Cost Analysis — Final Exam Study Guide

Modules 7–10: ABC, Pricing, Master Budget, CVP

How to use this guide

Your final exam will be handwritten, closed-book, and held in person (Curtin Stadium). The lecturer has stated:

• Every calculation question will require you to show your workings. If your answer is wrong but workings are correct, you still earn marks. No workings = no partial credit.
• The exam contains both theory and calculation questions. Do not skip the theory.
• There will be one budgeting question — either a cash budget OR an operating budget. You must know how to do both.
• The budget question is the longest question. Tutor's advice: do the budget first in the exam to get it out of the way.
• ABC will likely require you to also compute the cost under traditional/simple costing first (prior knowledge from Module 5), then compute it under ABC. Be ready for both.

Round-up rule for CVP: any time units come out as a decimal (e.g., 231.2), always round UP to 232 — never down. Otherwise you have not actually broken even / hit your target.

MODULE 7 — Activity-Based Costing & Activity-Based Management

7.1 Why ABC exists: the problem of broad averaging

Broad averaging = taking total overhead and dividing it by total units (or by a single cost driver). Used in process costing and in the simple/traditional costing system from Module 5 (one cost pool, one cost driver — usually direct labour hours or machine hours).

The problem: when an organisation produces a diverse mix of products that consume overhead resources differently, one rate forces the high-volume / easy-to-make products to absorb too much overhead while low-volume / complex products absorb too little. This creates over-costing and under-costing.

Cross-subsidisation: if one product is over-costed, at least one other product must be under-costed, because total overhead is fixed at any given allocation. The "cheap-looking" product is being subsidised in the books by the "expensive-looking" one.

Strategic consequences of mis-costing

The damage is in decision-making: pricing, product mix, drop/keep, marketing focus.

7.2 When to refine the costing system (signs you need ABC)

Three drivers that have accelerated demand for refinement:

1. Increase in product diversity — different products consume different resources, so one rate can't capture them all.
2. Increase in indirect costs — as factories automate and grow, overhead dwarfs direct cost. One cost driver explains less and less of the cost behaviour (think Module 4 R² — if a single driver only explains 50% of cost variance, there are clearly others).
3. More competitive markets — wrong cost = wrong price = lost share or lost margin.

Specific signals it is time to look at ABC:

• Large indirect costs allocated with only 1–2 cost pools.
• All or most indirect costs treated as unit-level when they obviously aren't (e.g., setup costs being driven by units instead of batches).
• Products make diverse demands on resources (volume, batch size, complexity, process).
• Products you are well-suited to make show small profits; products you are poorly suited to make show large profits (a classic symptom of broad averaging — the easy/high-volume product is absorbing too much overhead).
• Operations staff dispute the reported product cost.
• Marketing staff dismiss reported costs and price from the market instead.

7.3 The three guidelines for refining any costing system

1. Direct-cost tracing — trace as many costs as economically feasible directly to the cost object. The fewer items left in the indirect bucket, the more accurate the allocation.
2. Indirect cost pools — split the one big overhead pool into multiple homogeneous pools. Homogeneous means every cost in that pool has the same cause-and-effect relationship with the same cost driver.
3. Cost allocation bases — use the actual cost driver as the allocation base wherever possible.

7.4 The four-level cost hierarchy

Every activity cost in ABC must be classified into one of four levels. The level determines what cost driver is appropriate.

Trap to avoid: you can always divide a batch-level cost by units to get a per-unit figure. That does not make it a unit-level cost. The cost is still incurred per batch, not per unit. Same for product-level and facility-level. The classification depends on when the cost is incurred, not on whether you can do the arithmetic.

7.5 The 7 steps to cost a product (same framework, ABC just does steps 3–6 multiple times)

These mirror Module 5's job costing exactly. ABC just repeats steps 3–6 once per cost pool.

1. Identify the cost object (product, service, batch).
2. Identify direct costs of the cost object (direct material, direct labour, plus anything else economically traceable — sometimes things like moulds, cleaning, maintenance can be traced).
3. Select the cost-allocation base(s) for indirect costs (i.e., the cost driver for each pool).
4. Identify the indirect cost pools associated with each base (group homogeneous costs).
5. Compute the rate per unit of each cost-allocation base = Budgeted indirect costs in pool ÷ Budgeted total quantity of cost driver.
6. Compute indirect costs allocated to the product = Rate × Actual quantity of cost driver used by the product.
7. Compute total cost = Direct costs + Allocated indirect costs.

Critical reminder for the exam: if the question asks for total/manufacturing cost per unit, you must add direct materials and direct labour to the allocated overhead. If the question only asks for overhead allocated, stop at step 6. Read the question.

7.6 ABC vs simple costing — worked illustration (from tutorial Q5-19, Q5-27, Q6)

Standard layout you should use in the exam

For each cost pool, build a small table:

Then a second table allocating to each product:

Critical: divide each pool's budgeted overhead by the total driver quantity across all products, NOT by each product's quantity separately. There is only one pool of money; it gets one rate.

Worked example — heat-testing and stress-testing services (Q5-19)

Cost pools and totals:

• Direct labour: $276,000 (traced directly: $204,000 to HT, $72,000 to ST)
• Equipment-related: $495,000, allocated by test hours. Total test hours = 90,000 (HT 50,000 + ST 40,000).
• Setup costs: $630,000, allocated by setup hours. Total setup hours = 21,000 (HT 15,000 + ST 6,000).
• Design costs: $399,000, allocated by design hours. Total design hours = 6,000 (HT 4,000 + ST 2,000).

Pool rates:

• Equipment: 495,000 / 90,000 = $5.50 per test hour
• Setup: 630,000 / 21,000 = $30 per setup hour
• Design: 399,000 / 6,000 = $66.50 per design hour

Allocate to HT:

• Direct labour: $204,000
• Equipment: 5.50 × 50,000 = $275,000
• Setup: 30 × 15,000 = $450,000
• Design: 66.50 × 4,000 = $266,000
• HT total = $1,195,000 over 50,000 test hours = $23.90/hour

Allocate to ST:

• Direct labour: $72,000
• Equipment: 5.50 × 40,000 = $220,000
• Setup: 30 × 6,000 = $180,000
• Design: 66.50 × 2,000 = $133,000
• ST total = $605,000 over 40,000 test hours = $15.13/hour

Compare to simple costing rate = 1,800,000 / 90,000 = $20/hour for both.

Interpretation: Under broad averaging, HT was under-costed ($20 vs real $23.90) and ST was over-costed ($20 vs real $15.13). HT is less profitable than the simple system suggests; ST is more profitable. Management should rebalance focus toward ST.

7.7 Benefits and limitations of ABC

Benefits

• More accurate product/service costs → better pricing, product-mix, drop/keep, and customer-profitability decisions.
• Reveals where overhead is actually being consumed → opens the door to Activity-Based Management (see 7.9).
• Better identification of unused capacity.
• Strong fit for service firms with little or no inventory but heavy indirect costs (banks, hospitals, consultancies).

Limitations

• Costly and time-consuming to implement (identifying activities, pools, drivers, measuring driver volumes) and to maintain (data must be kept current or accuracy decays).
• Estimation everywhere — pool composition, driver selection, driver measurement. ABC is only as good as the driver–cost relationships you choose. Wrong drivers = no accuracy gain.
• Often forces firms to use a second-best driver because the ideal driver has no available data, undermining the accuracy gain.
• Not GAAP-compliant for external financial reporting (ABC includes non-manufacturing costs in product cost). A firm using ABC for management decisions still needs a separate simple costing system for financial statements → potentially two systems = double the cost.
• Many firms find a less-detailed ABC "good enough" — perfect accuracy isn't worth the marginal cost.

Behavioural issues when implementing ABC

1. Get top-management support and create urgency.
2. Build a cross-functional guiding coalition along the value chain.
3. Educate and train employees — otherwise they fear ABC as a job-cutting exercise.
4. Celebrate short-run wins to prove ABC is yielding results.
5. Acknowledge that ABC is not perfect — it is a cost-estimation system.

7.8 Time-driven ABC (TDABC)

Uses time as the single allocation base across activities. Common in banks and other service firms. Not assessable in this unit — but be aware it exists.

7.9 Activity-Based Management (ABM)

ABM uses the activity information produced by ABC to manage activities, not just cost them. The core question: which activities add value and which do not?

• Value-adding = the customer is willing to pay for it.
• Non-value-adding = the customer is not willing to pay for it — the cost is borne by the firm.

Some non-value-adding activities are still necessary (e.g., inspections, internal handoffs) but are being done inefficiently — these are candidates for redesign, not elimination. Others can be eliminated entirely.

ABC/ABM benefits:

• Distinguish cost of resources used from cost of resources supplied → reveals unused capacity that can be redeployed.
• Evaluate effects of current product and process design choices, supporting redesign for cost reduction.

MODULE 8 — Pricing Decisions and Cost Management

8.1 The three influences on price

Price is governed by demand and supply, but three forces shape that:

1. Customers — set the ceiling: the maximum they will pay before walking away. Their willingness depends on features and quality.
2. Competitors — set a competitive ceiling: if rivals price lower, your customers will switch. You can guess competitors' costs by looking at their prices (they won't price below cost).
3. Costs — set the floor: the minimum you can charge. Below cost, every sale is a loss.

Which force dominates depends on the market:

8.2 Long-run vs short-run pricing

• Long-run pricing = strategic, stable across years, must recover all costs (including R&D, design, customer service across the product life cycle).
• Short-run pricing = tactical, e.g. a special order. Often only needs to cover variable cost plus some contribution, because fixed costs are sunk if capacity exists. Don't include fixed cost in a special-order price.

8.3 Market-based approach — Target Pricing & Target Costing

Used when the market sets the price (competitive markets, commodity-like products).

Sequence:

1. Target Price = what customers will pay, given competitors' offerings (market gives it to you).
2. Target Operating Income per unit = what the firm wants to earn per unit (strategic decision).
3. Target Cost per unit = Target Price − Target Operating Income per unit.
4. Compare target cost to current achievable cost. If current cost > target cost, the firm must reduce cost through value engineering to make the product at the target.

You don't get to raise the price — the market already fixed it. The only lever is cost.

Value engineering

Cross-functional analysis of the value chain to identify and eliminate non-value-adding activities (those customers won't pay for) and improve value-adding ones.

Cost incurrence vs locked-in (designed-in) costs — critical distinction

• Cost incurrence = when the cost is actually paid. Hard to change once it has happened.
• Locked-in (designed-in) cost = a future cost that has been committed by today's decisions, typically at the design stage. Not yet incurred, but already committed to be incurred.

Implication: most opportunity to reduce cost exists at the design stage, before costs are locked in. Once production starts, the room to manoeuvre shrinks dramatically. Wait until execution to question a process and you'll already be paying for it.

Pitfalls of value engineering and how to avoid them

• Targets too aggressive → employees give up. Fix: break the target into small steps (e.g., 20¢ at a time, not $1 at once); celebrate small wins.
• Cross-functional teams add too many features → product becomes bloated and cost goes UP. Fix: focus on what customers want, not what each department wants to ship.
• Endless redesign → product never launches. Fix: enforce deadlines and schedules.
• Departmental conflict over who absorbs the cuts. Fix: set targets for all functions, build teamwork.

8.4 Cost-Plus Pricing

Used in non-competitive markets and many service businesses. The price is computed from cost + a markup.

Formula: Price = Cost base × (1 + Markup %)

Or equivalently: Price = Cost base + Markup $.

Choice of cost base (matters because the smaller the base, the larger the markup must be)

Why most firms use full cost:

• Simpler to apply.
• Promotes price stability for the long run.
• Customers find it more acceptable: they expect price to recover all costs plus a reasonable profit, not just variable costs.
• A small full-cost markup looks fairer to customers than a huge variable-cost markup.

Target Rate of Return on Investment (one way to set the markup)

1. Target operating income (annual) = Investor capital × Target rate of return on investment.
2. Target operating income per unit = Annual target operating income ÷ Units produced and sold.
3. Markup per unit = Target operating income per unit; price = Cost base + Markup.
4. Markup % = Markup ÷ Cost base.

Cost-plus vs target costing — direction of the calculation

8.5 Worked illustration of target costing (Q14-35/36 logic)

Estimated current cost per unit = DM 50 + DL 30 + Variable OH 30 + Fixed OH 55 = $165.
Market price = $310.
Target operating income per unit = $165.
Target cost = 310 − 165 = $145.
Current cost is $165 → need to cut $20 per unit through value engineering (more efficient labour, less material waste, better processes).

If instead the firm used cost-plus with the $165 target profit:
Cost-plus price = 165 + 165 = $330. But the market only pays $310 — so cost-plus fails.
Only two ways to make cost-plus work at $310: (a) reduce cost, or (b) reduce target profit.

8.6 Service pricing — Time-and-Materials method

A form of cost-plus used heavily in service businesses (e.g., garages, consultants):

• Materials price = cost of materials + materials markup.
• Labour price = cost of labour + labour markup.

Two separate markups. Not the focus of this unit.

8.7 Life-cycle costing and budgeting

Product life cycle spans R&D → design → production → marketing → distribution → customer service / warranty. Costs are incurred across the whole life. Many costs (especially R&D and design) are locked in early and dominate total spend, yet under traditional financial accounting they're expensed in the period as period costs — not capitalised into the product.

Life-cycle costing/budgeting ensures the price you set will recover all costs over the product's life, not just current-period manufacturing cost. Spread R&D and design across the expected sales life so each unit absorbs its share.

Managing environmental and sustainability costs — bake them into early-stage design. Late-stage retrofitting is much costlier than early-stage design choices.

Customer life-cycle costing — consider what it costs the customer to acquire, use, maintain, and dispose of your product over its life. The higher their lifecycle cost, the less you can charge upfront. The lower their lifecycle cost, the more they will pay.

8.8 Legal and ethical pricing restrictions

MODULE 9 — Master Budget and Responsibility Accounting

9.1 What a budget is and why we make one

A budget is a plan with numbers attached — financial AND non-financial. It is most useful when integrated with strategy. Strategy and budgets influence each other in both directions: strategy shapes the budget, but feedback from the budget can change the strategy.

The budgeting cycle (3 phases)

1. Before the year — analyse past performance, market feedback, environment; plan.
2. At the start of the year — communicate financial and non-financial expectations (targets) to managers.
3. During / end of the year — measure actual performance against the budget; investigate variances; adjust strategy and budget for next period.

Advantages of budgeting

1. Coordinates and forces communication — e.g., the sales manager cannot promise 1M units if production can only make 500K. Budgeting forces those conversations.
2. Provides a performance framework — without numerical targets, "doing better" is meaningless. With a budget, results can be compared, root causes investigated, and learning extracted.
3. Motivates managers and employees — concrete targets are more motivating than vague aspirations.

Challenges

1. Time-consuming negotiation — lower-level proposals get pushed back by senior managers; back-and-forth eats time.
2. Requires genuine top-management support — if leadership pays lip service, lower managers won't take the budget seriously.
3. Must not be applied rigidly — if conditions change (e.g., a recession, a supply shock), sticking to an obsolete budget is harmful.

9.2 Master budget = Operating budget + Financial budget

Rolling budget vs static annual budget

• Annual budget — set once for 12 months. Problem: once managers hit (or clearly miss) their annual target early, they stop trying. Also hard to remember details of January when planning the next year in October.
• Rolling budget — always maintains a 12-month forward horizon. As each month closes, a new month is added at the end. Easier to plan because the last completed month is fresh in memory; keeps managers focused continuously.

9.3 Sequence and dependencies of the operating budget

Always: the first line of any sub-budget = the last line of the previous sub-budget. This is the golden rule.

1. Revenue (Sales) budget = Selling price × Units sold (per product). Easiest to prepare. Drives everything.
2. Production budget (in units, per product):
   • Sales units (from revenue budget)
   • + Target ending inventory of finished goods
   • = Total units needed
   • − Beginning inventory of finished goods
   • = Units to be produced
3. Direct materials budgets — done in two parts:
   • Materials Usage budget: convert units produced into units of each material (e.g., if 1 chair needs 0.5 kg of plastic, multiply). Sum across products to get total material usage. No inventory adjustment at this step.
   • Materials Purchases budget:
     • Material needed for production (from usage budget)
     • + Target ending inventory of raw materials
     • − Beginning inventory of raw materials
     • = Materials to purchase (in units)
     • × Cost per unit of material = Total purchase cost
4. Direct labour budget — Units produced × Labour hours per unit × Wage rate per hour. No inventory because labour can't be stored. If there are multiple labour types (e.g., assemblers vs crafters), compute separately because the rates differ; then sum.
5. Manufacturing overhead budget — split into variable (apply per driver) and fixed (just stated total).
6. Ending inventories budget — values finished-goods and raw-materials inventory at year-end.
7. Cost of Goods Sold budget — uses the three production cost budgets + the ending-inventory budget to compute COGS.
8. Operating (period) expenses budget — selling, general, admin.
9. Budgeted income statement: Revenue − COGS = Gross margin − Operating expenses = Operating income.

9.4 The Cash Budget (financial budget — only part examinable here)

The operating budget is an accrual budget (revenue recognised when earned, expenses when incurred). The cash budget translates that into actual cash flows, because cash collection and cash payment happen on different timelines.

Why cash budgets matter

• Even profitable firms can run out of cash if customers pay slowly.
• Reveals when you need to borrow.
• Reveals when you have idle cash that could be invested (e.g., fixed deposit) rather than sitting in the bank.

How to build a cash budget — recommended approach

Build two supporting schedules first, then assemble the cash budget.

(a) Receipts (cash collections) schedule — for each month, work out how much of that month's sales is collected this month, how much next month, etc. If collection terms are "60% in month of sale, 25% in next month, 15% in month after," then for January receipts you need to go back to November and December sales as well as January, because part of those earlier sales will still be collected in January. Add insurance settlements, asset sales, and other one-off cash inflows.

(b) Disbursements (cash payments) schedule — same logic for purchases (e.g., 90% in month of purchase, 10% in following month). Then add:

• Wages (cash basis — usually paid in same period).
• Overheads in cash. Critical: subtract depreciation from overheads because depreciation is a non-cash expense. (e.g., if overhead is $20,000/month including $5,000 depreciation, cash overhead is $15,000.)
• Any one-off cash outflows (tax payments, dividends).

(c) Cash budget itself — done one month at a time, sequentially:

Opening cash balance
+ Total receipts (from schedule a)
= Cash available
− Total disbursements (from schedule b)
= Ending cash balance  →  becomes the opening balance for next month

You cannot run all months in parallel like the schedules — each month's opening balance depends on the previous month's ending balance.

How to improve / sustain a healthy cash level

• Collect faster — tighten credit terms; encourage prompt payment.
• Pay slower — negotiate longer payment terms with suppliers.
• Invest temporary cash surpluses in short-term interest-bearing accounts.

9.5 Sensitivity analysis ("what-if")

Once a model exists (typically in Excel), change one input — selling price, units sold, variable cost per unit, material cost — and observe the effect on operating income. This addresses uncertainty in the original assumptions.

9.6 Responsibility Accounting

Responsibility accounting = a system that holds a manager accountable for a specified set of activities. The key requirement is controllability — but "control" in practice means significant influence, not absolute control (no one has absolute control). Example: at the deli counter, you can't dictate the price (no absolute control), but you can choose whether to buy or go elsewhere (significant influence) — so you influence what you pay.

Four theoretical responsibility centres

Investment centres > profit centres > cost centres in scope.

Why budgets and responsibility accounting interact

• Variances = actual minus budgeted. They are an early warning of problems, a performance evaluation basis, and feedback to revise strategy.
• The point of responsibility accounting is information, not blame. The moment people fear blame, they stop engaging honestly with the system.

9.7 Human aspects of budgeting

• Budgetary slack — managers deliberately under-estimate revenue or over-estimate cost to give themselves a buffer (and to look like high performers when they "beat" the budget). Some slack is inevitable; too much makes the budget useless. Senior management must stay close enough to operations to spot it.
• Stretch targets — targets that are difficult but achievable. If too easy, no effort; if too hard, demoralising. Analogy: 50% to pass — easy enough to be achievable, hard enough to require effort.
• Kaizen budgeting — incorporates continuous, small improvements over time (e.g., gradual cost reductions period by period). Not big leaps.
• Budgeting for carbon emissions — many firms now budget and report emissions, often because of government requirements. Currently in flux.

9.8 Multinational budgeting

Two cautions:

• Transfer pricing and legal practices vary by country.
• Budgets for performance evaluation lose meaning across countries — different economies, regulations, and conditions. Use budgets for planning across geographies, but for performance evaluation apply them locally.

MODULE 10 — Cost-Volume-Profit (CVP) Analysis

10.1 What CVP does

CVP is a planning tool. It models how operating income changes when any of these four inputs change:

• Units sold
• Selling price per unit
• Variable cost per unit
• Total fixed cost

You play with these four numbers to predict operating income, find the break-even point, find the units needed to hit a profit target, and test sensitivity to changes.

10.2 Key definitions

Contribution margin income statement vs gross-margin income statement

Revenue                          Revenue
− Total variable costs           − Cost of goods sold
= Contribution margin            = Gross margin
− Total fixed costs              − Operating (period) expenses
= Operating income               = Operating income

Both end at the same operating income, but the contribution-margin version separates costs by behaviour (variable vs fixed) and the gross-margin version separates them by function (manufacturing vs period). Gross margin ≠ contribution margin.

10.3 The three expressions of CVP

(a) Equation method

Operating income = Selling price × Q − Variable cost × Q − Fixed cost

For break-even, set operating income = 0:

0 = SP·Q − VC·Q − Fixed cost

Rearrange: Q = Fixed cost ÷ (SP − VC) = Fixed cost ÷ Contribution margin per unit

(b) Contribution margin method (same thing, one step shorter)

Break-even units = Fixed cost ÷ Contribution margin per unit

Break-even revenue ($) = Fixed cost ÷ Contribution margin ratio (use this when SP is unknown)

(c) Graphical method (Profit graph or CVP graph)

Plot total revenue and total cost; intersection = break-even. Or plot operating income directly (profit graph): two known points are (Q = 0, profit = −Fixed cost) and (Q = break-even, profit = 0); join with a straight line and read off profit at any volume.

Lecturer's recommendation: focus on equation and contribution-margin methods. Graphical is useful to know but not the focus.

10.4 Target operating income

Same formula, with the target added to fixed cost:

Units for target OI = (Fixed cost + Target operating income) ÷ Contribution margin per unit

Revenue for target OI = (Fixed cost + Target operating income) ÷ Contribution margin ratio

Trick worth seeing: the break-even formula is just this formula with Target OI = 0. One formula, not two. Memorise the target-income version and treat break-even as the special case where target = 0.

10.5 Income taxes in CVP

Operating income (pre-tax) is what the formulas use. If a question gives you a net (after-tax) target, convert it back first:

Pre-tax operating income = Net income ÷ (1 − Tax rate)

Then plug into the target-OI formula.

Critical exam trick: the tax rate has no effect on break-even. Why? Break-even means profit = 0. There is no profit to tax, so the tax rate is irrelevant. Tax only matters when the target is non-zero.

If the tax rate rises and you have a positive profit target, you must sell more units to keep the same after-tax income. If it falls, you can sell fewer.

10.6 CVP assumptions

You may be asked to list these. There are typically given as:

1. Changes in sales volume are the only driver of changes in cost and revenue (no other variables move).
2. Total cost can be split into fixed and variable components (mixed costs must be decomposed — Module 4 high-low or regression).
3. Cost and revenue functions are linear within the relevant range (no learning curves, no quantity discounts, no step costs within the range).
4. Selling price per unit, variable cost per unit, and total fixed cost are known and constant over the relevant range.
5. Single product — or, if multiple products, the sales mix is known and constant.
6. All units produced are sold (no inventory build-up or drawdown).
7. Time value of money is ignored — CVP is a short-term tool.

10.7 Margin of safety

• The cushion between budgeted/expected activity and break-even activity.
• Indicator of risk of loss: smaller margin = more sensitive to a downturn = more risky.
• Can be expressed in units, dollars, or as a % of budgeted revenue.

To grow the margin of safety: raise SP, cut VC, cut FC, or raise units.

10.8 Operating leverage

Degree of operating leverage (DOL) = Contribution margin ÷ Operating income (at a given activity level)

DOL tells you how a percentage change in sales (units or revenue) translates into a percentage change in operating income:

% change in operating income = DOL × % change in sales

• High DOL = high fixed costs relative to variable. A 1% revenue change → a big operating income change (both ways). Higher upside AND higher downside risk.
• Low DOL = mostly variable costs. Operating income tracks revenue more proportionally — safer but slower upside.

There is no single "right" DOL — it depends on the firm's risk appetite and cost structure.

10.9 CVP with multiple products

Formula unchanged. Just replace "contribution margin per unit" with weighted-average unit contribution margin (WAUCM), based on the sales mix.

Procedure

1. Find the sales mix as proportions. E.g., if Product A = 40,000 units, B = 120,000, C = 80,000, total = 240,000, mix = 0.167 / 0.500 / 0.333.
2. WAUCM = (CM_A × mix_A) + (CM_B × mix_B) + (CM_C × mix_C).
3. Break-even total units = Fixed cost ÷ WAUCM.
4. Split back into products using the sales mix: each product's break-even units = total break-even units × that product's mix proportion. (Otherwise "break-even = 500 units total" is meaningless — you need to know how many of each.)

Trap: changing the sales mix changes the answer

If the mix shifts toward the lower-CM products, total units to break even rises (because each "average" unit now contributes less). Selling lower-CM products is less profitable per unit, so the firm needs more volume to cover fixed costs.

A lower break-even point is not always "better" — it could mean the firm is over-weighting low-CM products in the mix. Strategically you want to push the higher-CM products.

Sales-mix arithmetic — three valid methods (proportion method preferred)

Lecturer's strong recommendation: use the percentage / proportion method (compute mix as decimals like 0.167, 0.500, 0.333). It works for any numbers. The "lowest-ratio" method (e.g., 1:3:2) only works when the numbers happen to be whole-number multiples; if you get 7,000 / 13,000 / 19,000, it falls apart.

10.10 Rounding rule (memorise it)

If the formula gives 231.2 units, the answer is 232, never 231. Round UP. Rationale: at 231 units you have not actually reached break-even / your target. CVP rounding ignores normal mathematical rounding because of what the number represents.

10.11 Worked example — basic CVP with taxes (Q3-26)

Refrigerator dealer:

• Selling price = $5,000 per unit
• Cost from manufacturer (variable) = $4,200 per unit
• Rent = $52,800/month (fixed)
• Salaries = $75,200/month (fixed)
• Sales commission = 4% × selling price = 4% × $5,000 = $200 per unit (variable)
• Advertising = $18,400/month (fixed)
• Tax rate = 30%

Variable cost per unit = 4,200 + 200 = $4,400.
Contribution margin per unit = 5,000 − 4,400 = $600.
Total fixed cost = 52,800 + 75,200 + 18,400 = $146,400.

Break-even = 146,400 ÷ 600 = 244 refrigerators per month.

For target net income of $63,000 (after tax) with 30% tax:
Pre-tax target OI = 63,000 ÷ (1 − 0.30) = 63,000 ÷ 0.70 = $90,000.
Units = (146,400 + 90,000) ÷ 600 = 236,400 ÷ 600 = 394 refrigerators.

10.12 Worked example — choosing between two cost structures (Q3-31)

Carpet sale — two rental options:

• Option 1: 25% of total revenue (purely variable; no fixed)
• Option 2: $30,000 flat (purely fixed)

Selling price = $1,500; cost of carpet = $900.

Option 1 break-even: Variable cost per carpet = 900 + 0.25 × 1,500 = 1,275. CM = 1,500 − 1,275 = $225. Fixed = 0. Break-even = 0 ÷ 225 = 0 units.
Option 2 break-even: CM = 1,500 − 900 = $600. Break-even = 30,000 ÷ 600 = 50 units.

Indifference point: set the two operating-income equations equal:
225·Q = 600·Q − 30,000 → 375·Q = 30,000 → Q = 80 carpets. Both options give the same operating income at 80 units (= $18,000).

Decision rule:

• If expected sales < 80 → choose Option 1 (low/no fixed cost).
• If expected sales > 80 → choose Option 2 (lower variable cost beats the fixed cost).

Operating leverage at 80 units:

• Option 1 DOL = (225 × 80) ÷ 18,000 = 1.0
• Option 2 DOL = (600 × 80) ÷ 18,000 = 2.67

A 10% sales increase under Option 2 → 26.7% operating-income increase. But a 10% drop → 26.7% operating-income drop. Higher DOL = higher fixed cost = more upside AND more downside.

10.13 Worked example — multi-product break-even (Q3-34)

Three products A, B, C:

• Unit CM: $7, $5, $4
• Units sold: 40,000, 120,000, 80,000 (total 240,000)
• Fixed cost: $552,000

Sales mix = 40/240, 120/240, 80/240 = 0.167, 0.500, 0.333.

WAUCM = (7 × 0.167) + (5 × 0.500) + (4 × 0.333) = 1.169 + 2.500 + 1.332 = $5.00 per "weighted-average unit".

Total break-even units = 552,000 ÷ 5 = 110,400 units.

Split back by mix:

• A: 110,400 × 0.167 = 18,400
• B: 110,400 × 0.500 = 55,200
• C: 110,400 × 0.333 = 36,800
• Total: 110,400 ✓

If the mix shifts so B and C swap (e.g., B = 80,000, C = 100,000), the firm is selling more of the lower-CM product → WAUCM drops → break-even units rise. Lesson: push the high-CM products if you want to lower the break-even point and grow profit.

10.14 CVP in service and not-for-profit organisations

Same formulas. Replace "units sold" with output units — e.g., patient-days for a hospital, billable hours for a consultancy, meals served for a not-for-profit. Fixed costs and contribution per unit still drive the analysis. CVP works wherever you can define a measurable output and split costs into fixed and variable.

Cross-module synthesis — how the four modules connect

These modules build a chain from costing → pricing → planning → decision modelling:

1. Module 7 (ABC) improves the accuracy of product cost by recognising that overhead is consumed at different levels (unit, batch, product, facility).
2. Module 8 (Pricing) uses cost (and market data) to set a price. The choice of method depends on whether the market is competitive (target costing) or not (cost-plus).
3. Module 9 (Master Budget) rolls up unit costs and prices into a full operating plan for the firm — production, materials, labour, overhead, income statement, cash budget.
4. Module 10 (CVP) asks: given the cost structure and price, what volume do we need to break even or hit a profit target, and how sensitive is profit to changes?

Quick cross-references the exam may probe:

• ABC affects CVP: Better cost allocation (ABC) changes per-unit variable and fixed cost estimates used in CVP. Wrong costing → wrong break-even.
• Target costing uses CVP logic: Once a target cost is set, value engineering must hit it; if not, the target operating income won't materialise.
• Budgets use CVP for sensitivity: What-if analysis on price, volume, or cost cascades through the budgeted income statement.
• Responsibility accounting needs costs that managers can influence: ABC's better cost data helps identify what each manager actually controls.

Final exam tactics

1. Read the question. Twice. The lecturer flags this repeatedly — wrong cost driver, wrong cost classification, wrong rate base all stem from skimming.
2. Show your workings. Even wrong answers with right workings get partial marks. No workings = no partial marks.
3. Lay out tables. For ABC and budgets, the layout itself helps you avoid mistakes. Pool-rate table, then allocation table; sub-budget by sub-budget.
4. Practise with pen and paper. The exam is handwritten. Get used to formatting and showing workings by hand, not on Excel.
5. Do the budget question first. It's the longest. Get it out of the way while you have energy and time.
6. Round CVP units UP, always.
7. For multi-product CVP, never forget to split the total break-even back into individual products using the sales mix.
8. For target costing, remember the price is fixed by the market — your only lever is cost, via value engineering at the design (locked-in) stage.
9. For ABC, remember to add direct material and direct labour if the question asks for total product cost. Overhead allocation is only part of the answer.
10. For cash budgets, remove depreciation from overheads before treating overheads as cash outflows.