Cost function using high-low and regression; quality of cost estimates Following are sales and administrative cost data for Big Jack Burgers for four

Cost function using high-low and regression; quality of cost estimates

Following are sales and administrative cost data for Big Jack Burgers for four months:

 Administrative cost is a mixed cost, and sales is a potential cost driver.

Required

(a)          Using the high-low method, create a cost function for administrative costs.

(b)          In your own words, explain why the high-low method might not be a good method for estimating the cost function.

(c)           Create a scatter plot and add a trend line. After examining the plot, use your judgement to determine whether the cost is fixed, variable, or mixed.

(d)          Perform regression analysis to create a cost function for administrative costs.

(e)           Can we know for certain that the cost function from part (d) provides a good estimate for next month’s administrative costs? Why or why not?

(f)           Discuss whether sales are an economically plausible driver for administration costs for Big Jack Burgers.(a)     Total revenue (TR) instead of quantity (Q) in the cost function because sales is a potential cost driver. Under the high-low method, the cost function is calculated using the highest and lowest values of the cost driver. First, the variable cost is calculated:

($68 333 – $43 333)/($1 132 100 – $632 100)

= $25 000/$500 000

= 0.05  or 5% of sales

The fixed cost is determined by substituting the variable cost into one of the high-low data points:

$68 333 = F + 5%×$1 132 100

F = $68 333 – $56 605 = $11 728

Thus, the total cost function is:

TC = $11 728 + 5%×Sales

(b)        The high-low method uses the most extreme cost driver values, which could

be outliers, that is, not represent the cost most of the time. That means that the cost function might not represent the actual cost, on average. Therefore, this cost function might provide poor estimates of future costs.

(c)     Chart of data with trend line added by Excel; trend line extended to Y-axis (dashed line) using Word:

It appears that the cost is most likely mixed. There is a general downward slope     (variable cost) that appears to meet the intercept enough above zero to suggest a    fixed cost. The upward slope of the line indicates that there are variable costs.

(d)     Following is the regression output. A t-statistic greater than 2 is often interpreted as meaning that the coefficient is significantly different from zero. Notice that the t-statistic for the intercept coefficient is 2.172, but the p-value is greater than 10% at 0.162. Based on the p-value, there is a 16% probability that the intercept (fixed cost) is not different from zero. Because this regression has few observations, the p-value result for the t-statistic is atypical. Additional judgement is required to decide whether it is appropriate to include a fixed cost in the cost function.

          Analysis at the account level can be used to increase the understanding of this cost. If this cost pool includes items such as salaries and other fixed costs (insurance, etc.), the regression intercept can be used as an estimate of the fixed costs. Then, the cost function would be TC = $16 800 + 4.5% × sales. Alternatively, analysis at the account level might indicate that there are few fixed costs. In that case, fixed costs are likely to be zero and would be excluded from the cost function. Then, the cost function would be: TC = 4.5% × sales

(e)     Because of unforeseen changes in cost behaviour, a cost function may not provide a good estimate for the next month’s costs. The past costs used for estimation might not be representative, especially because so few observations were used in the estimation. Sales might not be the activity that drives administrative costs. There might be a change in business operations or in the economy that would cause future costs to be different than in the past. There might be a large discretionary component in administrative costs, causing fluctuations in cost that are unrelated to any cost driver.

(f)      The cons of the high-low method as an estimation technique were discussed in Part B above. If there are only two or three data points, however, the high-low method may be the best option available. This method can be used in cases where there is not enough data to perform regression, and it can be further improved by adopting more representative data points than the highest and lowest values of the cost driver. If there are more data points, regression analysis incorporates all of the observations into the analysis. Therefore, the results rely on more complete information and provide a better estimate, on average. Both methods assume that the cost function is linear and that all data points come from a single relevant range. If these assumptions do not hold, then both methods may be unsuitable for estimating future costs. In addition, both of these methods assume that the data points are representative of future costs. Unusual cost items are assumed to continue in the future, and possible changes in costs such as those described in Part E are ignored.