Question 11.1: A business has the following figures for production overhead...
A business has the following figures for production overheads over the past five weeks:
| Production overheads ($) | Output |
| 30,500 | 20,000 |
| 31,000 | 22,000 |
| 28,500 | 18,000 |
| 29,000 | 19,000 |
| 29,800 | 20,000 |
These figures can be plotted on a graph and a line fit put by eye, as shown in Figure 11.4. When putting in a line of best fit in this way, the line is inevitably approximate and there is scope for error.
From this graph, estimates of fixed and variable costs can be made. The fixed costs are those associated with an output level of zero. In the graph, these are approximately $16,000. The variable cost, which is effectively the slope of the line, can be calculated by deducting the fixed costs of $16,000 from total costs at any level of output, and dividing it by that output. If we assume that the right- hand cross reflects a point of the graph at which 22,000 units of output causes $31,000 of costs, of which $16,000 is fixed, variable costs associated with an output of 22,000 must be $15,000 = $0.68 per unit of output. (The slope of the line is $15,000/22,000 units = $0.68.) Hence, if we were to produce 24,000 units, we would expect the total costs to be around $16,000 + (24,000 × $0.68) = $32,320.
If the high-low method were adopted, the process would be as follows:
| $ | Output | |
| $28,500 | 18,000 | Lowest figure |
| $31,000 | 22,000 | Highest figure |
| $2,500 (all of which is presumed to relate to the variable element of cost ) | 4,000 | Difference |
Hence, the variable cost per unit could be calculated by dividing $2,500 by 4,000 units = 62.5¢.
Since at an output level of 18,000 units variable costs would be 18,000 × 62.5¢ = $11,250, and total costs are $28,500, fixed costs can be estimated as $17,250. Clearly, these result are slightly different from those obtained when all five observations were used.
