Many people find the topic of variance analysis in a standard costing environment difficult. However, the underlying principles are relatively easy to grasp when a simple example is worked through to completion. Below is an approach which is fully described and explained to solving such problems. It is advisable to pay particular attention to the checking process at the end which allows verification of the calculations performed.
It is essential for management to monitor and contain costs and revenues to ensure the successful delivery of the overriding objective of the organisation  usually delivery of increases in shareholder wealth. As a result, systems of costing are introduced within an organisation to enable management of the processes within the business.
Let's suppose a manufacturing business wishes to produce 100 units of a particular product. Of those, 80 are budgeted to be sold for $200 each  the rest are to be held in inventory. The budgeted fixed overhead are envisaged to be $4000 for the period. The standard cost card for the unit is as follows:
1 Unit
Materials: 5kg @ $6/kg = $30
Labour: 4hr @ $7/hr = $28
Variable Overheads: 4hr @ $8/hr = $32
Fixed Overheads*: = $40
TOTAL = $130
* The fixed overhead is calculated by dividing the BUDGETED fixed overhead by the BUDGETED units of production. In this case $4000/100 units = $40 each unit produced.
Actual Results
During the period the company actually manufactured only 80 units and sold 75 of those with a total revenue of $14250. In addition, purchases of materials were 440kg for $1980, labour used was 340hr at a cost of $2210, variable overheads charged were 340hr at a cost of $6/hr and, finally, fixed overhead expenditure amounted to $4200.
In order to analyse this information it is useful to break the various elements into smaller segments for dissemination:
Materials Variances
The Materials Price Variance measures the difference between what the materials cost and the budgeted standard:
Actual cost: = $1980
Standard cost for 440kg @ $6/kg = $2640
Materials Price Variance: = $660 Favourable
Materials Usage Variance compares how much material was used compared to the set standard:
Actual usage: = 440kg
Standard usage for 80 units @ 5kg/unit = 400kg
Materials Usage Variance: = 40kg x standard cost $6/kg = $240 Adverse
The Total Materials Price Variance is the sum of the usage and price variances = $420 Favourable.
Labour Variances
We will also need to consider variances to the labour element of budgeted production.
The Labour Efficiency Variance analyses the actual level of output achieved by the workers in relation to the rate budgeted:
Labour Efficiency Variance = (standard time for actual output  actual time taken) x standard labour cost
= [(80 Units x 4hr)  340hr] x $7/hr = $140 Adverse
The Labour Rate Variance contrasts the rate of pay the workforce are remunerated to the budgeted pay level:
Labour Rate Variance = (Standard pay rate  actual pay rate) x hours worked
= ($7/hr  $6.5/hr) x 340hr = $170 Favourable
The Total Labour Variance is the aggregate of the efficiency and rate variances = $30 Favourable
Variable Overhead Variances
One of the most tricky aspects to this form of analysis is the variable overhead variances. But it is worth considering that these variances are just an extension of the labour rate and efficiency calculation performed above.
Variable Overhead Efficiency Variance = (standard time for actual output  actual time taken) x standard variable overhead cost
= (320hr  340hr) x $8/hr = $160 Adverse
Variable Overhead Rate Variance = (standard overhead rate  actual rate) x hours worked
= ($8/hr  $6/fr) x 340hr = $680 Favourable
Again, the total Variable Overhead Variance is the sum of the efficiency and rate variances = $520 Favourable
Fixed Overhead Variances
The budgeted number of units to be produced for the period is 100 units with the budgeted fixed overhead expenditure of $4000. By absorbing the fixed overhead costs into the produced units an accurate true cost of production can be established. This will facilitate correct decision making by management and will reflect the costs of the business accordingly. Thus, each unit of production will absorb $40 of fixed overhead. [The amount of fixed overhead allocated to each unit is referred to as the Budgeted Overhead Absorption Rate (BOAR)]. However, the information states only 80 units are produced in the period. Just because fewer units are produced does not mean to say that the costs have not been incurred and these costs will still need to be reflected in the calculations to reflect the under absorption of the overhead:
Fixed Overhead Volume Variance = Under/over production x BOAR
= 20 Units x $40/unit = $800 Adverse
It is worth remembering that the volume variance can be favourable if a greater number of units are produced as too much overhead will be absorbed into production!
We must also consider that it actual expenditure may differ to that budgeted at the period start:
Fixed Overhead Expenditure Variance = Budgeted fixed overhead  Actual cost
= $4000  $4200 = $200 Adverse
The Total Fixed Overhead Variance is the sum of the volume and price variances = $1000 Adverse
Sales Variances
As the question states, only 75 units were sold during the period out of a budgeted 80. This shortfall gives rise to a Sales Volume Variance ie a difference to the budgeted amount:
Sales Volume Variance = No. of units under/over sold x budgeted profit/unit
= 5 units x $70 = $350 Adverse
In addition to the volume variance, it is also noted that there is a variance to the budgeted selling price which leads to a Sales Price Variance. The organisation sold 75 units for a total revenue of $14250. This equates to $190/unit against a budgeted $200/unit:
Sales price variance = No. of units sold x variance to budgeted sales price
= 75 x $10/unit = $750 Adverse
The Total Sales Variance is the sum of the volume and sales price variances = $1000 Adverse
In order to see the full impact of the above variances we collate all the information together and reconcile the budgeted and actual profit as follows:
Budgeted
Profit [80 Units x ($200  $130)] 
$5600 

Material Price Variance 
$660 
Favourable 
Materials Usage
Variance 
($240) 
Adverse 
Labour Rate Variance 
$120 
Favourable 
Labour Efficiency
Variance 
($140) 
Adverse 
Variable Overhead Rate
Variance 
$680 
Favourable 
Variable Overhead
Efficiency
Variance 
($160) 
Adverse 
Fixed Overhead Volume
Variance 
($800) 
Adverse 
Fixed Overhead
Expenditure
Variance 
($200) 
Adverse 
Sales Volume Variance 
($350) 
Adverse 
Sales Price Variance 
($750) 
Adverse 
Actual
Profit 
$4470 
How can we verify that all the above data is actually correct?
A simple income/expenditure calculation should confirm the actual profit calculated.
Revenue 
$14250 
Closing inventory @
standard
cost
(5 Units x $130) 
$650 
Cost of materials 
($1980) 
Cost of labour 
($2210) 
Cost of variable
overheads 
($2040) 
Cost of fixed overhead 
($4200) 
Actual
profit 
$4470 