1. Core Concept & Methodology

In Exercise 3, you are analyzing Total Material Costs (K), which are driven by three distinct factors:

1. Production Volume (Q): The total number of finished units produced.

2. Material Efficiency / Usage Rate (Z): The amount of raw material consumed per finished unit (e.g., kg per unit).

3. Raw Material Price (C): The unit price of the raw material.

Formula:

Total Material Cost (K) = Q * Z * C

2. The Cascade Rule for Chain Substitution (Sequence: Q -> Z -> C)

When evaluating a multi-factor model using chain substitution, the impact of any middle variable—such as Material Efficiency (Z)—is calculated using the Cascade Rule:

• Factors preceding Efficiency (Volume - Q): Because Volume comes before Efficiency in the sequence, it has already been actualized. Use its Actual value (Q1).

• The Target Factor (Efficiency - Z): Isolate the net operational change in material consumption per unit: (Z1 - Z0).

• Factors succeeding Efficiency (Price - C): Because Price comes after Efficiency in the sequence, it has not yet been substituted. Keep it frozen at its Baseline/Budget value (C0).

Formula for Material Efficiency Impact (Delta K_Z):

Delta K_Z = Q1 * (Z1 - Z0) * C0

Important Hint on Sign:

• Negative Result (-): Decreased material consumption per unit (Z1 < Z0). This represents cost savings (operational efficiency).

• Positive Result (+): Increased material consumption per unit (Z1 > Z0). This represents cost overrun (wastefulness).

Example Case Study: Analyzing Factory Material Variance

Scenario Data:

• Budget / Baseline (Period 0):

  • Production Volume (Q0) = 500 units

  • Material Efficiency (Z0) = 12 kg per unit

  • Material Price (C0) = $20 per kg

  • Baseline Material Cost (K0) = 500 * 12 * $20 = $120,000

• Actual Results (Period 1):

  • Production Volume (Q1) = 700 units

  • Material Efficiency (Z1) = 10 kg per unit

  • Material Price (C1) = $25 per kg

  • Actual Material Cost (K1) = 700 * 10 * $25 = $175,000

Goal: Calculate the Material Efficiency Impact (Delta K_Z) using the sequence Q -> Z -> C.

Step-by-Step Solution:

Step 1: Identify the required factors

• Actual Volume (Q1) = 700 units (Factor before Z -> use Actual)

• Change in Consumption (Z1 - Z0) = 10 kg - 12 kg = -2 kg (Decreased usage by 2 kg/unit)

• Baseline Price (C0) = $20 (Factor after Z -> keep at Baseline)

Step 2: Plug the values into the Cascade Formula

Delta K_Z = Q1 * (Z1 - Z0) * C0

Delta K_Z = 700 * (10 - 12) * 20

Delta K_Z = 700 * (-2) * 20

Delta K_Z = -28,000

Step 3: Managerial Interpretation

The Material Efficiency Impact is -$28,000.

The negative sign indicates a cost reduction of $28,000 due to improved factory efficiency (using 2 kg less raw material per chair across 700 actual units produced, evaluated at the budgeted price of $20/kg).