Chapter 8, Problem 59P

1.

To determine

Compute estimated cost equation for delivery costs using high-low method.

Explanation of Solution

Fixed Cost: Fixed cost refers the cost which remains constant for particular time duration and there is no effect on it of the level of production. For example, lease rental and interest on debts.

Compute variable cost.

$\begin{array}{c}\text{Variable cost}=\frac{\left(\begin{array}{l}\text{5th observation delivery costs}\\ -\text{1st observation delivery cost}\end{array}\right)}{\left(\begin{array}{l}\text{5th observation number of deliveries}\\ -\text{1st observation number of deliveries}\end{array}\right)}\\ =\frac{203,695-148,620}{16,685-11,540}\\ =\$10.7046\end{array}$

Compute fixed cost.

$\begin{array}{c}\left(\begin{array}{l}\text{5th observation }\\ \text{delivery costs}\end{array}\right)=\left(\begin{array}{l}\text{Variable cost}\\ \times \left(\begin{array}{l}\text{Number of deliveries }\\ \text{for 5th observatio}\end{array}\right)\\ +\text{Fixed cost}\end{array}\right)\\ 203,695=\left(\$10.7046\times 16,685+\text{Fixed cost}\right)\\ \text{Fixed cost}=\$25,089.29\end{array}$

Compute cost equation.

$\begin{array}{c}\text{Cost equation}=\left(\begin{array}{l}\text{Fixed cost}\\ +\text{Variable cost}\\ \times \text{Number of deliveries}\end{array}\right)\\ =\left(\begin{array}{l}\$25,089.29+\$10.71\\ \times \text{Number of deliveries}\end{array}\right)\end{array}$

2.

To determine

Compute estimated cost equation for delivery costs using regression.

Explanation of Solution

Summery output:

Regression Statistics
Multiple R	0.910908263
R square	0.82975864
Adjusted R square	0.816658007
Standard error	9317.550058
Observation	15

Table (1)

ANOVA
Particulars	df	SS	MS
Regression	1	5500711165	5.50E+09
Residual	13	1128617608	86816739
Total	14	6629328773

Table (2)

Particulars	Coefficients	Standard error	t-star
Intercept	18694.19925	19144.10277	0.976499
Number of deliveries	11.08553486	1.392672391	7.959901

Table (3)

Determine cost equation.

$\begin{array}{c}\text{Cost equation}=\left(\begin{array}{l}\text{Intercept coefficients}\\ +\left(\begin{array}{l}\left(\begin{array}{l}\text{Number of deliveries}\\ \text{in coefficients}\end{array}\right)\\ \times \text{Number of deliveries}\end{array}\right)\end{array}\right)\\ =\left(\begin{array}{l}118694.20+11.09\\ \times \text{Number of deliveries}\end{array}\right)\end{array}$

3.

To determine

Draw a graph to compute adjustments made to the regression analysis made in part 2.

Explanation of Solution

Draw a graph to compute adjustments.

Figure (1)

The graph shows that observation 8 is an outlier. There are changes for error in recording the data or something unusual happened during those period. In any event data point affects the predictive ability of the regression analysis.

4.

To determine

Explain the conclusion about various cost equation.

Explanation of Solution

In case of error in the data, it has to be rectified and regression analysis has to be rerun. If the data are accurate then the observation 8 should be estimated and dropped and rerun the regression. The results dropping the outlier is shown below:

Summary output:

Regression Statistics
Multiple R	0.989929239
R square	0.979959898
Adjusted R square	0.97828989
Standard error	3174.447074
Observation	14

Table (4)

ANOVA
Particulars	df	SS	MS
Regression	1	5913244065	5.50E+09
Residual	12	120925370.7	10077114
Total	13	6034169436

Table (5)

Particulars	Coefficients	Standard error	t-star
Intercept	10183.34352	6577.604102	1.5481843
Number of deliveries	11.54822861	0.476727891	24.223942

Table (6)

Compute cost equation.

$\begin{array}{c}\text{Cost equation}=\left(\begin{array}{l}\text{Intercept coefficient}\\ +\left(\begin{array}{l}\text{Number of deliveries}\\ \text{in coefficients}\end{array}\right)\\ \times \text{Number of deliveries}\end{array}\right)\\ =\left(\begin{array}{l}10183.34+11.55\\ \times \text{Number of deliveries}\end{array}\right)\end{array}$

In summary, the cost equations are:

High-low:

$\begin{array}{c}\text{Cost equation}=\left(\begin{array}{l}\text{Fixed cost}+\text{Variable cost}\\ \times \text{Number of deliveries}\end{array}\right)\\ =\left(\begin{array}{l}\$25,089.29+\$10.71\\ \times \text{Number of deliveries}\end{array}\right)\end{array}$

Regression with all data:

$\begin{array}{c}\text{Cost equation}=\left(\begin{array}{l}\text{Intercept coefficients}\\ +\left(\begin{array}{l}\left(\begin{array}{l}\text{Number of deliveries}\\ \text{in coefficients}\end{array}\right)\\ \times \text{Number of deliveries}\end{array}\right)\end{array}\right)\\ =\left(\begin{array}{l}118694.20+11.09\\ \times \text{Number of deliveries}\end{array}\right)\end{array}$

Regression without observation 8.

$\begin{array}{c}\text{Cost equation}=\left(\begin{array}{l}\text{Intercept coefficient}\\ +\left(\begin{array}{l}\text{Number of deliveries}\\ \text{in coefficients}\end{array}\right)\\ \times \text{Number of deliveries}\end{array}\right)\\ =\left(\begin{array}{l}10183.34+11.55\\ \times \text{Number of deliveries}\end{array}\right)\end{array}$

The controller has to be careful about use of cost equation to estimate delivery costs in the future.   While R-squared of the first regression is high, the R-squared of the regression without outlier is higher. In second regression also the t-value is higher.