Profit$-$Linked Productivity Measurement

The profit$-$linked productivity measure is designed to evaluate a profit change from one period to the next and to determine how much of that change is related to productivity change.

Example: Carson Company produces an industrial solvent. In Year $2,$ Carson implemented a new process that was meant to reduce waste. The following data were provided for year $1$ and year $2.$

Year $1$ Year $2$

Number of gallons of solvent produced $50,00055,000$

Labor hours used $10,00010,500$

Primary material used $($lbs$.)75,00078,000$

Unit selling price of solvent $$40$ $$40$

Wages per labor hour $$20$ $$20$

Cost of material per lb$.$ $$15\mathrm{.}00$ $$14\mathrm{.}50$

Productivity ratio labor $5\mathrm{.}005\mathrm{.}24$

Productivity ratio materials $0\mathrm{.}670\mathrm{.}71$

The first step is to compare the actual cost of inputs in Year $2$ with the cost that would have occurred in Year $2$ if productivity had stayed the same as Year $1.$

Year $2$ labor hours would have been $=55,000/5\mathrm{.}00=11,000$ hours

Year $2$ material would have been $=55,000/0\mathrm{.}67=82,090$ lbs$.$

Calculate the total cost of labor and materials in Year $2,$ then calculate the cost of the labor and materials that would have been used in Year $2$ if Year $1$ productivity had been in effect.

Actual Cost in Year $2$ Cost in Year $2$ with

Year $1$ Productivity Ratios

Labor:

$($$$20\backslash$times $10,500$ hrs$.)$ $fill in the blank $2$ef$2$e$203$d$053$fe$6\_1$

$(11,000\backslash$times $$20)$ $fill in the blank $2$ef$2$e$203$d$053$fe$6\_2$

Materials:

$($$$20\backslash$times $10,500$ hrs$.)$ $fill in the blank $2$ef$2$e$203$d$053$fe$6\_3$

$(11,000\backslash$times $$20)$ $fill in the blank $2$ef$2$e$203$d$053$fe$6\_4$

Total $fill in the blank $2$ef$2$e$203$d$053$fe$6\_5$ $fill in the blank $2$ef$2$e$203$d$053$fe$6\_6$

Clearly, the company would have spent more on inputs in Year $2$ if Year $1$ productivity had been in effect. In fact, it would have spent $$69,305$ more.

The profit$-$linked productivity measure is most easily computed using the following table:

First we define abbreviations:

PQi $=$ amount of input i that would have been used for the current period if there was no change in productivity from the base period

Pi $=$ Current period price of input i

AQi $=$ Actual amount of input i used in the current period

Input PQ PQ $\backslash$times P AQ AQ $\backslash$times P $($PQ$-$AQ$)\backslash$times P

Labor $11,000$ $$220,00010,500$ $$210,000$ $$10,000$

Materials $82,0901,190,30578,0001,131,00059,305$

$$69,305$