Variance Analysis: Every Formula, Every Variance, With Worked Examples

What Standard Costs Are

Standard costs are predetermined costs — what a unit should cost under efficient operating conditions. They are set at the beginning of a period based on engineering studies, historical data, and management targets for materials prices, labour rates, and overhead. Three types of standards exist: ideal standards (perfection, rarely achievable), attainable standards (challenging but achievable with efficient operation — the most common), and historical standards (based purely on past performance, which embeds inefficiencies).

A standard cost for a product consists of: standard quantity of materials × standard price per unit of material, plus standard labour hours × standard wage rate per hour, plus standard overhead rate × standard cost driver quantity. Comparing actual costs incurred to these standards produces variances that pinpoint operational deviations.

Materials Price Variance

The materials price variance (MPV) measures whether materials were purchased at a higher or lower price than standard.

Example: Standard price: $4.00/kg. Actual price: $4.50/kg. Actual quantity purchased: 12,000 kg.
MPV = ($4.50 − $4.00) × 12,000 = $0.50 × 12,000 = $6,000 Unfavourable

The purchasing manager is typically responsible for this variance. An unfavourable price variance may result from rush orders, choosing premium suppliers, or market price increases beyond the company's control. The timing of recognition: MPV is recorded at purchase, using actual quantity purchased — not quantity used.

Materials Quantity Variance

The materials quantity variance (MQV) measures whether more or fewer materials were used than the standard quantity allowed for actual production.

Example (continuing): Standard: 2 kg per unit. Actual production: 5,000 units. Standard quantity allowed: 2 × 5,000 = 10,000 kg. Actual used: 11,500 kg.
MQV = (11,500 − 10,000) × $4.00 = 1,500 × $4.00 = $6,000 Unfavourable

The production manager is responsible for this variance. Unfavourable MQV may indicate spoilage, theft, defective materials (which causes additional usage), inefficient cutting, or poor handling. Note that MQV uses standard price — this isolates the quantity decision from the price paid. Always use standard price in the quantity variance to keep the variances independent.

Labour Rate Variance

The labour rate variance (LRV) measures whether actual wages paid were higher or lower than the standard rate.

Example: Standard rate: $18.00/hour. Actual rate: $19.50/hour (overtime premium). Actual hours: 6,200.
LRV = ($19.50 − $18.00) × 6,200 = $1.50 × 6,200 = $9,300 Unfavourable

Common causes of unfavourable LRV: overtime (employees paid at premium rates), using higher-skilled (higher-paid) workers than the standard assumed, or negotiated wage rate increases. Sometimes a favourable LRV (using lower-paid workers) causes an unfavourable LEV (those workers are less efficient) — the variances are often related.

Labour Efficiency Variance

The labour efficiency variance (LEV) — also called the labour usage variance — measures whether actual hours worked were more or fewer than standard hours allowed for actual production.

Example: Standard: 1.2 hrs per unit. Actual production: 5,000 units. Standard hours allowed: 1.2 × 5,000 = 6,000 hrs. Actual hours: 6,200.
LEV = (6,200 − 6,000) × $18.00 = 200 × $18.00 = $3,600 Unfavourable

Causes include: machine downtime, poor scheduling, using inexperienced workers, or poor quality materials that take longer to process (creating a link between the materials quantity variance and the labour efficiency variance — unfavourable MQV can cause unfavourable LEV).

Overhead Spending and Volume Variances

Overhead variances are more complex and vary somewhat between textbooks. The two most commonly tested are:

Variable Overhead Spending Variance

Fixed Overhead Volume Variance

The volume variance arises because fixed overhead is applied based on standard hours for actual production, but budgeted fixed overhead is set at a planned production level. When actual production differs from planned production, the applied overhead differs from budgeted overhead — creating a volume variance. An unfavourable volume variance means the company produced fewer units than planned, failing to fully absorb fixed overhead into product costs.

Journal Entries for Variances

Standard costing systems record variances in separate variance accounts, enabling management to see at a glance where deviations occurred.

Unfavourable variances are debits (they represent additional costs beyond standard). Favourable variances are credits (they represent savings versus standard). At period-end, if immaterial, all variance accounts are closed to Cost of Goods Sold.

Connecting the Variances: The Big Picture

A good management accountant does not just report variances — they investigate the connections between them. An unfavourable MPV (buying cheap materials) might cause an unfavourable MQV (more waste because the cheap materials are inferior) and an unfavourable LEV (workers spend more time handling poor-quality inputs). Understanding these interactions is what turns variance analysis from a reporting exercise into a genuine management tool. Practise all six variances with variance analysis questions on PrepQBank.