Pricing, Product Mix and Constraint Decisions

Introduction

Management accounting supports decisions in which prices, product volumes, scarce resources and customer relationships interact. These decisions cannot be made reliably by applying a single rule such as “price at cost plus markup” or “produce the product with the highest unit contribution.” Managers must understand demand, capacity, relevant costs, opportunity costs and strategic value.

Pricing decisions determine revenue; product-mix decisions determine how scarce capacity is allocated; customer and channel profitability analysis determines where value is created or destroyed. The central principle is that a decision should be evaluated by comparing the incremental benefits and relevant costs caused by that decision.

Learning Objectives

By the end of this chapter, students should be able to:

1. Explain cost-based, market-based and value-based pricing.
2. Calculate prices using markup, margin and target-return methods.
3. Distinguish relevant costs from allocated or sunk costs.
4. Optimize product and service mix when resources are constrained.
5. Apply limiting-factor analysis and the theory of constraints.
6. Evaluate customer, segment and channel profitability without double counting costs.
7. Recognize strategic, ethical and practical limitations of quantitative decision models.

1. Pricing Foundations

A price is both a financial measure and a market signal. It affects demand, perceived quality, competitive position, capacity utilization and customer relationships. Management accountants therefore provide information rather than determine price in isolation.

Three broad approaches are common:

Cost-based pricing

Under full-cost-plus pricing:

The markup is normally expressed as a percentage of cost. If full cost is $80 and the markup is 25%, price is $100. This is not the same as a 25% profit margin on sales: a $100 price and $80 cost produce a margin of 20% of sales.

The markup required to obtain a target profit margin m on sales is:

For a 20% target margin, the required markup is 0.20 ÷ 0.80 = 25%.

For a target return on investment, a simplified annual pricing model is:

where:

This method assumes that expected volume, cost structure and capital employed are reasonably reliable. It can produce a price that the market will not accept, particularly when demand is weak or competitors have lower costs.

Market-based pricing

Market-based pricing begins with customer demand and competitive conditions. The firm may estimate demand at alternative prices and select a price that best supports its objective. A simple profit model is:

where p is price per unit, v is variable cost per unit, Q(p) is demand at price p and F is fixed cost. The model is useful only if the demand estimate is credible and the relevant capacity conditions are known.

Price elasticity of demand is:

Demand is commonly called elastic when the absolute value of elasticity exceeds 1. A price increase under elastic demand may reduce total revenue, although profit could still increase if the contribution margin is sufficiently high.

Value-based pricing

Value-based pricing starts with the customer’s next-best alternative. A practical ceiling price is the customer’s reservation price: the maximum amount the customer is willing to pay. Economic value to the customer can be represented as:

Reference value is the value of the best alternative; differentiation value is the measurable additional benefit of the supplier’s offering. The actual price normally lies between the supplier’s cost floor and the customer’s value ceiling:

This interval is not automatically achievable. Bargaining power, competition, switching costs, information and regulation determine how the value is divided.

Price discrimination and ethical boundaries

Different prices may be economically justified when customer segments have different willingness to pay, service requirements or demand timing. However, discriminatory pricing must comply with competition, consumer-protection, tax and sector-specific laws. Managers should document objective criteria and avoid deceptive reference prices, hidden charges and exploitative treatment of vulnerable customers.

2. Relevant Costs and Contribution

A decision-relevant cost is a future cost that differs between alternatives. Variable costs are often relevant, but not always; fixed costs are often irrelevant in the short run, but may become relevant if the decision changes capacity or commitments.

Important classifications include:

• Sunk cost: a past cost that cannot be changed by the decision.
• Avoidable cost: a cost eliminated by choosing an alternative.
• Committed cost: a cost arising from an existing obligation.
• Opportunity cost: the benefit sacrificed by rejecting the next-best alternative.
• Incremental revenue or cost: the additional amount caused by a decision.

Unit contribution is:

Total contribution is:

For a short-run decision with unchanged fixed costs, the alternative with the greater total relevant contribution is normally preferred. Allocated fixed overhead should not be included merely because it appears in product cost; it is relevant only if the decision changes that cost.

3. Product Mix Under a Scarce Resource

When demand exceeds available capacity, the scarce resource is a limiting factor. Examples include machine hours, skilled labour hours, production batches, materials, warehouse space and delivery capacity.

The correct ranking measure is:

This ranking is valid when:

1. There is one binding limiting factor.
2. Products are divisible or whole-unit effects have been checked.
3. Demand limits are known.
4. Contributions and resource usage are linear over the relevant range.
5. Fixed costs do not change, or changing fixed costs are included separately.

Worked example: continuous approximation

A company produces products A and B.

Available machine time is 4,800 hours. Contributions per machine hour are:

• A: $48 ÷ 4 = $12 per hour.
• B: $60 ÷ 6 = $10 per hour.

The continuous solution first satisfies A demand: 1,000 A uses 4,000 hours. The remaining 800 hours produce 133⅓ units of B. The contribution is:

If units must be whole, rounding is not a trivial presentation issue. The best nearby combinations must be tested. Producing 999 A and 134 B uses:

Contribution is:

Producing 1,000 A and 133 B uses 4,798 hours and yields $55,980. Therefore, among these feasible whole-unit alternatives, 999 A and 134 B is superior. The small improvement occurs because giving up one A releases four hours, allowing one additional B while using the capacity exactly.

The example demonstrates why the ranking rule is a starting point rather than a substitute for integer feasibility checks. In larger problems, linear programming or integer programming may be required.

Multiple constraints

With several scarce resources, a simple contribution-per-hour ranking may fail. The problem can be written as a linear program:

subject to:

and:

where cᵢ is contribution per unit of product i, xᵢ is quantity, aᵢⱼ is resource j used by one unit of product i, bⱼ is available resource j and dᵢ is maximum demand. If products must be whole units, xᵢ must be integer. Shadow prices from a linear-programming solution estimate the value of one additional unit of a constrained resource, within the valid range of the model.

4. Theory of Constraints

The theory of constraints (TOC) views an organization as a system whose performance is limited by one or a small number of constraints. Its five focusing steps are:

1. Identify the system constraint.
2. Exploit it by ensuring that its time is not wasted.
3. Subordinate other activities to the constraint.
4. Elevate the constraint by adding capacity or reducing its load.
5. When the constraint moves, return to step one.

TOC emphasizes throughput accounting. A simplified throughput measure is:

In many TOC applications, direct material is treated as the principal truly variable cost in the short run, while labour and overhead are treated as operating expense. The treatment must be adapted to the actual cost behaviour of the organization; TOC is not a licence to classify all costs mechanically.

A useful short-run measure is:

TOC complements, rather than replaces, traditional contribution analysis. It adds attention to flow, bottleneck protection, queues, setup time, quality failures and system-wide consequences.

5. Make-or-Buy, Special Orders and Capacity Decisions

A special order should be accepted when its incremental contribution is positive and it does not displace a more valuable use of constrained capacity. The relevant opportunity cost must be included.

For a special order:

A positive result is necessary but not always sufficient. Managers should also consider quality, strategic customers, contractual effects, future price expectations, employee capability and reputational risk.

Integrated illustrative case: Orion Components

The following is a fictional case. Orion produces regular product Y and premium product X. Product X has a maximum market demand that is already fully satisfied. A distributor offers an additional order for a modified version of Y.

The distributor would pay $150 per unit. Incremental variable cost is $65, so the apparent contribution is $85 per unit. However, each distributor unit requires capacity that would otherwise produce one regular Y unit. Regular Y contributes $104 per unit. There is no unused capacity and no possibility of expanding it during the decision period.

The correct calculation is:

If the distributor order requires a further customer-specific cost of $4 per unit that is genuinely incremental and not already included in the $65, the effect becomes:

The important point is that the order displaces regular Y, not X. Product X demand is already satisfied and therefore cannot be displaced by this order. The loss relative to regular Y’s contribution is $19 per unit before any additional service cost, not $61.

The order could become attractive if the distributor paid more, used less bottleneck capacity, or could be fulfilled using genuinely idle capacity. It might also have strategic value, but such value should be identified explicitly rather than hidden in an arithmetic error.

6. Customer, Segment and Channel Profitability

Revenue does not equal profitability. A customer who buys large volumes may require frequent deliveries, technical support, returns processing, special packaging and extensive credit administration. Profitability analysis makes these resource demands visible.

A defensible customer-profit formula is:

The categories must be defined carefully. Cost to serve should be a single, non-overlapping pool containing identified incremental activities such as order processing, delivery, returns, technical support and account management. If product/service cost already includes a particular customer-specific service cost, that amount must not be deducted again.

A clearer contribution format is often preferable:

Shared facility costs can then be shown separately for long-run profitability analysis. This avoids implying that an arbitrary allocation caused by a volume-based overhead rate is an avoidable cost.

Activity-based customer analysis

Activity-based costing assigns resource costs through cost drivers. For an activity pool:

Customer cost for that activity is:

For example, if delivery costs are $120,000 and practical delivery capacity is 6,000 deliveries, the rate is $20 per delivery. A customer requiring 18 deliveries consumes $360 of delivery-resource cost. The analysis should use practical capacity where appropriate and distinguish unused capacity from customer-caused usage.

A customer profitability statement might include:

No additional “customer-specific service” deduction should be made unless it represents a separately defined cost not already included above.

Segment and channel decisions

Profitability should be examined across dimensions such as product, region, customer type, sales representative and channel. Managers should ask:

• Is the revenue genuinely incremental?
• Which costs disappear if the segment is abandoned?
• Does the channel consume scarce capacity?
• Are returns, discounts and warranty claims included?
• Does the channel create future customers or merely shift existing sales?
• Are transfer prices or internal allocations distorting the result?

A segment should not be discontinued solely because it reports an allocated loss. If its avoidable contribution is positive and common costs remain unchanged, discontinuation may reduce total profit.

7. Strategic and Behavioural Considerations

Quantitative models depend on assumptions. Demand may be uncertain, cost functions may be nonlinear and capacity may not be perfectly divisible. Managers should perform sensitivity analysis by changing prices, volumes, costs, resource availability and opportunity costs.

Product-mix decisions can create behavioural conflict. A production manager rewarded for utilization may produce low-value inventory, while a sales manager rewarded for revenue may accept unprofitable orders. Balanced measures should include contribution, throughput, delivery reliability, quality, working capital and customer retention.

Transfer pricing between divisions can affect reported performance without changing total organizational profit. A transfer price should support goal congruence, preserve autonomy where appropriate and recognize external opportunity costs. No single transfer-pricing rule is ideal for every capacity condition.

8. Technology, Data and Governance

Enterprise-resource-planning systems, customer profitability tools and business-intelligence dashboards can combine sales, production, logistics and service data. Machine-learning models may improve demand forecasts and identify unusual discounting or high-cost service patterns. However, prediction is not causation. A model may mistake correlation for customer cost responsibility or reproduce historical pricing discrimination.

Good governance requires:

• documented definitions of revenue, variable cost and cost to serve;
• reconciliations to the general ledger;
• version-controlled assumptions;
• review of outliers and data quality;
• access controls for customer and price data;
• human approval for material pricing decisions; and
• monitoring for discriminatory or misleading outcomes.

Challenges and Limitations

Cost-based pricing may ignore willingness to pay. Market-based pricing may produce a price below sustainable long-run cost. Value-based pricing can be difficult when benefits are intangible or customers have unequal bargaining power. Limiting-factor rankings can fail with multiple constraints, indivisible units, setup costs, nonlinear learning effects or changing demand. Customer profitability can be distorted by arbitrary allocations and double counting. Consequently, management accounting analysis should combine numerical evidence with operational, commercial and ethical judgment.

Chapter Summary

Pricing may be cost-based, market-based or value-based. Cost-based methods provide a cost floor and return target but do not guarantee market acceptance. Market-based methods use demand and competitive information, while value-based methods focus on the customer’s alternative and measurable differentiation value.

Relevant-cost analysis includes future differential costs and opportunity costs, but excludes sunk costs. When a resource is scarce, products should generally be ranked by contribution per unit of the limiting factor, subject to demand, capacity and whole-unit constraints. Multiple constraints require a formal optimization model. The theory of constraints focuses on identifying, exploiting, subordinating and elevating the bottleneck.

Special orders are attractive only when incremental revenue exceeds incremental cost and the opportunity cost of displaced activity. Customer profitability requires a clear, non-overlapping definition of cost to serve. Product cost, activity costs, traceable account costs and shared costs must be distinguished to prevent double counting. Finally, all quantitative decisions require sensitivity analysis, governance and ethical review.

Key Terms

Cost-based pricing: Pricing based primarily on calculated cost plus a required markup or return.

Market-based pricing: Pricing informed by demand, competitors and market conditions.

Value-based pricing: Pricing based on customer-perceived economic value.

Markup: Percentage added to cost to determine price.

Margin: Profit expressed as a percentage of sales revenue.

Reservation price: Maximum price a customer is willing to pay.

Relevant cost: Future cost that differs between alternatives.

Sunk cost: Past cost that cannot be changed by a current decision.

Opportunity cost: Benefit sacrificed by selecting one alternative over another.

Contribution: Revenue less relevant variable cost.

Limiting factor: Scarce resource restricting output or activity.

Product mix: Combination and quantities of products or services provided.

Shadow price: Estimated value of one additional unit of a constrained resource.

Theory of constraints: System-management approach focused on the primary bottleneck.

Throughput contribution: Sales revenue less truly variable cost in a TOC framework.

Cost to serve: Incremental costs of activities required to support a customer or channel.

Activity-based costing: Costing method assigning resource costs through activities and drivers.

Customer profitability: Profit attributable to a customer after relevant product and service costs.

Goal congruence: Alignment between local decisions and total organizational objectives.

Review Questions

Short Answer Questions

1. Distinguish markup from margin.
2. What is an opportunity cost, and why is it relevant to a special order?
3. Define a limiting factor.
4. State the five focusing steps of the theory of constraints.
5. Why can customer profitability analysis double count costs?

Long Answer Questions

1. Compare cost-based, market-based and value-based pricing, including one advantage and limitation of each.
2. Explain why contribution per unit of the scarce resource is usually more useful than contribution per unit.
3. Describe how multiple constraints affect product-mix analysis.
4. Explain how activity-based costing can improve customer and channel profitability analysis.
5. Discuss the ethical and governance risks associated with data-driven pricing.

Analytical / Application Questions

1. A product earns $36 contribution and uses 3 bottleneck hours. A second product earns $50 contribution and uses 5 bottleneck hours. Which should be prioritized if demand exists for both and all other assumptions of single-constraint analysis hold? Show the calculation.
2. A customer generates $40,000 revenue, product variable cost of $24,000, delivery cost of $1,000 and support cost of $1,500. The delivery and support costs are already included in a reported “cost to serve” total of $2,500. Calculate customer contribution after cost to serve and explain how double counting could occur.
3. A special order offers $130 per unit and requires $70 incremental cost. It displaces a regular unit contributing $48. Calculate the net effect per order unit and state two nonfinancial factors that should be investigated before acceptance.

Multiple Choice Questions with Answers

Question 1

A product sells for $120 and has variable cost of $75. What is its unit contribution?

A. $45

B. $75

C. $120

D. $195

Correct Answer: A. $45

Question 2

A product costing $80 is priced using a 25% markup on cost. What is the price?

A. $96

B. $100

C. $105

D. $125

Correct Answer: B. $100

Question 3

Product A provides $48 contribution and uses 4 bottleneck hours. What is its contribution per bottleneck hour?

A. $8

B. $10

C. $12

D. $192

Correct Answer: C. $12

Question 4

In the corrected whole-unit example, what combination uses all 4,800 machine hours?

A. 1,000 A and 133 B

B. 999 A and 134 B

C. 998 A and 134 B

D. 1,000 A and 134 B

Correct Answer: B. 999 A and 134 B

Question 5

Which cost is generally irrelevant to a short-run decision if it cannot be changed by any available alternative?

A. Avoidable future cost

B. Incremental material cost

C. Opportunity cost

D. Sunk cost

Correct Answer: D. Sunk cost

Question 6

A special order contributes $85 before opportunity cost and displaces regular production contributing $104. What is its net effect per unit before other costs?

A. $19 gain

B. $85 gain

C. $104 loss

D. $19 loss

Correct Answer: D. $19 loss

Question 7

Which formula best represents customer contribution after cost to serve?

A. Revenue + allocated cost − variable cost

B. Revenue − product variable cost − identified cost-to-serve activities

C. Revenue − sunk costs only

D. Revenue × markup percentage

Correct Answer: B. Revenue − product variable cost − identified cost-to-serve activities

Question 8

What is the first step in the theory of constraints?

A. Elevate the constraint

B. Subordinate all other activities

C. Identify the system constraint

D. Eliminate all fixed costs

Correct Answer: C. Identify the system constraint

Question 9

If an activity pool costs $120,000 and has practical capacity of 6,000 deliveries, what is the activity rate?

A. $5 per delivery

B. $20 per delivery

C. $114 per delivery

D. $720,000 per delivery

Correct Answer: B. $20 per delivery

Question 10

A product has a $50 contribution and uses 5 scarce hours. Another has a $36 contribution and uses 3 scarce hours. Which has the higher contribution per scarce hour?

A. The first product, at $10 per hour

B. The first product, at $50 per hour

C. The second product, at $12 per hour

D. The second product, at $36 per hour

Correct Answer: C. The second product, at $12 per hour