Developing A Cost Formula (Function) For Repairs And Maintenance Costs At Sultan Company

Background

Questions:

Sultan Company wants to develop a cost formula (function) for its repairs and maintenance costs (R&M Costs) so it can deal with its contractors in a way that helps maximizing the Company’s return. Currently, the contractors are charging the Company a monthly flat rate of 20,000 AED plus AED 20 per labor hour. Some managers argue that labor hours are the best predictor of repair and maintenance costs. Others are claiming that machine hours are a better predictor of repair and maintenance costs.

The accountant suggested collecting data about repairs and maintenance costs, number of labor hours, and number of machine hours for the last 24 months. He indicated that analyzing these data will help judge the fairness of the fees charged by the contractors.

The following table presented collected data for possible analysis:

1. Using the high-low method, estimate R&M cost formula. Do the results of the high-low method cause you any concern about the current fees charged by the contractors?
2. Employ a least-square regression analysis with the relevant data points to estimate R&M cost formula using machine hours as the cost driver. Attach the print-out of your results.
3. Employ a least-square regression analysis with the relevant data points to estimate R&M cost formula using labor hours as the cost driver. Attach the print-out of your results.
4. Which regression analysis would you consider better than the other? Do the results of the regression analysis cause you any concerns about the accuracy of the high-low method??
5. Would the results of the regression analysis cause you any concerns about the current fees charged by the contractors? 

High Low method is method of dividing a mixed cost into fixed cost and variable cost.

If total cost is given by y= a+ b*x, where a is the fixed cost and b is the variable cost per unit then the formula used to determine variable and foxed cost is

b = (y2- y1)/ (x2- x1)

y2 = total cost at highest level of activity

y1 = total cost at lowest level of activity

x2 = number of units at highest level of activity

x1 = number of units at lowest level of activity

& a = y2- b*x1

In this case, Y (R&M cost) = a (fixed cost) + b (variable cost per unit)* (labor hours)

y1 = 64500, y2 = 99500

x1 = 7500 ,x2 = 16000

Thus b = (99500- 64500)/ (16000 – 7500) = 4.11

a = 99500 – 4.11*16000 = 33617.65 

Thus the rate that should be charged by the contractor = 33617.65 + 4.11 *labor hour.

It can be seen that the company currently charges 20000 + 20 * labor hours. Thus if the company does not get work for long hours it will be charging a low amount from the customers and if they are working for very long hours it will be charging a high amount from the customer. Thus to stay competitive in the market, the company should look at its price policy again and take corrective actions.  

Using Machine hours as input and R&M cost as out the regression analysis was conducted.

The output generated using the least regression method is given below

Thus the R squared value of the regression analysis is 0.868, the co-efficient of intercept is 44032.32 and the co-efficient of X variable 1 is 1.932.

Thus the equation of the cost can be given by

Y (R&M cost) = 1.932* X (Machine hours) + 44032.32 

Using Labor hours as input and R&M cost as out the regression analysis was conducted.

The output generated using the least regression method is given below

Thus the R squared value of the regression analysis is 0.619, the co-efficient of intercept is 50754 and the co-efficient of X variable 1 is 2.164.

Data Collection and Analysis

Thus the equation of the cost can be given by

Y (R&M cost) = 2.164* X (Labor hours) + 50754  

A linear regression analysis results in co-efficient of independent variable, co-efficient of constant term and the R square value.  The co-efficient of the independent variable is used to understand its effect on the independent variable. If the value of the co-efficient of the independent variable is positive, then the variables are positively correlated i.e. the value of dependent variable will rise with the surge in independent variable. In the first case the machine hours and R&M costs are positively correlated. Also in the second case the labor hours and R&M costs are positively correlated. Thus increase in machine hours or labor hours will cause R&M cost to increase.

The co-efficient of the constant term provides the fixed cost incurred by the company i.e. the cost that the company will suffer even if no production is done by the company. The fixed cost in both the cases are positive.

P value of a regression analysis helps us understand the statistical significance of the co-efficient obtained from the regression. It tells us how confident we can be about the relation between the dependent and independent variable. In this case we can be 95% confident about the results from the regression analysis in both the cases.

The R square value of the regression is the fraction of variation that can be forecasted by the independent variables. The R squared value helps to check how closely the data are related to each other. The R squared value varies from 0$and 1. The greater the value of R squared the more accurately the regression line can predicted the output for a particular input. In the first case the R square value for the regression between the machine hours and the R&M costs is 0.868. Thus with the help of machine hours 86% of the total cost can be predicted. In the second case the R square value for the regression between the labor hours and the R&M costs is 0.619. Thus with the help of labor hours 61% of the total cost can be predicted.

Thus we should use machine hours to determine the total cost to the company.

The equation of the cost from regression analysis is given by

Y (R&M cost) = 1.932* X (Machine hours) + 44032.32

And the equation of the cost from High low method is given by

Y (R&M cost) = 4.11* X (Machine hours) + 33617.65

Comparing both the results, it can be found that the fixed cost charged by the company using regression analysis is higher than the fixed cost charged by the company for high low method. While the variable cost per unit using regression analysis is lower than the variable cost per unit for high low method.

Thus if the company does work for longer hours then it will earn more money using high low method but if the company works for a shorter duration of time, then it should use cost variables obtained from regression analysis. 

The data obtained from regression analysis takes into account all the data points and is not dependent on the only two points as is the case with high low method. This makes it more accurate than the high low method.   

The company currently charges the customers using the equation Total cost = 20000 + 20 * labor hours.

Whereas from the regression analysis it was found that the Total cost, Y (R&M cost) = 1.932* X (Machine hours) + 44032.32

From the regression analysis it was observed that the total cost to the company can be predicted more accurately if we use machine hours instead of the labor hours. Thus the company should change the cost driver from labor hours to machine hours. Also the fixed cost charge by the company currently is less than the half it is found from the regression analysis while the rate per unit currently used is very high compared to the regression analysis.

Thus if the company continues using the current method to determine cost, and if does not get work for long hours it will be charging a low amount from the customers Whereas if they are working for very long hours it will be charging a high amount from the customer. Thus to stay competitive in the market, the company should look at its price policy again and take corrective actions and change the cost driver from labor hours to machine hours and increase the fixed cost while decreasing the variable cost per unit.  

References

High-Low Method. (n.d.). 

Frost Jim (2013). How to Interpret Regression Analysis Results: P-values and Coefficients. 

Interpreting Regression Output. (n.d.). 

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