Source: Final Exam Review, Cost Accounting, The Ohio State University
Tags: variable overhead, fixed overhead, spending variance, efficiency variance, production-volume variance, allocated overhead, budgeted overhead, overhead rate, cost-allocation base, machine hours, setup hours, batch-level costs
Difficulty: Intermediate to Advanced | Prerequisites: Flexible budgets and direct cost variances (see companion notes), variable vs. fixed cost behaviour.
Overhead variance analysis extends the price-and-efficiency framework you already know from direct materials and direct labour, but with a twist. Variable overhead has a spending variance and an efficiency variance, just like direct costs. Fixed overhead, however, does not vary with volume by definition, so it gets a spending variance and a production-volume variance instead. The production-volume variance exists purely because of how fixed overhead is allocated to units using a predetermined rate. It disappears if you do not allocate fixed overhead to products.
This topic trips students up because the mechanics look similar to direct cost variances but the logic behind fixed overhead is fundamentally different. Spend time understanding why the production-volume variance exists, not just how to calculate it.
Variable overhead variances work like direct cost variances: a spending variance (price) and an efficiency variance (quantity of the allocation base). Fixed overhead variances split into a spending variance (actual vs. budgeted fixed overhead) and a production-volume variance (budgeted vs. allocated fixed overhead, driven by the gap between actual and denominator-level output). An unfavourable spending variance means the actual rate per unit of cost-allocation base exceeded the budgeted rate.
Variable overhead spending variance
(Actual rate per unit of allocation base - Budgeted rate) x Actual quantity of allocation base used. Measures whether the company paid more or less per unit of allocation base than planned. Think of it as the "price" variance for variable overhead.
Variable overhead efficiency variance
(Actual quantity of allocation base - Standard quantity of allocation base allowed for actual output) x Budgeted rate. Measures whether the company used more or fewer units of the allocation base than the standard allowed for actual output. Think of it as the "usage" variance for variable overhead, driven by how efficiently the allocation base (e.g. machine hours) was used.
Fixed overhead spending variance
Actual fixed overhead - Budgeted fixed overhead. Measures whether total fixed overhead spending was higher or lower than the budget. In simple terms, did you spend more or less on fixed costs than you planned? This has nothing to do with volume.
Production-volume variance (denominator-level variance)
Budgeted fixed overhead - Allocated fixed overhead. Allocated fixed overhead = Budgeted fixed overhead rate per unit x Actual output. This variance arises because fixed overhead is spread across units using a predetermined rate; when actual output differs from the denominator level used to set that rate, the amount allocated differs from the budget. Think of it as the gap between what you budgeted for fixed overhead and what you "charged" to production through the allocation rate.
Budgeted variable overhead rate
Total budgeted variable overhead / Budgeted quantity of the allocation base. This is the rate per machine-hour (or per labour-hour, etc.) used in standard costing.
Fixed overhead allocation rate
Total budgeted fixed overhead / Denominator-level output (budgeted units or budgeted allocation-base quantity).
Cost-allocation base
The measure used to assign overhead to products (e.g. machine-hours, direct labour hours, setup hours). Choosing the right base matters because the efficiency variance reflects how well this base was used.
Given data:
Budgeted output: 29,000 units
Budgeted machine-hours: 10,150
Budgeted variable manufacturing overhead: $324,800
The budgeted variable overhead cost rate per output unit = $324,800 / 29,000 = $11.20 per unit.
Note: the rate per machine-hour = $324,800 / 10,150 = $32 per machine-hour. The exam asked for per output unit, not per machine-hour, so divide by units.
Given data:
Actual production: 90,000 units (same as budget)
Actual machine-hours: 9,800 at $5.15 per hour
Budgeted machine-hours: 9,000 at $5.05 per hour
Spending variance: (Actual rate - Budgeted rate) x Actual hours = ($5.15 - $5.05) x 9,800 = $0.10 x 9,800 = $980 unfavourable
The company paid $0.10 more per machine-hour than budgeted, across 9,800 actual hours.
What an unfavourable variable overhead spending variance means: It can be safely assumed that the actual rate per unit of the cost-allocation base is higher than the budgeted rate. The company is paying more per machine-hour (or per labour-hour, etc.) than planned.
Given data:
Actual production: 55,500 units
Static-budget production: 55,000 units
Actual machine-hours: 985
Budgeted machine-hours: 1,100
Actual fixed overhead: $50,500
Budgeted fixed overhead: $50,600
Fixed overhead allocation rate per unit: $50,600 / 55,000 units = $0.92 per unit
Fixed overhead allocated to production: $0.92 x 55,500 actual units = $51,060
Fixed overhead spending variance: Actual fixed overhead - Budgeted fixed overhead = $50,500 - $50,600 = -$100 → $100 favourable (Spent $100 less than budgeted on fixed overhead.)
Production-volume variance: Budgeted fixed overhead - Allocated fixed overhead = $50,600 - $51,060 = -$460 → $460 favourable (Produced more than the denominator level, so more overhead was allocated than budgeted, which is favourable.)
This example adds complexity because the cost-allocation base is setup-hours (a batch-level cost driver), not a unit-level measure.
Given data:
Actual: 15,000 units, 250 units/batch = 60 batches, 5 setup-hours/batch = 300 setup-hours, $40/setup-hour variable, $12,000 fixed
Static budget: 11,250 units, 225 units/batch = 50 batches, 5.25 hours/batch = 262.5 setup-hours, $38/setup-hour variable, $9,975 fixed
Step 1: Calculate the flexible-budget setup hours. Flexible budget adjusts to actual output but uses budgeted efficiency. Flexible-budget batches: 15,000 units / 225 units per batch = 66.67 batches Flexible-budget setup-hours: 66.67 x 5.25 = 350 hours
Actual setup-hours: 60 batches x 5 hours = 300 hours
Variable overhead efficiency variance: (Actual hours - Flexible-budget hours) x Budgeted rate = (300 - 350) x $38 = (-50) x $38 = -$1,900 → $1,900 favourable (Used 50 fewer setup-hours than the flexible budget allowed.)
Variable overhead spending variance: (Actual rate - Budgeted rate) x Actual hours = ($40 - $38) x 300 = $2 x 300 = $600 unfavourable (Paid $2 more per setup-hour than planned.)
Fixed overhead spending variance: Actual fixed costs - Budgeted fixed costs = $12,000 - $9,975 = $2,025 unfavourable
Fixed overhead production-volume variance: Budgeted fixed overhead rate per setup-hour = $9,975 / 262.5 = $38 per setup-hour
Allocated fixed overhead = $38 x 300 actual setup-hours = $11,400 Wait, that gives a different answer. Let me reconsider.
The production-volume variance compares budgeted fixed overhead to allocated fixed overhead. Allocated = rate x actual allocation-base quantity. Rate = $9,975 / 262.5 = $38 per setup-hour. Allocated = $38 x 300 = $11,400. But wait: some formulations use the flexible-budget hours or denominator hours.
Actually, allocated fixed overhead uses the budgeted rate x actual quantity of the allocation base: $38 x 300 actual setup-hours = $11,400. Production-volume variance = Budgeted - Allocated = $9,975 - $11,400 = -$1,425.
Hmm, the exam answer is $3,325 favourable. Let me reconsider using output units.
Alternative: Allocated fixed overhead = budgeted FOH rate per unit x actual units. Rate per unit = $9,975 / 11,250 = $0.8867 per unit. Allocated = $0.8867 x 15,000 = $13,300. Production-volume variance = $9,975 - $13,300 = -$3,325 → $3,325 favourable.
This approach works because more units were produced than the denominator level (15,000 vs. 11,250), so more fixed overhead was allocated than budgeted. The exam answer confirms: $3,325 favourable (C).
The key lesson: the production-volume variance is driven by the difference between actual output and budgeted (denominator) output, multiplied by the fixed overhead rate per unit.
Production-volume variance = (Denominator units - Actual units) x Budgeted FOH rate per unit = (11,250 - 15,000) x $0.8867 = (-3,750) x $0.8867 = -$3,325 → favourable.
Variable overhead spending variance: (Actual rate - Budgeted rate) x Actual allocation-base quantity
Variable overhead efficiency variance: (Actual allocation-base quantity - Standard allocation-base quantity for actual output) x Budgeted rate
Fixed overhead spending variance: Actual fixed overhead - Budgeted fixed overhead
Fixed overhead production-volume variance: (Denominator output - Actual output) x Budgeted fixed overhead rate per unit Or equivalently: Budgeted fixed overhead - (Budgeted FOH rate per unit x Actual output) Unfavourable when actual output < denominator; favourable when actual output > denominator.
Fixed overhead allocated to production: Budgeted fixed overhead rate per unit x Actual output units
Budgeted variable overhead rate per allocation-base unit: Total budgeted variable overhead / Budgeted allocation-base quantity
Students often confuse the variable overhead efficiency variance with a "price" concept. It is not about the price of overhead. It measures how efficiently the allocation base (machine-hours, setup-hours) was used. If workers use more machine-hours than the standard, variable overhead goes up simply because overhead is applied on machine-hours.
The production-volume variance does not exist for variable overhead. It is unique to fixed overhead and exists only because of the allocation process. If you did not allocate fixed overhead to units, this variance would not arise.
Students sometimes calculate the fixed overhead spending variance using allocated amounts. It is simply: actual fixed overhead minus budgeted fixed overhead. Allocation plays no role here.
A favourable production-volume variance means more was produced than the denominator level. This sounds good, but it may also signal overproduction or inventory build-up, not necessarily a positive outcome.
⚠️ The variable overhead spending variance uses actual hours, not budgeted hours and not standard hours for actual output.
⚠️ The production-volume variance = (denominator - actual output) x FOH rate. Favourable when actual > denominator. This is a very common exam calculation.
⚠️ Fixed overhead allocated to production = FOH rate per unit x actual units produced. Do not confuse this with budgeted or actual fixed overhead.
⚠️ For batch-level costs (like setup), the allocation base is setup-hours, not units. Be careful to convert units into batches, then batches into setup-hours.
⚠️ When the exam says "variable overhead spending variance is unfavourable," the safe conclusion is that the actual rate per unit of cost-allocation base exceeded the budgeted rate.
Fill in the blank: The production-volume variance arises because actual output differs from the ________ level used to set the fixed overhead rate. Denominator (budgeted output) level.
True or false: A favourable variable overhead efficiency variance means the company used fewer allocation-base units than the standard allowed for actual output. True.
True or false: The fixed overhead spending variance depends on how many units were produced. False. It is simply actual fixed overhead minus budgeted fixed overhead. Volume does not enter this calculation.
Fill in the blank: Fixed overhead allocated to production = ________ x actual output units. Budgeted fixed overhead rate per unit.
Q: Budgeted variable overhead is $324,800 for 29,000 units. What is the budgeted variable overhead rate per output unit?
A: $324,800 / 29,000 = $11.20 per unit.
Q: Actual variable overhead rate is $5.15 per machine-hour, budgeted rate is $5.05, and 9,800 actual machine-hours were used. What is the variable overhead spending variance?
A: ($5.15 - $5.05) x 9,800 = $980 unfavourable.
Q: Actual fixed overhead is $50,500, budgeted is $50,600. What is the fixed overhead spending variance?
A: $50,500 - $50,600 = $100 favourable.
Q: Budgeted fixed overhead is $50,600 for a denominator of 55,000 units. Actual production is 55,500. What is the fixed overhead allocated to production?
A: ($50,600 / 55,000) x 55,500 = $0.92 x 55,500 = $51,060.
Q: A setup department budgeted $9,975 in fixed overhead for 11,250 units. Actual production was 15,000 units. What is the production-volume variance?
A: Rate per unit = $9,975 / 11,250 = $0.8867. Allocated = $0.8867 x 15,000 = $13,300. Variance = $9,975 - $13,300 = $3,325 favourable (more produced than denominator, so more overhead absorbed).
Q: Actual setup-hours are 300 at $40/hr. Flexible-budget setup-hours are 350 at $38/hr. What are the variable overhead spending and efficiency variances?
A: Spending = ($40 - $38) x 300 = $600 unfavourable. Efficiency = (300 - 350) x $38 = $1,900 favourable.
Overhead variances connect to activity-based costing (ABC), which uses multiple cost pools and cost drivers instead of a single allocation base, potentially producing more accurate variances. The production-volume variance ties into capacity management decisions: if a company consistently produces below its denominator level, it may be carrying excess capacity, which links back to the relevant cost decisions about whether to accept special orders to fill that capacity. Standard costing, which underpins all variance analysis, also connects to inventory valuation methods (absorption vs. variable costing), since the production-volume variance only exists under absorption costing.
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