Strategic Cost & Performance Management: formula sheet

Key formulas

Target cost

Target cost = Target selling price − Target profit

Target profit may be given as a percentage of selling price or of cost. Read which one it is.

Cost reduction gap

Cost gap = Current (estimated) cost − Target cost

This is the amount the team must remove through design and process changes.

Cost driver rate (ABC)

Rate per unit of driver = Cost of activity cost pool ÷ Total quantity of cost driver

Compute one rate per cost pool.

Overhead assigned to a product (ABC)

Overhead = Σ (Driver quantity used by product × Rate per unit of driver)

Add the charge from every pool, then divide by units to get overhead per unit.

Kaizen cost target

Target cost for period = Previous period cost × (1 − Kaizen reduction %)

Applied to cost already in production.

Life cycle cost per unit

Life cycle cost per unit = Total life cycle cost ÷ Total units produced over the life

Total includes design, development, production, marketing, distribution, service and disposal costs as given.

Cost-plus price

Price = Cost base + Mark-up % × Cost base

State the cost base used. Mark-up is on cost; margin is on selling price.

Mark-up and margin link

Margin % = Mark-up % ÷ (100 + Mark-up %)

A 25% mark-up on cost equals a 20% margin on price.

Target cost

Target cost = Target selling price − Target profit

Used in market-led pricing. The gap to current cost is the cost reduction needed.

Minimum transfer price (general rule)

Minimum TP = Variable cost per unit + Contribution lost per unit on external sales forgone

With spare capacity at the seller, the lost contribution is nil, so the minimum is variable cost.

Maximum transfer price

Maximum TP = Lower of (external purchase price net of savings, buyer's net realisable value per unit)

The buyer will not pay more than this.

Special order test

Accept if Order revenue > Incremental cost + Opportunity cost

Ignore sunk and unchanged fixed costs.

Limiting factor ranking

Contribution per unit of scarce resource = Contribution per unit ÷ Scarce resource per unit

Use when capacity is short and several uses compete.

Contribution

Contribution = Sales − Variable cost

Use this as the base for most short-term decisions. Fixed costs come in only if they change.

Relevant cost of material

Material to be bought: current purchase price. Held and regularly used (will be replaced): replacement cost. Held with an alternative use and not replaced: contribution from the alternative use. Held with no other use: higher of resale/scrap value and value in the job

Historic cost is never relevant. For material with no other use, the relevant cost is the opportunity cost: the higher of its resale or scrap value and its value in the job.

Relevant cost of labour

Spare capacity: nil extra cost (if paid anyway). Fully used: wage paid + contribution lost per hour

Idle time paid in any case is not a relevant cost.

Make-or-buy rule

Make if avoidable cost of making < purchase price. Buy if purchase price < avoidable cost of making

Avoidable cost = variable cost + fixed costs that would be saved. Add any benefit from using freed capacity.

Shutdown rule (short run)

Continue if Contribution > Avoidable fixed costs. Shut if Contribution < Avoidable fixed costs

Allocated fixed costs that continue after closure are ignored.

Limiting factor ranking

Contribution per unit of limiting factor = Contribution per unit ÷ Units of scarce resource per unit

Rank products by this figure and allocate the scarce resource in that order, up to the demand limit.

Special order rule

Accept if Incremental revenue > Incremental cost

Include extra fixed costs and lost sales from existing customers if any.

Material cost variance

MCV = (SQ × SP) − (AQ × AP)

SQ is standard quantity for actual output. MCV = price variance + usage variance.

Material price and usage

MPV = AQ × (SP − AP); MUV = SP × (SQ − AQ)

Positive is favourable, negative is adverse. Calculate price on quantity purchased if the question says price is isolated at purchase.

Material mix and yield

Mix = SP × (RSQ − AQ); Yield = SP × (SQ − RSQ); MUV = Mix + Yield

RSQ is total actual input quantity split in the standard mix ratio. Apply per material and add.

Labour variances

LCV = (SH × SR) − (AH paid × AR); LRV = AH paid × (SR − AR); Idle time = idle hours × SR (adverse); LEV = SR × (SH − AH worked)

SH is standard hours for actual output. Labour rate variance uses hours paid. Efficiency uses hours worked.

Variable overhead variances

Expenditure = (AH × SR) − Actual VOH; Efficiency = SR × (SH − AH)

SR is the standard variable overhead rate per hour.

Fixed overhead variances

Expenditure = Budgeted FO − Actual FO; Volume = Absorbed FO − Budgeted FO; Absorbed FO = Standard rate × Actual output (in the same unit)

Volume splits into capacity, efficiency and, if given, calendar variances. Expenditure plus volume gives the total fixed overhead variance.

Sales price and volume (profit method)

Price = AQ × (AP − SP); Volume = Standard profit per unit × (AQ − BQ)

BQ is budgeted quantity. Price plus volume gives the sales profit variance.

Sales mix and quantity

Mix = Std profit per unit × (AQ − RAQ); Quantity = Std profit per unit × (RAQ − BQ)

RAQ is total actual quantity split in the budgeted mix. Mix plus quantity equals volume.

Flexible budget

Flexed cost = Variable cost per unit × Actual activity + Fixed cost

Use for semi-variable costs after splitting them into fixed and variable parts.

Return on Investment (ROI)

ROI = Divisional profit ÷ Capital employed (investment) × 100

Use the profit and capital basis stated in the question. A manager may reject a project whose return is above the cost of capital but below the current ROI.

Residual Income (RI)

RI = Divisional profit − (Capital employed × Required rate of return)

Gives a money figure. Accept projects with positive RI.

Economic Value Added (EVA)

EVA = NOPAT − (Capital employed × WACC)

NOPAT = operating profit after tax, with adjustments if the question asks (for example R&D treated as investment). Positive EVA means value is created.

NOPAT

NOPAT = EBIT × (1 − tax rate)

Use operating profit before interest, as the capital charge already covers financing cost.

Weighted Average Cost of Capital

WACC = (E ÷ V × Ke) + (D ÷ V × Kd × (1 − t))

Use market or given weights. Cost of debt is taken after tax.

Four Balanced Scorecard perspectives

Financial, Customer, Internal Business Process, Learning and Growth

Each has objectives, measures, targets and initiatives.

Throughput

Throughput = Sales revenue − Totally variable cost (usually direct material)

Direct labour is normally treated as an operating expense in throughput accounting unless the question says it is variable with output.

Throughput per unit

Throughput per unit = Selling price per unit − Direct material cost per unit

Use the same basis for every product when ranking.

Throughput per bottleneck hour

Throughput per bottleneck hour = Throughput per unit ÷ Bottleneck hours per unit

Rank products on this figure, highest first, to use the scarce resource best.

Total Factory Cost (TA)

Total factory cost = Direct labour + Factory overheads (operating expenses)

Used in the cost per factory hour calculation.

Cost per factory hour

Cost per factory hour = Total factory cost ÷ Total hours available on the bottleneck resource

Use bottleneck hours as the denominator.

Throughput accounting ratio (TAR)

TAR = Throughput per bottleneck hour ÷ Cost per factory hour

TAR > 1 means the product earns more than the cost of the factory time it uses. TAR < 1 means it does not cover factory cost. A higher TAR is better.

Net profit under TA

Net profit = Total throughput − Total operating expenses

Operating expenses are treated as fixed in the short run.

Target cost

Target cost = Target selling price − Target profit margin

The market sets the price. The firm must design cost down to the target cost.

Quick revision

• Relevant cost is a future, incremental cash flow that differs between alternatives.
• Sunk costs and committed costs are not relevant to the decision.
• Opportunity cost counts as relevant when a resource is scarce or has an alternative use.
• Target cost = target selling price − target profit margin.
• Life cycle costing looks at costs from design through to disposal, not only production.
• ABC assigns overheads through cost drivers to activities, then to products.
• Variance = actual − standard, read as favourable or adverse by its effect on profit.
• With a limiting factor, rank products by contribution per unit of that factor.
• Penetration pricing starts low to win share; skimming starts high and reduces over time.
• The balanced scorecard has financial, customer, internal process, and learning and growth perspectives.
• Always add qualitative factors such as quality, capacity, supplier reliability and morale to a make-or-buy recommendation.
• Reconcile your numbers: totals of variances must match the difference between standard and actual.

Common mistakes

• Treating target profit as a percentage of cost when it is given on selling price. Fix: Underline the base in the question. If profit is 20% of selling price, target cost is 80% of price.
• Confusing target costing with Kaizen costing. Fix: Remember: target costing is at design stage and market-driven; Kaizen is at production stage and compares with last period's actual cost.
• Using full cost for a special order when spare capacity exists. Fix: Use incremental cost. Ignore fixed costs that do not change.
• Forgetting the opportunity cost when capacity is full. Fix: Ask what is displaced. Add its lost contribution to the variable cost.
• Including apportioned fixed overheads in a make-or-buy or shutdown comparison. Fix: Split fixed costs into avoidable and unavoidable. Include only the avoidable ones.
• Using the historic purchase cost of material already in stock. Fix: Use replacement cost, resale value or the contribution lost from the next best use, whichever the facts support.
• Calculating usage or efficiency variance on budgeted output instead of actual output. Fix: Always compute SQ or SH for the actual output first. Only fixed overhead volume uses a comparison with budget.
• Using the wrong sign convention so favourable and adverse are swapped. Fix: For costs, standard minus actual is favourable when positive. For sales and profit, actual minus standard is favourable when positive. State F or A next to each answer.
• Using profit after interest in EVA instead of NOPAT. Fix: Start from operating profit (EBIT), apply tax, then charge capital at WACC. Financing cost is covered by the capital charge.
• Using pre-tax cost of debt in WACC. Fix: Always write Kd × (1 − t) unless the question gives the after-tax cost.

Exam tips

• In case studies, name the technique first and then link it to facts from the case. Generic theory earns fewer marks.
• For ABC numericals, show the rate for each pool and a check total. Marks are given for method even if one figure slips.
• Expect questions asking you to distinguish between two techniques, such as target and Kaizen costing. Prepare a short comparison on stage, focus and benchmark.
• Since Paper 6 is open book, keep a one-page summary of formulas and definitions in your file, but practise enough that you do not need to search for them.
• End every descriptive answer with a recommendation that fits the case, in provision-facts-conclusion style: concept, case fact, advice.
• Read the capacity line first. It decides whether opportunity cost enters the answer.
• In case studies, quote the facts from the scenario when naming a strategy, such as inelastic demand for skimming.
• Show the minimum and maximum transfer prices separately, then the negotiated range.