Assessing the effects of productivity changes on current profits is one way to value productivity changes. Profits change from the base period to the current period. Some of that profit change is attributable to productivity changes. Measuring the amount of profit change attributable to productivity change is defined as profit-linked productivity measurement. Assessing the effect of productivity changes on current-period profits will help managers understand the economic importance of productivity changes. Linking productivity changes to profits is described by the following rule:
Profit-Linkage Rule. For the current period, calculate the cost of the inputs that would have been used in the absence of any productivity change and compare this cost with the cost of the inputs actually used. The difference in costs is the amount by which profits changed because of productivity changes.
To apply the linkage rule, the inputs that would have been used for the current period in the absence of a productivity change must be calculated. Let PQ represent this productivity-neutral quantity of input. To determine the productivity-neutral quantity for a particular input, divide the current-period output by the input’s base-period productivity ratio:
PQ = Current-period output/Base-period productivity ratio
To illustrate the application of the profit-linked rule, let’s return to the Nevada example with input trade-offs. We must add some cost information to the data. The expanded Nevada data set is as follows:
Profit-Linkage Rule. For the current period, calculate the cost of the inputs that would have been used in the absence of any productivity change and compare this cost with the cost of the inputs actually used. The difference in costs is the amount by which profits changed because of productivity changes.
To apply the linkage rule, the inputs that would have been used for the current period in the absence of a productivity change must be calculated. Let PQ represent this productivity-neutral quantity of input. To determine the productivity-neutral quantity for a particular input, divide the current-period output by the input’s base-period productivity ratio:
PQ = Current-period output/Base-period productivity ratio
To illustrate the application of the profit-linked rule, let’s return to the Nevada example with input trade-offs. We must add some cost information to the data. The expanded Nevada data set is as follows:
Current output (2007) is 250,000 frames. From Exhibit 15-4, we know that the baseperiod productivity ratios are 4 and 0.200 for labor and materials, respectively. Using this information, the productivity-neutral quantity for each input is computed as follows:
For our example, PQ gives labor and material inputs that would have been used in 2007, assuming no productivity change. What the cost would have been for these productivity-neutral quantities in 2007 is computed by multiplying each individual input quantity (PQ) by its current price (P) and adding:2
The actual cost of inputs is obtained by multiplying the actual quantity (AQ) by current input price (P) for each input and adding
Finally, the productivity effect on profits is computed by subtracting the total current cost from the total PQ cost as follows:
The calculation of the profit-linked effect is summarized in Exhibit 15-5 on the following page. The summary in Exhibit 15-5 reveals that the net effect of the process change was favorable. Profits increased by $12,500 because of the productivity changes. Notice also that profit-linked productivity effects can be assigned to individual inputs. The increase in labor productivity creates a $187,500 increase in profits; however, the drop in materials productivity caused a $175,000 decrease in profits. Most of the profit decrease came from an increase in materials usage apparently, waste, scrap, and spoiled units are much greater with the new process. Thus, the profit-linked measure provides partial measurement effects as well as a total measurement effect. The total profit-linked productivity measure is the sum of the individual partial measures. This property makes the profit-linked measure ideal for assessing trade-offs. A much clearer picture of the effects of the changes in productivity emerges. Unless waste and scrap can be brought under better control, the company ought to return to the old assembly process. Of
course, it is possible that the learning effects of the new process are not yet fully captured and further improvements in labor productivity might be observed. As labor becomes more proficient at the new process, it is possible that the materials usage could also decrease.
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