Lecture Notes: Multi-product Break-even Analysis

Introduction

• Topic: Multi-product Break-even Analysis
• Context: Second part of Cost-Volume-Profit (CVP) Analysis
• Purpose: Analyze break-even for companies selling multiple products

Key Concepts

Single vs. Multi-product Break-even Analysis

• Single Product Break-even: Used when selling only one product
• Multi-product Break-even: Used when selling multiple products

Break-even Calculations

• Break-even Point in Pesos:
  • Formula: Fixed Costs / Weighted Average Contribution Margin Ratio (WACMR)
• Break-even Point in Units:
  • Formula: Fixed Costs / Weighted Average Contribution Margin per Unit (WACM per U)

Solving Multi-product Break-even Problem

Problem Statement

• Company: ABC Company
• Products: A, B, and C
• Data Provided:
  • Selling price per unit
  • Variable cost per unit
  • Contribution margin per unit
  • Sales in units
  • Total sales in units
  • Total fixed costs

Requirement 1: Break-even Point in Pesos

• Compute Sales in Pesos for Each Product:

  • Product A: 1000 units x 100 pesos = 100,000 pesos
  • Product B: 2000 units x 120 pesos = 240,000 pesos
  • Product C: 5000 units x 50 pesos = 250,000 pesos

• Total Sales in Pesos: 590,000 pesos

• Calculating WACMR:

  • Contribution Margin Ratio (CMR) for each product:
    • A: 40% (40/100)
    • B: 25% (30/120)
    • C: 20% (10/50)
  • Sales Mix for each product:
    • A: 16.95% (100,000 / 590,000)
    • B: 40.68% (240,000 / 590,000)
    • C: 42.37% (250,000 / 590,000)
  • Weighted CMR Calculation:
    • A: 6.78% (40% x 16.95%)
    • B: 10.17% (25% x 40.68%)
    • C: 8.47% (20% x 42.37%)
  • Total WACMR: 25.42%

• Break-even Point Calculation:

  • Break-even Point in Pesos = 400,000 pesos
  • Explanation: At this point, ABC Company neither makes a profit nor incurs a loss.
  • Sales to Break-even for Each Product:
    • A: 67,800 pesos
    • B: 162,720 pesos
    • C: 169,480 pesos

Requirement 2: Break-even Point in Units

• Calculating WACM per Unit:

  • Contribution Margin per Unit:
    • A: 40 pesos
    • B: 30 pesos
    • C: 10 pesos
  • Sales Mix in Units:
    • A: 12.5% (1000 / 8000)
    • B: 25% (2000 / 8000)
    • C: 62.5% (5000 / 8000)
  • Weighted CMR per Unit Calculation:
    • A: 5 pesos (40 x 12.5%)
    • B: 7.5 pesos (30 x 25%)
    • C: 6.25 pesos (10 x 62.5%)
  • Total WACM per Unit: 18.75 pesos

• Break-even Point Calculation:

  • Break-even Point in Units = 5423 units (rounded)
  • Sales Mix Units to Break-even for Each Product:
    • A: 678 units
    • B: 1356 units
    • C: 3389 units