatives of these data. Revenues are primarily represented by preserved properties during the liquidation of accidents. Property owners and insurance companies usually have different views on the amount of damages. Forensic expert opinion and/or the court proceedings decide in these disputes thereafter. The total amount of investment, bank loans, the tax rate for the calculation of investment income taxes and annual depreciation might be examples of detectable data. Further reason for the impossibility of using this calculation method is the requirement of the initial setting of the technical system's lifetime. The approximate lifetime can be only theoretically assumed from the Machinery Service Order [10].
Therefore, the calculation of the monitored vehicles' economic life was performed by use of two simple and generally known methods, both exponential trends method, and the Brown method [11 and 12]. Calculations according to both methods were performed for 5-year operation time period. The residual value of appliances, which is one of data used for calculations, was variously calculated according to the Act No. 586/1992 Coll. on Income Taxes [13], and according to the Expert Standard No. I/2005 -Valuation of motor vehicles [14].

Exponential trend method
The exponential trends method is based on the theoretical assumption that the value of firefighting appliances in time N p (t) has the shape of downward sloping exponential curve [11]. The curve is defined by the equation: ZAD parameter is the basic percent reduction during the operation defined in Annex No. 1.4 of the Expert standard [14] and ranges from 20 % in the first year of operation to 90 % in the tenth and following year of operation. ZAP parameter [%] determines the percentage of the basic reduction for the mileage (see ibid.).

Results
Overall results of calculations are stated in the following tables and graph exemplifications of which are evident constants and coefficients exponents values used for the calculations in equations (4) and (5).
The difference of calculated results of the vehicle's residual value was set in Figs. 1 and 2, as demonstrated on the case of the vehicle registration number 3Z2 6957, deployed at the fire station Uhersky Brod. It is evident that the Expert Standard is more suitable for both longer amortization time, and mileage consideration. These factors can significantly affect the vehicle wearing. Expert Standard gives even higher residual value of the particular vehicle in the final outcome.
The difference in resulting functions of repair costs (for the same vehicle) obtained by the method of exponential trends and Brown's method can be seen in Figs. 3 and 4. The vehicle registration number 3Z2 3957 of the station Uhersky Brod was chosen as an example because due to the highest calculated value of economic life, which is closest to the expected present reality. The appliance was included into exit vehicles on December 31, 2007. Unfortunately, even in these calculations is reflected the fact that operation records were not conducted complexly before 2010 [1 and 2]. Thus, it was found that the vehicle mileage had reached 13,600 km in years 2008 and 2009 but recorded repair costs had been zero in the same period.
Results acquired by the Brown method with using linear trends are shown in Table 4. Calculations show that the Brown method application is inappropriate for fire equipment. Calculation results are completely out of reality. Correlation coefficients of each regression curve are very low. The optimal economic life calculations by the equation (5) for negative values of constant B cannot be accomplished thereafter.
Recovery time in accordance with the Brown method Table 4 Vehicle Using this method has its disadvantages. The method was formulated for rail vehicles, which have high initial costs, and the expected optimum life is considerably longer than 10 years. For  Table 2 [13]. Table 3 presents alternative results of calculations while using the depreciation according to the Expert Standard [14]. Both results are counted when applying the method of exponential trends. As written above next to Figs. 1 and 2, the influence of valuation methods is reflected in the final size of the recovery time.
Recovery time in accordance with the Act on Income Tax  Table 2 Vehicle firefighting vehicle lifetime can be prolonged by relocating trucks from the group of emergency vehicles to reserves that are in lower service load. Using the Expert Standard for more accurate and more realistic residual vehicle value determination than using the Act on Income Tax is the next recommendation. Confirmation of the Brown method unsuitability for these calculations is the last major finding.