The Complete Set B Formula Sheet

Set B is mandatory, and it is the module where students most often lose marks to arithmetic conventions rather than to concepts. The formulas below are written in the order the study material introduces them. Where a sign convention decides the answer, it is stated explicitly.

Part 1Formulas by chapter

Marginal costing and CVP analysis

• Contribution = Sales − Variable cost
• P/V Ratio = Contribution ÷ Sales × 100, or Change in profit ÷ Change in sales × 100
• Break-even point (units) = Fixed cost ÷ Contribution per unit
• Break-even point (value) = Fixed cost ÷ P/V Ratio
• Margin of safety = Actual sales − Break-even sales, also equal to Profit ÷ P/V Ratio
• Margin of safety ratio = Margin of safety ÷ Actual sales × 100
• Sales required for a target profit = (Fixed cost + Target profit) ÷ P/V Ratio
• Sales for a target profit after tax = [Fixed cost + Target profit ÷ (1 − tax rate)] ÷ P/V Ratio
• Indifference point = Difference in fixed cost ÷ Difference in variable cost per unit
• Composite P/V Ratio = Total contribution of the mix ÷ Total sales of the mix × 100

Standard costing — material and labour variances

• Material cost variance = (Standard quantity for actual output × Standard price) − (Actual quantity × Actual price)
• Material price variance = Actual quantity × (Standard price − Actual price)
• Material usage variance = Standard price × (Standard quantity for actual output − Actual quantity)
• Material mix variance = Standard price × (Revised standard quantity − Actual quantity)
• Material yield variance = Standard price × (Standard quantity for actual output − Revised standard quantity)
• Labour cost variance = (Standard hours for actual output × Standard rate) − (Actual hours paid × Actual rate)
• Labour rate variance = Actual hours paid × (Standard rate − Actual rate)
• Labour efficiency variance = Standard rate × (Standard hours for actual output − Actual hours worked)
• Labour idle time variance = Standard rate × Idle hours, always adverse
• Labour mix or gang variance = Standard rate × (Revised standard hours − Actual hours worked)
• Labour yield variance = Standard rate × (Standard hours for actual output − Revised standard hours)

Standard costing — overhead variances

• Variable overhead cost variance = (Standard hours for actual output × Standard variable rate) − Actual variable overhead
• Variable overhead expenditure variance = (Actual hours × Standard variable rate) − Actual variable overhead
• Variable overhead efficiency variance = Standard variable rate × (Standard hours for actual output − Actual hours)
• Fixed overhead cost variance = Absorbed fixed overhead − Actual fixed overhead
• Fixed overhead expenditure variance = Budgeted fixed overhead − Actual fixed overhead
• Fixed overhead volume variance = Absorbed fixed overhead − Budgeted fixed overhead
• Fixed overhead capacity variance = Standard rate × (Actual hours − Budgeted hours)
• Fixed overhead efficiency variance = Standard rate × (Standard hours for actual output − Actual hours)
• Fixed overhead calendar variance = Standard rate per day × (Actual days − Budgeted days)

Sales variances

• Sales value variance = Actual sales − Budgeted sales
• Sales price variance = Actual quantity × (Actual price − Standard price)
• Sales volume variance = Standard price × (Actual quantity − Budgeted quantity)
• Sales mix variance = Standard price × (Actual quantity − Revised standard quantity)
• Sales quantity variance = Standard price × (Revised standard quantity − Budgeted quantity)
• The same set can be computed on a contribution or profit basis by substituting standard contribution or standard profit per unit for standard price.

Activity-based costing and target costing

• Cost driver rate = Total cost of the activity pool ÷ Total cost driver volume
• Overhead allocated to a product = Cost driver rate × Cost driver units consumed
• Target cost = Target selling price − Target profit margin
• Cost gap = Estimated current cost − Target cost
• Value index = Value to the customer ÷ Percentage of cost incurred
• Life cycle cost = Sum of all costs from research and development through to abandonment

Transfer pricing

• General rule (minimum transfer price) = Marginal cost + Opportunity cost of the transferring division
• Where there is spare capacity, the opportunity cost is nil and the minimum transfer price is marginal cost.
• Where the division is at full capacity, the opportunity cost is the lost contribution and the minimum transfer price becomes market price less any savings on internal transfer.
• Maximum transfer price = The lower of the external market purchase price and the net marginal revenue of the receiving division.
• Cost plus transfer price = Full cost × (1 + mark-up percentage)
• Dual pricing — the transferring division is credited at one price and the receiving division debited at another, with the difference eliminated on consolidation.

Divisional performance measurement

• Return on Investment = Divisional profit ÷ Divisional investment × 100
• Expanded as Profit margin × Asset turnover, that is (Profit ÷ Sales) × (Sales ÷ Investment)
• Residual Income = Divisional profit − (Divisional investment × Cost of capital)
• Economic Value Added = Net Operating Profit After Tax − (Capital employed × Weighted average cost of capital)
• NOPAT = Earnings before interest and tax × (1 − tax rate), adjusted for accounting distortions
• Weighted average cost of capital = (Cost of equity × Equity weight) + (Cost of debt after tax × Debt weight)

Relevant costing and decision making

• Relevant cost = Future cost + Cash cost + Differential cost. Sunk costs and committed costs are excluded.
• Material relevant cost — if in regular use, replacement cost; if not in regular use, the higher of net realisable value and value in alternative use.
• Labour relevant cost — if spare capacity exists, nil; if labour must be diverted, wages plus contribution lost.
• Contribution per unit of limiting factor = Contribution per unit ÷ Units of the limiting factor consumed. Rank products in descending order of this figure.
• Shadow price = The increase in total contribution arising from one additional unit of a scarce resource.

Learning curve

• Cumulative average time model — Y = ax^b, where Y is the cumulative average time per unit, a is the time for the first unit, x is the cumulative number of units, and b is the learning index.
• Learning index b = log of the learning rate ÷ log 2. For an 80% curve, b = log 0.80 ÷ log 2, which is approximately −0.3219.
• Total time = Cumulative average time × Cumulative units
• Incremental time for a batch = Total time for x units − Total time for the previous quantity
• Doubling of cumulative output reduces the cumulative average time to the learning rate percentage of its previous level.

Budgetary control and other ratios

• Efficiency ratio = Standard hours for actual output ÷ Actual hours worked × 100
• Activity ratio = Standard hours for actual output ÷ Budgeted hours × 100
• Capacity ratio = Actual hours worked ÷ Budgeted hours × 100
• These three are linked: Activity ratio = Efficiency ratio × Capacity ratio
• Calendar ratio = Actual working days ÷ Budgeted working days × 100
• Throughput accounting ratio = Throughput per bottleneck hour ÷ Factory cost per bottleneck hour
• Throughput = Sales − Direct material cost

Part 2Repeated questions

Part 3Recall rail