Math Problem Statement

Muriel Ltd has prepared the following standard data for the first quarter of 2024:

£ per unit

£ total @ 4,200 units

Sales

300.00

1,260,000

Less variable costs:

Materials (Note i)

(67.20)

(282,240)

Labour (Note ii)

(18.00)

(75,600)

Other variable overheads

(62.00)

(260,400)

Contribution

152.80

641,760

Less fixed overheads

(175,000)

Profit

466,760

The actual results for the first quarter of 2024, where 4,130 units were produced and sold, were as follows:

Sales

£1,263,780

Less variable costs:

Materials (Note iii)

(£223,020)

Labour (Note ii)

(£75,166)

Other variable overheads

(£226,800)

Contribution

£738,794

Less fixed overheads

(£182,000)

Profit

£556,794

Notes:

(i)Under the standard costing system, each unit produced and sold by the firm in the first quarter of 2024 will use 16kg of material.

(ii)Under the standard costing system, each unit produced and sold by the firm in the first quarter of 2024 will require 2.5 hours of labour. The actual number of labour hours needed per unit was the same for the first quarter of 2024.

(iii) In the first quarter of 2024, each unit produced and sold used 14.4kg of materials.

What is the materials usage variance for the first quarter of 2024? (to two decimal places)

Show answer choices

£27,753.60 Favourable

£26,762.40 Favourable

£59,220 Favourable

£32,457.60 Adverse

Solution

The Materials Usage Variance can be calculated using the formula:

Materials Usage Variance=(Standard QuantityActual Quantity)×Standard Price per kg\text{Materials Usage Variance} = (\text{Standard Quantity} - \text{Actual Quantity}) \times \text{Standard Price per kg}

Step 1: Gather information

  1. Standard Quantity (SQ):
    SQ=Standard material per unit×Actual units produced and sold=16kg/unit×4,130units=66,080kg.SQ = \text{Standard material per unit} \times \text{Actual units produced and sold} = 16 \, \text{kg/unit} \times 4,130 \, \text{units} = 66,080 \, \text{kg}.

  2. Actual Quantity (AQ):
    AQ=Actual material used per unit×Actual units produced and sold=14.4kg/unit×4,130units=59,472kg.AQ = \text{Actual material used per unit} \times \text{Actual units produced and sold} = 14.4 \, \text{kg/unit} \times 4,130 \, \text{units} = 59,472 \, \text{kg}.

  3. Standard Price per kg (SP):
    From the standard data, materials cost per unit is £67.20.
    SP=Standard material cost per unitMaterial per unit=67.2016=4.20£/kg.\text{SP} = \frac{\text{Standard material cost per unit}}{\text{Material per unit}} = \frac{67.20}{16} = 4.20 \, \text{£/kg}.

Step 2: Calculate variance

Materials Usage Variance=(66,08059,472)×4.20\text{Materials Usage Variance} = (66,080 - 59,472) \times 4.20 Materials Usage Variance=6,608kg×4.20=27,753.60£ (Favourable).\text{Materials Usage Variance} = 6,608 \, \text{kg} \times 4.20 = 27,753.60 \, \text{£ (Favourable)}.

Final Answer:

£27,753.60 Favourable.


Let me know if you'd like more details or further clarification! Here are 5 related questions to expand your understanding:

  1. How would the materials price variance be calculated from the given data?
  2. What factors contribute to a favourable materials usage variance?
  3. How does the change in labour hours affect the variance calculation?
  4. What is the significance of analysing variance in standard costing systems?
  5. How can Muriel Ltd improve its materials planning process?

Tip: Always compare standard and actual results side by side to pinpoint areas of improvement in cost management.

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Math Problem Analysis

Mathematical Concepts

Variance Analysis
Standard Costing
Material Costing

Formulas

Materials Usage Variance = (Standard Quantity - Actual Quantity) × Standard Price per kg

Theorems

Materials Variance Analysis

Suitable Grade Level

Grades 11-12