Source: Horngren's Cost Accounting: A Managerial Emphasis, 16th ed. (Datar/Rajan), Chapters 6–7, 10–13, 19–23
Tags: CVP analysis, break-even, contribution margin, budgeting, master budget, flexible budget, variance analysis, standard costing, pricing, transfer pricing, capital budgeting, performance measurement, ROI, residual income, balanced scorecard, theory of constraints, ACCTMIS 3300
Difficulty: Intermediate to Advanced | Prerequisites: Parts 1 and 2. You need cost-behaviour classification, overhead allocation, and the manufacturing cost-flow sequence before working with budgets and variances.
Parts 1 and 2 covered how to measure and assign costs. This unit covers what managers do with that information: plan (budgeting), monitor (variance analysis), evaluate performance, make pricing and capacity decisions, and decide where to invest capital. These are the management control techniques referenced in the course's third learning goal.
The topics here are tightly connected. CVP analysis informs pricing. Budgets set the plan. Flexible budgets and variance analysis tell you where the plan went off track and why. Performance measurement closes the loop by evaluating whether managers responded effectively. Capital budgeting extends the time horizon to multi-year investment decisions.
For students heading into corporate or public accounting, budget analysis and performance measurement are unavoidable regardless of industry. These are not niche manufacturing topics.
CVP analysis determines how profit changes with volume, price, and cost structure. The master budget is the overall financial plan, and flexible budgets adjust that plan for actual volume so variances isolate price and efficiency effects separately from volume effects. Standard costing and variance analysis pinpoint where and why costs deviated from plan. Capital budgeting evaluates long-term investments using time-value-of-money methods. Performance measurement ties it all together with metrics like ROI and residual income.
Contribution margin (CM)
Sales revenue minus all variable costs. It represents the amount available to cover fixed costs and generate profit. Can be expressed in total, per unit, or as a ratio.
In simple terms, every unit sold "contributes" this amount toward paying off fixed costs. Once fixed costs are covered, each additional unit's contribution margin goes straight to profit.
Break-even point
The level of sales (in units or revenue) at which total revenue equals total costs, resulting in zero profit. Below break-even, the firm has a loss; above it, a profit.
Margin of safety
The excess of actual (or budgeted) sales over break-even sales. It measures how much sales can drop before the firm incurs a loss.
In simple terms, it is the cushion between where you are and where you start losing money.
Operating leverage
The degree to which a firm's cost structure is weighted toward fixed costs rather than variable costs. Higher operating leverage means profit is more sensitive to changes in sales volume, both upward and downward.
Master budget
The comprehensive financial plan for the organisation, covering a specific period (usually one year). It includes the operating budget (sales budget, production budget, direct materials budget, etc.) and the financial budget (cash budget, budgeted income statement, budgeted balance sheet).
Static budget
A budget prepared for a single planned level of activity. It does not adjust if actual volume differs from the plan.
Flexible budget
A budget that adjusts revenue and variable costs for the actual level of output achieved, while keeping fixed costs and budgeted prices/rates unchanged. It allows a meaningful comparison: was the difference from plan caused by volume being different, or by prices and efficiency being different?
Variance
The difference between an actual result and a budgeted (or standard) amount. Favourable (F) if the actual result improves operating income; unfavourable (U) if it worsens it.
Standard cost
A carefully predetermined cost for one unit of output, based on efficient operating conditions. Standards are set for direct materials (price and quantity), direct labour (rate and hours), and overhead.
Direct materials price variance
(Actual Price – Standard Price) x Actual Quantity Purchased. Measures whether the firm paid more or less per unit of material than planned.
Direct materials efficiency variance (quantity variance)
(Actual Quantity Used – Standard Quantity Allowed) x Standard Price. Measures whether the firm used more or less material than the standard allows for the actual output.
Direct labour rate variance
(Actual Rate – Standard Rate) x Actual Hours Worked. Measures whether the hourly wage paid was higher or lower than planned.
Direct labour efficiency variance
(Actual Hours Worked – Standard Hours Allowed) x Standard Rate. Measures whether workers took more or fewer hours than the standard allows for the actual output.
Variable overhead spending variance
(Actual Variable OH Rate – Budgeted Variable OH Rate) x Actual Allocation-Base Hours. Measures whether variable overhead cost per hour was higher or lower than budgeted.
Variable overhead efficiency variance
(Actual Allocation-Base Hours – Standard Hours Allowed) x Budgeted Variable OH Rate. Measures whether the allocation base (e.g., machine hours) was used more or less efficiently than the standard.
Fixed overhead budget variance (spending variance)
Actual Fixed OH – Budgeted Fixed OH. Measures whether total fixed overhead spending was more or less than planned.
Fixed overhead volume variance (production-volume variance)
Budgeted Fixed OH – Fixed OH Applied (Standard Hours Allowed x Fixed OH Rate). Measures the impact of producing more or fewer units than the denominator level used to set the fixed OH rate. An unfavourable volume variance means under-utilisation of capacity.
Capital budgeting
The process of evaluating long-term investment proposals. The main methods are net present value (NPV), internal rate of return (IRR), payback period, and accounting rate of return (ARR).
Net present value (NPV)
The sum of the present values of all future cash inflows and outflows of a project, discounted at the required rate of return. A positive NPV means the project earns more than the cost of capital.
Internal rate of return (IRR)
The discount rate at which the NPV of a project equals zero. If the IRR exceeds the required rate of return, the project is acceptable.
Return on investment (ROI)
Operating income / Invested capital. Widely used to evaluate divisional performance. A higher ROI suggests more efficient use of assets, but it can discourage managers from accepting projects that earn above the cost of capital but below the division's current ROI.
Residual income (RI)
Operating income minus (Required rate of return x Invested capital). Unlike ROI, residual income encourages managers to accept any project earning above the required rate of return, because it adds to the absolute RI even if it lowers the percentage ROI.
Transfer price
The price charged when one division of a company sells goods or services to another division of the same company. Transfer pricing affects divisional performance measurement and can influence managerial decision-making and tax liabilities.
Theory of constraints (TOC)
A management approach that focuses on identifying and managing the binding constraint (bottleneck) that limits the organisation's throughput. The key metric is throughput contribution per unit of the constrained resource.
CVP examines how changes in selling price, variable cost per unit, fixed costs, and sales volume affect profit.
Key assumptions: costs are linear within the relevant range, sales mix is constant (for multi-product analysis), and inventory levels do not change.
Contribution margin per unit = Selling price per unit – Variable cost per unit.
Contribution margin ratio = CM per unit / Selling price per unit.
Break-even in units = Total Fixed Costs / CM per Unit.
Break-even in revenue = Total Fixed Costs / CM Ratio.
Target profit in units = (Total Fixed Costs + Target Operating Income) / CM per Unit.
Margin of safety = Actual Sales – Break-Even Sales.
Degree of operating leverage = Contribution Margin / Operating Income. It tells you the multiplier: if operating leverage is 4, a 10% increase in sales yields a 40% increase in operating income.
When a firm sells more than one product, use the weighted-average contribution margin per unit (weighted by the sales mix).
Break-even in total units = Total Fixed Costs / Weighted-Average CM per Unit.
Allocate total break-even units back to individual products using the sales-mix ratio.
The master budget begins with the sales budget (the foundation; everything else derives from it).
Flow: Sales Budget → Production Budget → Direct Materials Budget → Direct Labour Budget → Manufacturing Overhead Budget → Ending Inventory Budget → COGS Budget → Selling and Administrative Expense Budget → Budgeted Income Statement.
The cash budget integrates all cash inflows and outflows, accounts for the timing of collections and payments, and shows whether borrowing is needed.
The budgeted balance sheet and budgeted income statement are the culminating outputs.
A static budget is set at one planned volume. If actual volume differs, comparing actual results to the static budget confuses volume effects with price/efficiency effects.
A flexible budget holds prices and rates at their budgeted values but adjusts to the actual volume achieved.
Static-budget variance = Actual Results – Static Budget Amount.
This can be decomposed:
Flexible-budget variance = Actual Results – Flexible Budget Amount (isolates price/efficiency differences).
Sales-volume variance = Flexible Budget Amount – Static Budget Amount (isolates the volume effect).
Favourable (F) means the variance increases operating income; unfavourable (U) means it decreases it.
Standards are set for each cost element: direct materials, direct labour, variable overhead, and fixed overhead.
Direct materials variances:
Price variance = (AP – SP) x AQ Purchased.
Efficiency (quantity) variance = (AQ Used – SQ Allowed) x SP.
Direct labour variances:
Rate variance = (AR – SR) x AH.
Efficiency variance = (AH – SH Allowed) x SR.
Variable overhead variances:
Spending variance = (Actual VOH Rate – Budgeted VOH Rate) x Actual Hours.
Efficiency variance = (Actual Hours – Standard Hours Allowed) x Budgeted VOH Rate.
Fixed overhead variances:
Budget (spending) variance = Actual FOH – Budgeted FOH.
Volume (production-volume) variance = Budgeted FOH – Applied FOH.
Variances are signals, not verdicts. An unfavourable materials price variance might mean the purchasing manager paid too much, or it might mean a market-wide price increase that no one could control.
Look for interdependencies: buying cheaper (lower-grade) materials might produce a favourable price variance but an unfavourable efficiency variance if the material causes more waste.
Investigate variances that are large, persistent, or controllable.
Cost-plus pricing: start with total cost (or variable cost), then add a markup.
Markup on full cost: Target Price = Full Cost per Unit x (1 + Markup %).
Markup on variable cost: covers fixed costs and profit within the markup.
Target costing: start with the market price the customer will pay, subtract the desired profit margin, and work backward to the allowable cost. The firm then designs the product and process to meet that cost target.
Short-run pricing decisions may accept prices above variable cost but below full cost (to contribute toward fixed costs), as long as the firm has idle capacity and no long-run negative effects.
A constraint (bottleneck) limits the rate at which the organisation can generate throughput (revenue minus direct materials cost).
To maximise profit, maximise the throughput contribution per unit of the constrained resource.
Throughput contribution = Revenue – Direct Material Costs.
Ranking products by throughput contribution per constraint-hour (or per constraint-unit) tells the manager which products to prioritise.
Steps: identify the constraint, exploit it (maximise its use), subordinate everything else to the constraint, elevate the constraint (invest to increase its capacity), repeat.
Capital budgeting evaluates long-term investments with cash flows spanning multiple years.
Net present value (NPV): discount all future net cash flows at the required rate of return, subtract the initial investment. Accept if NPV > 0.
Internal rate of return (IRR): the discount rate that makes NPV = 0. Accept if IRR > required rate of return.
Payback period: the time required to recover the initial investment from net cash inflows. Simple to calculate but ignores the time value of money and cash flows beyond the payback period.
Accounting rate of return (ARR): Average annual operating income / Initial (or average) investment. Uses accrual accounting numbers rather than cash flows, so it is conceptually weaker than NPV and IRR.
NPV is generally preferred because it directly measures the increase in firm value.
Return on investment (ROI) = Operating Income / Invested Capital. Widely used; easy to compare across divisions of different sizes. Drawback: may discourage investment in projects that earn above the cost of capital but below the division's current ROI.
Residual income (RI) = Operating Income – (Required Rate of Return x Invested Capital). Eliminates the ROI disincentive problem.
Economic value added (EVA) is a specific form of residual income popularised by Stern Stewart, using adjusted accounting measures and the weighted-average cost of capital (WACC).
Balanced scorecard: a performance measurement framework with four perspectives: financial, customer, internal business process, and learning and growth. It broadens evaluation beyond financial metrics alone.
When divisions trade internally, the transfer price affects each division's reported profit.
General guideline for setting the minimum transfer price:
Minimum transfer price = Incremental cost per unit + Opportunity cost per unit to the selling division.
Common methods: market-based, cost-based (variable or full cost), and negotiated.
Market-based transfer prices are generally preferred when an active external market exists, because they lead to decisions consistent with the firm's overall interest.
CVP:
Break-Even Units = Fixed Costs / CM per Unit
Break-Even Revenue = Fixed Costs / CM Ratio
Target Profit Units = (Fixed Costs + Target Profit) / CM per Unit
Degree of Operating Leverage = Contribution Margin / Operating Income
Variances (general form):
Price/Rate Variance = (Actual Price – Standard Price) x Actual Quantity
Efficiency/Quantity Variance = (Actual Quantity – Standard Quantity Allowed) x Standard Price
Fixed overhead volume variance:
Volume Variance = Budgeted Fixed OH – (Standard Hours Allowed x Fixed OH Rate)
NPV:
NPV = Σ [Cash Flow_t / (1 + r)^t] – Initial Investment
ROI:
ROI = Operating Income / Invested Capital
Residual Income:
RI = Operating Income – (Required Rate x Invested Capital)
TOC throughput contribution per constraint unit:
Throughput Contribution per Constraint Unit = (Revenue per Unit – Direct Materials per Unit) / Constraint Units Required per Unit
CVP analysis is how a restaurant owner decides how many covers per night are needed to break even, or how a SaaS company determines its subscriber target for profitability. Flexible budgets are used by virtually every sizeable company to evaluate departmental performance, because comparing actual costs at 110,000 units to a budget built for 100,000 units is meaningless without adjusting for volume.
The theory of constraints is applied in manufacturing scheduling (which product to run through a bottleneck machine first) and in service settings (which patients to schedule in a limited number of operating rooms to maximise throughput). Capital budgeting drives decisions from whether to buy a new machine to whether to build an entire new facility.
"A favourable variance is always good." A favourable materials price variance from buying cheap materials may cause unfavourable efficiency variances from higher waste rates. Variances must be read together.
"The static budget is useless once actual volume is known." The static budget is still needed to compute the sales-volume variance. The flexible budget isolates price and efficiency effects; the sales-volume variance isolates the volume effect. Both matter.
"Payback period is a reliable capital budgeting criterion." Payback ignores the time value of money and ignores cash flows that occur after the payback period. A project with a quick payback can still have a negative NPV.
"A division with a lower ROI is always performing worse." A newer division with heavy recent investment may have a lower ROI temporarily. Residual income can be a better measure in this situation because it rewards any return above the cost of capital.
⚠️ CVP calculations, especially break-even in units and target-profit analysis, are very likely exam questions. Know the formulas cold and be able to handle multi-product CVP with a weighted-average contribution margin.
⚠️ Variance analysis is typically the most heavily tested area. Be able to compute all four pairs of variances (materials, labour, variable OH, fixed OH) and interpret them. Watch for interdependencies between price and efficiency.
⚠️ Know the difference between a static budget, a flexible budget, and actual results. Be able to decompose the static-budget variance into the flexible-budget variance and the sales-volume variance.
⚠️ For capital budgeting, be comfortable computing NPV given a table of cash flows and a discount rate. Know why NPV is theoretically preferred over IRR and payback.
⚠️ ROI vs. residual income: understand the behavioural incentive problem with ROI (a manager may reject a project that benefits the firm) and how residual income fixes it.
⚠️ Theory of constraints questions ask you to rank products by throughput contribution per unit of the scarce resource. Do not rank by contribution margin per unit or by revenue per unit; rank by contribution per constraint-unit.
Fill in the blank: Break-even in units equals total fixed costs divided by __________.
True or false: A flexible budget adjusts both fixed and variable costs for the actual level of output.
Fill in the blank: The direct labour efficiency variance is calculated as (AH – SH Allowed) x __________.
True or false: NPV and IRR will always rank mutually exclusive projects in the same order.
True or false: Under the theory of constraints, products should be ranked by their contribution margin per unit.
Answers: 1. Contribution margin per unit. 2. False (it adjusts only variable costs and revenues; fixed costs remain at the budgeted amount). 3. Standard rate (SR). 4. False (they can rank differently due to differences in scale or timing of cash flows). 5. False (rank by throughput contribution per unit of the constrained resource).
Q: A product sells for £50, has a variable cost of £30 per unit, and total fixed costs are £200,000. What is the break-even point in units and in revenue?
A: CM per unit = £50 – £30 = £20. Break-even units = £200,000 / £20 = 10,000 units. CM ratio = £20 / £50 = 0.40. Break-even revenue = £200,000 / 0.40 = £500,000.
Q: A company budgeted 10,000 units of output with total variable costs of £80,000 and fixed costs of £50,000. Actual output was 12,000 units with actual variable costs of £100,000 and actual fixed costs of £52,000. Compute the flexible-budget variance for total costs.
A: Flexible budget at 12,000 units: variable costs = (£80,000 / 10,000) x 12,000 = £96,000; fixed costs = £50,000 (unchanged). Flexible budget total = £146,000. Actual total = £100,000 + £52,000 = £152,000. Flexible-budget variance = £152,000 – £146,000 = £6,000 unfavourable.
Q: The standard for direct materials is 3 kg per unit at £5 per kg. During the period, 4,500 kg were purchased and used to produce 1,400 units. The actual price paid was £5.20 per kg. Compute the materials price variance and the materials efficiency variance.
A: SQ allowed = 1,400 x 3 = 4,200 kg. Price variance = (£5.20 – £5.00) x 4,500 = £900 U. Efficiency variance = (4,500 – 4,200) x £5.00 = £1,500 U.
Q: A firm is considering a project costing £100,000 that will generate net cash inflows of £30,000 per year for 5 years. The required rate of return is 10%. The present value of an annuity of £1 for 5 years at 10% is 3.7908. Should the firm accept the project based on NPV?
A: NPV = (£30,000 x 3.7908) – £100,000 = £113,724 – £100,000 = £13,724. NPV is positive, so the project should be accepted.
Q: Division A has operating income of £180,000 and invested capital of £1,200,000. The required rate of return is 12%. Compute ROI and residual income.
A: ROI = £180,000 / £1,200,000 = 15%. RI = £180,000 – (0.12 x £1,200,000) = £180,000 – £144,000 = £36,000.
CVP analysis relies on the cost-behaviour classifications from Part 1 (variable vs. fixed). Variance analysis uses the overhead allocation mechanics from Part 2 (the predetermined overhead rate becomes the standard overhead rate). Performance measurement connects to transfer pricing and capital budgeting because ROI and residual income are used to evaluate whether divisional managers made good investment and operational decisions. The theory of constraints links back to relevant-cost analysis and opportunity cost from Part 1.
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