Lecture: Differential (Relevant) Accounting
1. Definition of the Theoretical Concept (Differential Accounting)
Meaning
Differential Accounting (also called Relevant Costing) is a managerial accounting technique used to compare alternative decisions by focusing only on costs and revenues that change between alternatives.
Key Idea
If a cost or revenue does not change between alternatives, it is irrelevant and ignored.
Formal Definition
Differential cost is the difference in total cost between two or more alternatives.
Differential revenue is the difference in total revenue between those alternatives.
Purpose
- Make or buy decisions
- Accept or reject a special order
- Drop or retain a product/segment
- Continue or discontinue operations
Important Rules
- Only future costs are relevant
- Sunk costs are ignored
- Fixed costs are relevant only if they change
- Opportunity cost is always relevant
2. Numerical Example (Most Important Part – Step-by-Step)
Problem Statement
A company produces a component in-house at a cost of Rs. 120 per unit.
A supplier offers to supply the same component at Rs. 100 per unit.
Additional information:
- Direct materials = Rs. 40
- Direct labor = Rs. 30
- Variable overhead = Rs. 20
- Fixed overhead = Rs. 30 (will not change if production stops)
The company must decide whether to make or buy the component.
Step 1: Identify Relevant Costs
| Cost Item | Relevant? | Reason |
|---|---|---|
| Direct materials | ✅ Yes | Avoided if buying |
| Direct labor | ✅ Yes | Avoided if buying |
| Variable overhead | ✅ Yes | Avoided if buying |
| Fixed overhead | ❌ No | Will continue anyway |
Step 2: Calculate Relevant Cost of Making
❌ Fixed overhead (Rs. 30) is ignored because it does not change.
Step 3: Identify Relevant Cost of Buying
Step 4: Prepare Differential Analysis Table
| Alternative | Relevant Cost (Rs.) |
|---|---|
| Make | 90 |
| Buy | 100 |
Step 5: Compute Differential Cost
Step 6: Decision Rule
- If Make < Buy → Continue producing internally
- If Buy < Make → Outsource
✅ Decision: MAKE the component internally
Step 7: Interpretation (Very Important for Exams)
- The company saves Rs. 10 per unit by producing internally.
- Fixed costs are irrelevant because they remain unchanged.
- Decision is based only on differential (relevant) costs.
3. Key Examination Tips
- Never include sunk costs
- Ignore allocated fixed costs unless they change
- Always show step-by-step calculation
- Final decision must be numerically justified
4. One-Line Summary
Differential accounting helps managers choose the best alternative by comparing only those costs and revenues that change between decisions.
Lecture: Differential Accounting – Advanced Short-Term Decision Problems
1. Special Order Decisions
Theoretical Concept
A special order is a one-time order offered at a price below the normal selling price.
The decision is evaluated using differential (relevant) costs and revenues.
Decision Rule:
Accept the order only if incremental revenue ≥ incremental cost.
❗ Fixed costs are ignored if they do not change.
Numerical Example (Step-by-Step)
A company produces 10,000 units annually at full capacity of 15,000 units.
A foreign customer offers to buy 3,000 units at Rs. 45 each.
Normal cost per unit:
- Direct materials = Rs. 20
- Direct labor = Rs. 10
- Variable overhead = Rs. 5
- Fixed overhead = Rs. 15
Normal selling price = Rs. 70
Step 1: Identify Relevant Costs
| Cost | Relevant? | Reason |
|---|---|---|
| Direct materials | ✅ | Incremental |
| Direct labor | ✅ | Incremental |
| Variable overhead | ✅ | Incremental |
| Fixed overhead | ❌ | No change |
Step 2: Calculate Relevant Cost per Unit
Step 3: Compute Incremental Revenue
Step 4: Compute Incremental Cost
Step 5: Differential Profit
✅ Accept the special order (positive differential profit).
2. Utilization of a Constrained Resource
Theoretical Concept
A constrained (limiting) resource is a factor that restricts output, such as:
- Machine hours
- Skilled labor hours
- Raw materials
Decision Rule:
Maximize contribution margin per unit of constrained resource.
Numerical Example (Step-by-Step)
Two products: A and B
Limited machine hours = 3,000 hours
| Product A | Product B | |
|---|---|---|
| Selling price | 100 | 120 |
| Variable cost | 60 | 80 |
| Machine hours per unit | 2 | 1 |
Step 1: Contribution Margin per Unit
Step 2: Contribution per Machine Hour
Step 3: Rank Products
| Product | Contribution per Hour |
|---|---|
| B | Rs. 40 (1st) |
| A | Rs. 20 (2nd) |
✅ Produce Product B first, then Product A.
3. Joint Product Costs and the Contribution Approach
Theoretical Concept
Joint products are produced simultaneously from a common process up to the split-off point.
🔴 Joint costs are sunk and irrelevant for decisions made after split-off.
Decision is based on incremental revenue vs. incremental processing cost.
Numerical Example (Step-by-Step)
| X | Y | |
|---|---|---|
| Sales value at split-off | 200,000 | 150,000 |
| Further processing cost | 40,000 | 60,000 |
| Sales value after processing | 260,000 | 190,000 |
Step 1: Ignore Joint Cost
Joint costs already incurred → irrelevant
Step 2: Incremental Revenue
Step 3: Compare Incremental Revenue with Processing Cost
| Product | Incremental Revenue | Processing Cost | Decision |
|---|---|---|---|
| X | 60,000 | 40,000 | Process |
| Y | 40,000 | 60,000 | Do not process |
✅ Process X further
❌ Sell Y at split-off
4. Sell or Process Further Decisions
Theoretical Concept
This decision evaluates whether a product should be:
- Sold at split-off point, or
- Processed further for additional revenue
Decision Rule:
Process further only if incremental revenue > incremental cost.
Numerical Example (Step-by-Step)
A product can be sold at split-off for Rs. 80,000.
If processed further:
- Additional cost = Rs. 25,000
- Final sales value = Rs. 115,000
Step 1: Incremental Revenue
Step 2: Compare with Incremental Cost
| Amount | |
|---|---|
| Incremental revenue | 35,000 |
| Incremental cost | 25,000 |
Step 3: Incremental Profit
✅ Process further (positive incremental profit).
5. Overall Summary Table (For Students)
| Decision Type | Key Focus |
|---|---|
| Special Order | Incremental profit |
| Constrained Resource | Contribution per limiting factor |
| Joint Products | Ignore joint costs |
| Sell or Process Further | Incremental revenue vs cost |
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