Question

Sun Co.’s monthly unit sales and total cost data for its operating activities of the past year follow. Management wants to use these data to predict future fixed and variable costs. (Dollar and unit amounts are in thousands.)

Month	Unit sold	Total cost	Month	Unit sold	Total cost
1	195	\(97	7	145	\)93
2	125	87	8	185	105
3	105	73	9	135	85
4	155	89	10	85	58
5	95	81	11	175	95
6	215	110	12	115	79

Required

1. Prepare a scatter diagram for these data with sales volume (in units) plotted on the horizontal axis and total costs plotted on the vertical axis.

2. Estimate both the variable costs per unit and the total monthly fixed costs using the high-low method. Draw the total costs line on the scatter diagram in part 1.

3. Use the estimated line of cost behavior and results from part 2 to predict future total costs when sales volume is (a) 100 units and (b) 170 units.

Short answer

1. The fixed cost line is represented as a horizontal line on the scatter diagram because it is constant.
2. The variable cost per unit is$0.40, and the fixed cost is $24.
3. The total cost for 100 units is$64 and for 170 units is$92.

Step-by-step solution

Definition of Variable Cost

The cost that moves in the same direction as the production level is a variable cost. The total of such cost depends on the production level, but per unit variable cost remains the same.

Scatter diagram

Calculation of fixed and variable components of the total cost

$\begin{array}{rcl}\mathrm{Variable}\mathrm{cost}\mathrm{per}\mathrm{unit}& =& \frac{\mathrm{Highest}\mathrm{activity}\mathrm{cost}-\mathrm{Lowest}\mathrm{activity}\mathrm{cost}}{\mathrm{Highest}\mathrm{activity}\mathrm{units}-\mathrm{Lowest}\mathrm{activity}\mathrm{units}}\\ & =& \frac{\$110-\$58}{215-85}\\ & =& \$0.4\\ & & \\ \mathrm{Fixed}\mathrm{cost}& =& \mathrm{Highest}\mathrm{activity}\mathrm{cost}-\left(\mathrm{Variable}\mathrm{cost}\mathrm{per}\mathrm{unit}\times \mathrm{Highest}\mathrm{activity}\mathrm{units}\right)\\ & =& \$110-\left(\$0.4\times 215\right)\\ & =& \$110-\$86\\ & =& \$24\end{array}$

Calculation of estimated cost

Particular	100 Units	170 Units
Variable cost @ $0.40 per unit	$40	$68
Fixed cost	24	24
Total cost	$64	$92