After reviewing your request, Cougar Consulting performed an analysis to assist Lorex Pharmaceuticals in determining a target fill rate for Linatol. The target fill that we selected is intended to maximize expected contribution during the manufacturing process and was based on information contained in a report given to Cougar Consulting. The analysis that we performed is described in further detail. Current Situation Even though the automatic filling mechanism used for production can be set to a specific target fill, the information we obtained about Linatol suggested inconsistencies in the fill amount during operations.
Since revenues and specific variable costs of Linatol are directly affected by fill amounts and contribution is the difference of these costs subtracted from revenue, ultimately, contribution is affected by the inconsistent fill amounts. Once we establish how these revenues and costs are affected by the fill amounts, we need to determine how the filling mechanism will function when set at a specific target fill. These understandings will give us the information required to figure a target fill that maximizes contribution for Linatol.
Revenue Before we established a method to determine how the filling mechanism functioned at a specific target fill, we had to consider how the target fill affected the revenues and the variable costs when calculating contribution. Starting with revenue, we learned from the report that the bottles filled at or above 10 ounces would sell on the commercial market for $186 per case. On the other hand, bottles filled below the advertised 10 ounces would be sold for government use at $148. 80 per case and are referred to as “seconds. From this information, we created a formula (Figure 1) that calculated the revenue per case as a weighted average. The relationship between revenue and target fill is shown graphically in Attachment 1 Figure 1 Revenue = (% commercial) $186/case + (% seconds) $148. 80/case Costs As previously mentioned, calculating contribution for Linatol consists of subtracting specific variable costs from revenue. The variable costs related to target fill were found in the Projected Operating Profit exhibit provided to Cougar Consulting.
The first cost we determined for calculating contribution was the blending direct labor and active ingredients. To use this cost in calculating contribution, we divided the sum of these two costs by the total batch volume. The rounded cost of this calculation equaled $0. 4027 per ounce, and its positive linear relation to the fill amount is graphically shown in Attachment 2. In other words, the cost increases per unit as the fill amount increases per unit.
Another cost needed to calculate expected contribution consisted of an additional cost associated from the number of seconds produced by the automatic filling mechanism. This additional cost is a result from the special packaging required by seconds and is figured from dividing the labor rate by the number of cases the laborer can package in an hour. This cost equals $0. 7083 per case and diminishes as the fill amounts increase because a higher target fill results in less seconds produced. This relationship is shown as a graph in Attachment.
Since the cost associated for all cases is calculated in ounces, this unit was changed to cases by multiplying the cost by 12 bottles per case and a target fill amount in ounces per bottle. The additional cost per case from packaging seconds was figured by multiplying this cost by the probability of seconds created from the filling machine. This calculation will create an additional cost per case based on the number of seconds produced. The formula in Figure 2 was used to calculate costs. Figure 2 Costs = (12 bottles/case*target fill (oz)/bottle*$0. 027/oz) + (% of seconds) $0. 70833/case Statistical Survey Before we could determine a target fill to use for calculating maximum expected contribution, we needed to determine the probability of seconds produced by the automatic filling machine at different target fills. The best method we had to determine this probability came from the sample results provided in the Filling-Line Test performed by Lorex. These test results were found in Exhibit 2 from the provided report and allowed us to determine the probability of seconds produced at any target fill.
Assuming these samples were chosen truly at random and each sample was independent from one another, the sample data was analyzed and found to be very evenly distributed meaning the fill amounts precisely varied above and below the mean and median of the data set. In fact, the sample fill amounts were so evenly distributed that we could use a statistical method to determine the probability of seconds produce by the mechanism set at a specific target fill amount. For example, with a target fill amount set at 10. 2 ounces, the method used figures that 10. 6% of the bottles will be filled less than 10 ounces, and the rest will be filled at volume suitable for commercial retail. Based on this statistical method, we created a graph (Attachment 4) to show the probability of seconds produced as the target fill amount increased. Calculating Contribution Since we found a method to determine the probability of seconds that will be produced based on the target fill amount, we can determine a target fill that maximizes expected contribution per case because we have formulas for revenue and costs based on the expected production of seconds.
The completed formula is shown below as Figure 3. Figure 3 Contribution = (% commercial) $186/case + (% seconds) $148. 80/case – (12 bottles/case*target fill (oz)/bottle*$0. 4027/oz) + (% of seconds) $0. 70833/case Results The contribution formula in Figure 3 was used to determine the target fill that maximized contribution based on the probability of seconds produced. A chart was created below as Figure 4 using the formula to figure contribution at different target fills.
The results of this analysis were based on the data results from the Filling-Line Test and only apply if the filling mechanism performs consistent with these results. To ensure the filling mechanism is performing consistently with the data used for this analysis, we recommend that Lorex performs a frequent Filling-Line Test. If the data from a more recent test varies from the data used in this analysis, we also recommend that Lorex requests another analysis to be performed by Cougar Consulting to determine a new target fill that maximizes contribution for Linatol.
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