8.1 Sales Variances and Operating Statements (Marginal and Absorption Formats)

Standard costing systems culminate in the preparation of standard cost operating statements (also known as reconciliation statements). These management reports provide a clear, auditable bridge between budgeted performance and actual operational profit by methodically categorizing every sales and production cost variance.

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1. Sales Variances

Sales variances assess the commercial performance of the marketing and sales departments. They explain why actual revenue and contribution/profit diverged from the original master budget.

Sales Price Variance

The Sales Price Variance measures the impact on profit or revenue resulting from differences between the actual selling price achieved and the standard selling price budgeted. It is calculated strictly on the actual volume of units sold:

$$\text{Sales Price Variance} = (\text{Actual Selling Price} - \text{Standard Selling Price}) \times \text{Actual Sales Units}$$

Alternatively:

$$\text{Sales Price Variance} = \text{Actual Sales Revenue} - (\text{Actual Sales Units} \times \text{Standard Selling Price})$$

• Favourable ($F$): Actual selling price exceeded standard price (e.g., premium branding, strong demand, or successful price negotiation).
• Adverse ($A$): Actual selling price was discounted below standard price (e.g., promotional price cuts, competitor discounting, or selling off slow-moving stock).

Sales Volume Variance

The Sales Volume Variance measures the financial consequence of selling a different number of units than budgeted. The valuation of this variance depends fundamentally on whether the company uses Absorption Costing or Marginal Costing.

1. Under Standard Absorption Costing

In absorption costing, each unit sold is expected to generate standard profit after absorbing all production costs:

$$\text{Sales Volume Variance (Absorption)} = (\text{Actual Sales Units} - \text{Budgeted Sales Units}) \times \text{Standard Profit per Unit}$$

2. Under Standard Marginal Costing

In marginal costing, fixed costs are fixed in total and do not change with volume. Therefore, each incremental unit sold delivers standard contribution toward fixed costs and profit:

$$\text{Sales Volume Variance (Marginal)} = (\text{Actual Sales Units} - \text{Budgeted Sales Units}) \times \text{Standard Contribution per Unit}$$

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2. Standard Cost Operating Statements

An operating statement is a structured management accounting report that reconciles budgeted figures to actual results. It enforces managerial accountability by categorizing variances under their responsible functional managers.

Architecture of an Absorption Costing Operating Statement

1. Budgeted Operating Profit: Calculated as $\text{Budgeted Sales Units} \times \text{Standard Profit per Unit}$.
2. Sales Variances:
   • Sales Price Variance
   • Sales Volume Variance (at standard profit)
   • Resulting Subtotal: Standard Profit on Actual Sales
3. Cost Variances (grouped by category):
   • Direct Material (Price and Usage)
   • Direct Labour (Rate, Efficiency, and Idle Time)
   • Variable Overhead (Expenditure and Efficiency)
   • Fixed Overhead (Expenditure and Volume [or Capacity and Efficiency])
4. Actual Operating Profit: Standard profit on actual sales adjusted for net total cost variances.

Architecture of a Marginal Costing Operating Statement

1. Budgeted Contribution: Calculated as $\text{Budgeted Sales Units} \times \text{Standard Contribution per Unit}$.
2. Sales Volume Variance (at standard contribution): Reconciles to Standard Contribution on Actual Sales.
3. Sales Price Variance: Added/subtracted to yield Actual Sales minus Standard Variable Cost of Actual Sales.
4. Variable Cost Variances:
   • Material Price and Usage
   • Labour Rate, Efficiency, and Idle Time
   • Variable Overhead Expenditure and Efficiency
   • Resulting Subtotal: Actual Contribution
5. Fixed Overheads:
   • Less: Budgeted Fixed Production Overhead
   • Adjust: Fixed Overhead Expenditure Variance (Adverse increases cost; Favourable reduces cost)
   • Resulting Subtotal: Actual Fixed Overhead
6. Actual Operating Profit: Actual Contribution less Actual Fixed Overheads.

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3. Comprehensive Master Operating Statement Worked Example

Apex Precision Systems Ltd manufactures a specialized industrial sensor. Management has compiled the following standard cost card and operational records for May:

Standard Cost Card per Unit

• Standard Selling Price: $50.00
• Direct Material: 3 kg at $5.00/kg = $15.00
• Direct Labour: 2 hours at $6.00/hour = $12.00
• Variable Overhead: 2 hours at $2.00/hour = $4.00
• Standard Variable Cost per Unit: $31.00
• Standard Contribution per Unit: $\text{\textdollar}50.00 - \text{\textdollar}31.00 = \text{\textdollar}19.00$
• Fixed Production Overhead: 2 hours at $5.00/hour = $10.00
• Standard Absorption Cost per Unit: $\text{\textdollar}31.00 + \text{\textdollar}10.00 = \text{\textdollar}41.00$
• Standard Profit per Unit: $\text{\textdollar}50.00 - \text{\textdollar}41.00 = \text{\textdollar}9.00$

Budgeted Operational Data for May

• Budgeted Sales: 10,000 units
• Budgeted Production: 10,000 units
• Budgeted Sales Revenue: $10,000 \times \text{\textdollar}50.00 = \text{\textdollar}500,000$
• Budgeted Contribution: $10,000 \times \text{\textdollar}19.00 = \text{\textdollar}190,000$
• Budgeted Fixed Overhead: $10,000 \times \text{\textdollar}10.00 = \text{\textdollar}100,000$
• Budgeted Operating Profit: $10,000 \times \text{\textdollar}9.00 = \text{\textdollar}90,000$

Actual Operational Data for May

• Actual Production: 10,500 units
• Actual Sales: 9,500 units at an average selling price of $52.00 per unit
• Actual Sales Revenue: $9,500 \times \text{\textdollar}52.00 = \text{\textdollar}494,000$
• Opening Inventory: 0 units
• Closing Inventory: $10,500 - 9,500 = 1,000 \text{ units}$
• Direct Materials: 31,000 kg purchased and used at actual cost of $155,000
• Direct Labour: 20,500 hours worked at actual cost of $128,000
• Variable Overhead incurred: $41,000
• Fixed Production Overhead incurred: $104,000

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Step-by-Step Variance Calculations

1. Sales Variances:
   • Sales Price Variance:

$$(\text{Actual SP} - \text{Std SP}) \times \text{Actual Sales} = (\text{\textdollar}52.00 - \text{\textdollar}50.00) \times 9,500 = +\text{\textdollar}2.00 \times 9,500 = \text{\textdollar}19,000 \text{ Favourable } (F)$$

• Sales Volume Variance (Absorption):

$$(\text{Actual Sales} - \text{Budget Sales}) \times \text{Std Profit} = (9,500 - 10,000) \times \text{\textdollar}9.00 = -500 \times \text{\textdollar}9.00 = \text{\textdollar}4,500 \text{ Adverse } (A)$$

• Sales Volume Variance (Marginal):

$$(\text{Actual Sales} - \text{Budget Sales}) \times \text{Std Contribution} = (9,500 - 10,000) \times \text{\textdollar}19.00 = -500 \times \text{\textdollar}19.00 = \text{\textdollar}9,500 \text{ Adverse } (A)$$

1. Manufacturing Cost Variances (based on actual production of 10,500 units):
   • Direct Material Variances:
     • Standard kg allowed: $10,500 \times 3 \text{ kg} = 31,500 \text{ kg}$ at $5.00/kg = $157,500.
     • Material Price Variance: $(31,000 \text{ kg} \times \text{\textdollar}5.00) - \text{\textdollar}155,000 = \text{\textdollar}155,000 - \text{\textdollar}155,000 = \text{\textdollar}0$.
     • Material Usage Variance: $(31,500 \text{ kg} - 31,000 \text{ kg}) \times \text{\textdollar}5.00 = +500 \times \text{\textdollar}5.00 = \text{\textdollar}2,500 \text{ Favourable } (F)$.
   • Direct Labour Variances:
     • Standard hours allowed: $10,500 \times 2 \text{ hours} = 21,000 \text{ hours}$ at $6.00/hr = $126,000.
     • Labour Rate Variance: $(20,500 \text{ hrs} \times \text{\textdollar}6.00) - \text{\textdollar}128,000 = \text{\textdollar}123,000 - \text{\textdollar}128,000 = \text{\textdollar}5,000 \text{ Adverse } (A)$.
     • Labour Efficiency Variance: $(21,000 \text{ std hrs} - 20,500 \text{ actual hrs}) \times \text{\textdollar}6.00 = +500 \times \text{\textdollar}6.00 = \text{\textdollar}3,000 \text{ Favourable } (F)$.
   • Variable Overhead Variances:
     • Variable OH Expenditure: $(20,500 \text{ hrs} \times \text{\textdollar}2.00) - \text{\textdollar}41,000 = \text{\textdollar}41,000 - \text{\textdollar}41,000 = \text{\textdollar}0$.
     • Variable OH Efficiency: $(21,000 \text{ std hrs} - 20,500 \text{ actual hrs}) \times \text{\textdollar}2.00 = +500 \times \text{\textdollar}2.00 = \text{\textdollar}1,000 \text{ Favourable } (F)$.
   • Fixed Overhead Variances:
     • Fixed OH Expenditure: $\text{Budgeted FOH} - \text{Actual FOH} = \text{\textdollar}100,000 - \text{\textdollar}104,000 = \text{\textdollar}4,000 \text{ Adverse } (A)$.
     • Fixed OH Volume (Absorption only): $(10,500 \text{ actual units} - 10,000 \text{ budget units}) \times \text{\textdollar}10.00 = +500 \times \text{\textdollar}10.00 = \text{\textdollar}5,000 \text{ Favourable } (F)$.
     • Net Fixed Overhead Under/Over Absorption: $\text{\textdollar}4,000\text{ (A)} + \text{\textdollar}5,000\text{ (F)} = \text{\textdollar}1,000 \text{ Over-absorbed } (F)$.

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Absorption Costing Operating Statement for May

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Marginal Costing Operating Statement for May

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Reconciling Absorption and Marginal Operating Profit

Notice that the actual operating profit under absorption costing ($107,000) differs from marginal costing ($97,000) by exactly $10,000.

$$\text{Absorption Profit} - \text{Marginal Profit} = \text{\textdollar}107,000 - \text{\textdollar}97,000 = \text{\textdollar}10,000$$

This difference is explained by fixed overheads absorbed into inventory:

$$\text{Profit Difference} = (\text{Closing Inventory Units} - \text{Opening Inventory Units}) \times \text{Standard FOAR per Unit}$$ $$\text{Profit Difference} = (1,000 \text{ units} - 0 \text{ units}) \times \text{\textdollar}10.00 = \text{\textdollar}10,000$$

Because production (10,500 units) exceeded sales (9,500 units), inventory increased by 1,000 units. Under absorption costing, $10,000 of fixed overhead was deferred into inventory rather than expensed in the current month.