The development of a fleet vehicle replacement policy for a federal government contractor.(Instructor's Note)

Maheshwari, Sharad ; Credle, Sid Howard

CASE DESCRIPTION

This case presents a scenario to develop an equipment replacement policy for a large federal government contractor. This contractor serves as a facility maintenance manager for a federal government research and development organization. The maintenance company has a medium size fleet of cars, vans, pickup trucks and specialty vehicles. Currently, there is no vehicle replacement policy in the company. However, the company keeps some maintenance records of the vehicles that can be used in the development of a vehicle replacement policy. The objective of this case is to illustrate the basics of equipment replacement decision making and the practical application of the probability and statistics. The case is appropriate for use in a production/operations management, engineering, economics, business statistics or managerial accounting courses. The case should take no more than one hour of class lecture and two hours of preparation and research time from students. Total student time should not be more than four hours including research time.

CASE SYNOPSIS

The case is a simple but realistic application of business statistics models in the area of operations management and managerial accounting. It is an ideal case at the undergraduate level where students need practical application of statistical concepts. It superimposes generally difficult subject matter of statistics with easy to understand concepts of the operating cost of a small vehicle fleet. It will allow students to integrate simple regression, expected value and probability distribution concepts into vehicle replacement modeling.

INSTRUCTORS' NOTES

Replacement Policy

In this section a vehicle replacement policy (of the most simple type) is suggested for a maintenance operation's fleet. The process considers relevant vehicle age, maintenance cost, opportunity cost of downtime, depreciation, salvage value and the cost of capital. It presents a simple method of determining which vehicle should be replaced.

Basic Cost Calculations

Table 5 indicates the calculation of major maintenance cost by vehicle age. These calculations show that vehicle maintenance costs increases with the age of the vehicle. A slight decline in 1983 and 1986 is due to sample size. There are 23 vehicles from 1989, one from 1983 and two from 1986. Table 6 indicates the average number of major breakdowns by the vehicle age. This makes age the most important variable in determining both the number of major breakdowns and the associated repair costs.

Cost Considerations in the Replacement Model

As indicated in the assumptions of the case, several cost considerations are excluded. The replacement policy needs not consider insurance, fuel, taxation, and or parking/garaging, supervision and other incidental cost associated with vehicle maintenance. In this case many of the excluded costs are not charged on the contractors accounts, but paid by the contractor/federal government directly. Thus, this policy will consider only initial purchase cost, cost of capital, major maintenance cost, opportunity cost, and opportunity cost due to catastrophic failure. Note that the all costs are calculated based on the age of the vehicle at the end of three year from now. A three-year period is used as the time period to compare old and new vehicle as new vehicles are amortized over three years by the contractor.

The replacement model could be further expanded by calculating yearly cost over useful life of each vehicle and then calculating the present value of each cash-flow. However, it is required that the model can be used for quick assessment, therefore, tedious yearly assessments are not considered. As another option an instructor can decide the level of complexity desired based on the course level and learning objective.

Replacement Model:

The replacement model is to compare the cost of maintaining a current fleet vehicle versus the total cost of buying and owing a new vehicle. When the cost of maintaining a current fleet vehicle is more than the cost of owning a new one then the current fleet vehicle should be replaced, i.e.,

Cost of maintaining current fleet vehicle over next three years >= Cost of buying and maintaining a new vehicle over next three years. (1)

Where,

Current cost of maintaining a current fleet vehicle over three years = Expected sum of major maintenance cost over three years + Expected sum of opportunity cost over three years + Expected opportunity lost due to catastrophic failure--Present value of salvage value of vehicle three years from now (2)

Current cost of buying and maintaining a new vehicle over next three years= Purchase cost of vehicle + Cost of capital + Expected sum of major maintenance cost over three years + Expected sum of opportunity cost over three years + Expected opportunity lost due to catastrophic failure--Present value of salvage value of vehicle three years from now (3)

Calculation of Costs

As shown before, the age of vehicle is one of the most important factors in determining the expected cost of maintenance due to major breakdowns. Table 4 provided data for total major maintenance cost over the three year period. The linear regression model can also be used to determine expected total maintenance cost over three years, where the vehicle's age is treated as the independent variable. The vehicle age can be calculated from the year of make of the vehicle and the year of assessment (2007.) The regression equation is given below. The R-squared value is not very high for the model (55%) due to sample characteristics; however the regression model is highly significant (probability [approximately equal to] 0)

Expected of sum of major maintenance cost over three year = (-$120.30+ $102.80 * Age of the vehicle) (4)

The expected opportunity lost cost due to major breakdowns can also be calculated based on the age of the vehicle. Table 4 has provided data for total number of major breakdowns over three year period. It is also indicated that that every major breakdown reduces productivity of two repairmen by 50% for 8 hours. That is the opportunity lost cost of each breakdown is:

Opportunity lost cost per breakdown = 50%* 2 repairman *8 hours *$40/hour/repairman = $320 (5)

Another linear regression can be used to determine the expected number of breakdowns per three year period. Again, the vehicle age is treated as the independent variable. The regression equation is given below. The R-squared value is not very high for the model (60%) due to characteristics of the sample however; regression model is highly significant (Probability . 0.)

Expected of number of failures in three year = -0.297 + 0.362 * Age of the vehicle

Expected opportunity lost cost over next three years = $320 * (-0.297 + 0.362 * Age of the vehicle) = (-$95.04 + $115.84 * Age of vehicle) (6)

The opportunity cost due to catastrophic failure can be calculated based on the probability of a catastrophic failure. A catastrophic failure is defined as vehicle being unserviceable after the failure. It is given that age of vehicles follows a normal distribution with a mean of 16 years and a standard deviation of 1.5 years {N (16, 1.5)}. The cumulative probability of catastrophic failure will rise with the age. The probability can be calculated using Z table or Excel function NORMDIST(x, mean, Standard deviation, cum).

Opportunity lost cost due to catastrophic failure = Cum. probability of failure *$1,000 = $1,000 * NORMDIST(AGE,16,1.5,1) (7)

Furthermore, an investment into a new vehicle will use company's capital for replacement of an existing asset. Once used to buy a vehicle this capital is unavailable to the company. Hence, there will be an opportunity loss as capital is consumed for replacement purposes. A cost of capital and discount rate are provided as 10% per year. It is stated that a vehicle is depreciated over three years using straight line method. The net present value of cost of capital will be 17%, where cost of capital is calculated based on the book value of the vehicle. The cost of capital factor of 17% is calculated using Excel net present value formula, NPV(r, cost of capital each year for three years), i.e., NPV(10%,$1*10%, ($1-$1/3)*10%,($1-$2/3)*10%).

Cost of Capital = 17%* Purchase cost of the vehicle (8)

The replacement model will be as follows once equations 4, 5, 7 and 8 are substituted in the equations 1 and 2.

[(-$120.30+$102.80 * Age of the current vehicle) + (-$95.04 + $115.84 * Age of current vehicle) + $1,000*NORMDIST(Age of current vehicle,16,1.5,1)- Present value of salvage value of current vehicle three years from now) ]>=

[Purchase cost + .17*Purchase cost + (-$120.30+$102.80 * Age of the new vehicle) + (-$95.04 + $115.84 * Age of new vehicle) + $1,000*NORMDIST(Age of new vehicle,16,1.5,1)- (Present value of salvage value of new vehicle three years from now)]

That can be simplified as:

[$218.64 * Age of the current vehicle + $1,000*NORMDIST (Age of current vehicle, 16,1.5,1)- Present value of salvage value of current vehicle three years from now)]>=

[1.17* Purchase cost + $218.64 * Age of the new vehicle + $1,000*NORMDIST(Age of new vehicle,16,1.5,1)- (Present value of salvage value of new vehicle three years from now)] (9)

The present value of the salvage price of the vehicle can be obtained from sources like "Kelly Blue-Book (KBB)." Simply using the resell value of the car from KBB based on current vehicle age plus three year will eliminate any discounting requirement. The equation (9) can be automated in the EXCEL or other similar tool without much difficulty

Sharad Maheshwari, Hampton University

Sid Howard Credle, Hampton University Table 5: Avg. Maintenance Cost per Vehicle 2004-2006 by Year of Make. Year Average 3-year Major intenance Cost per Vehicle 1983 $1,553.84 1986 $1,259.48 1989 $1,885.28 1993 $1,338.45 1995 -- 2001 $353.42 2003 -- 2004 $198.48 2005 -- Table 6: Avg. Breakdowns per Vehicle for Three Year Period (2004-2006) by the Year of Make. Year of Make Average Number of Major Breakdowns per Vehicle in 3-years Period 1983 3 1986 4.5 1989 6.83 1993 5.25 1995 -- 2001 1 2003 -- 2004 0.79 2005 --