Price variance versus quantity variance, or rate variance versus efficiency variance.
Important elements of variance analysis, when reviewing costs.
Some people struggle with price variance versus quantity variance a lot.
If you approach it in a structured way, through both formulas and graphs, it is actually fairly
easy to understand! Let me show you.
Let’s say you are investigating the difference in spending between the budgeted standard
cost of $1000 and the actual cost of $900.
That’s nice, a saving of $100.
To figure out where the saving comes from, you have to go a level below “total spending”,
by comparing the standard quantity (SQ) and standard price (SP) that drove the expected
standard cost, with the actual quantity (AQ) and actual price (AP)
that drove the actual cost.
When I talk about quantity and price, I could be talking about direct materials, for example
the number of chunks of wood that I used to build a table,
and the price I paid per chunk of wood.
That would be called a direct materials variance analysis.
When I talk about quantity and price, I could also be talking about labor cost, for example
the number of hours that a software developer spent to write a section of code, and the
hourly rate that the software developer is paid.
That would be called a labor cost variance analysis.
Both of these are areas of spending that I can apply price variance vs efficiency variance
analysis to.
Here’s the underlying data: the budget, or standard cost, assumed 8 units at $125
per unit, $1000 in total.
The actual spend consisted of 6 units at $150 per unit, $900 in total.
The total variance is therefore favorable by $100.
Let’s draw a graph to help us in the analysis.
Quantity on the horizontal axis, price on the vertical axis.
Standard quantity of 8, standard price of $125.
Actual quantity of 6, actual price of $150.
The third point that is vital in our calculations is actual quantity (AQ)
times standard price (SP).
We used fewer units, but paid a higher price per unit.
The $ savings from the units is indicated in green, the $ of additional spending from
a higher price is indicated in red.
Actual quantity at the standard price is 6 times $125 is $750.
We now have actual quantity (AQ) listed at the top twice, standard price (SP) listed
at the top twice, actual price (AP) once, and standard quantity (SQ) once.
Price variance revolves around actual price versus standard price.
6 actual units used times $25 of incremental price,
leads to an unfavorable price variance of $150.
Instead of calling it price variance, I could also call this rate variance, in case we analyze
labor hours instead of direct materials.
Price variance is actual quantity (AQ) times the difference (delta)
between the actual price (AP) and the standard price (SP).
Quantity variance revolves around actual quantity used, versus standard quantity used.
2 units less times $125 of standard price,
leads to a favorable quantity variance of $250.
Instead of calling it quantity variance, I could also call this efficiency variance,
or usage variance.
Quantity variance is the difference (delta) between the actual quantity and the standard
quantity, times the standard price.
The total variance of $100 favorable is explained by an unfavorable price variance of $150,
more than offset by a favorable quantity variance of $250.
Going back to the earlier example, maybe I hired a software engineer with a higher hourly
rate, but who codes a lot better and faster.
In total, I still save $100.
If you are visually inclined, then the surface area of the rectangles is the key to solving
the problem. Go from right to left.
Standard quantity times standard price.
Deduct the savings from using fewer units.
You now have a smaller rectangle representing the actual quantity times the standard price.
Add the unfavorable price variance from paying a higher price.
The rectangle grows again.
In total, the AQ x AP rectangle is still smaller than the SQ x SP rectangle.
Hang on a minute!
In our company we take spending that’s within budget for granted, but investigate cases
where we overspend versus budget.
We can do that as well!
Budgeted standard cost of $1000 versus actual cost of $1500.
$500 of unfavorable total variance to explain.
8 times $125, versus 10 times $150.
Construct the graph of standard quantity times standard price, and actual quantity times
actual price.
More units used, and a higher price per unit.
To split the blame between price variance (which the sourcing manager tends to be accountable
for) and quantity variance (which the manufacturing or operations manager tends to be accountable
for), we also need to plot the actual quantity times the standard price.
Unfavorable price variance of $250: 10 actual units times $25 incremental price per unit.
Unfavorable quantity variance of $250: 2 additional units used times $125 standard price per unit.
What about the complete opposite?
Budgeted standard cost of $1000 versus actual cost of $600.
$400 of favorable total variance to explain.
8 times $125, versus 6 times $100.
Construct the graph of standard quantity times standard price, and actual quantity times
actual price.
Fewer units used, and a lower price per unit.
To split the praise between price variance and quantity variance, we also need to plot
the actual quantity times the standard price.
Favorable price variance of $150: 6 actual units times $25 lower price per unit.
Favorable quantity variance of $250: 2 units less times $125 standard price per unit.
Both the sourcing manager and the operations manager get a box of chocolate!
What about this one?
Budgeted standard cost of $1000 versus actual cost of $1000.
Bull’s eye! Spot on.
No need to investigate the drivers of that one, right?
Well, let’s take a look anyway.
Better be safe than sorry.
8 times $125, versus 10 times $100.
No variance in total, as the price variance and the quantity variance offset each other.
Construct the graph of standard quantity times standard price, and actual quantity times
actual price.
More units used, but at a lower price per unit.
The graph is a bit different from previous ones, as actual quantity times standard price
is now in the top right of the dashed area.
This dashed area with the green and red stripes actually needs to be counted twice: in both
price variance as well as quantity variance.
Favorable price variance of $250: 10 actual units times $25 lower price per unit.
Unfavorable quantity variance of $250: 2 incremental units used times $125 standard price per unit.
Total variance of $0, consisting of $250 favorable price variance fully offset by $250 unfavorable
quantity variance.
Let’s explain the visual part with the overlapping price variance and quantity variance.
Once again, the surface area of the rectangles is the key to solving the problem.
Go from right to left.
Standard quantity times standard price.
Add the incremental cost of using more units.
You now have a bigger rectangle representing the actual quantity times the standard price.
Deduct the favorable price variance from paying a lower price per unit.
The rectangle shrinks again.
In total, the surface area of the AQ x AP rectangle is the same as the surface area
of the SQ x SP rectangle, but the shape of the rectangles is very different.
Let’s watch those steps again: one, two, three, four, five.
Price variance versus quantity variance.
Useful calculations to make, to go below the level of total standard cost
and total actual cost.
Price variance and quantity variance provide important insights
into the drivers of cost performance.
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