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

Materials Usage Variance Calculation

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: Calculate Standard Quantity Allowed for Actual Production
Standard Quantity=Standard kg per unit×Actual units produced\text{Standard Quantity} = \text{Standard kg per unit} \times \text{Actual units produced}
Standard Quantity=16kg×4,130=66,080kg\text{Standard Quantity} = 16 \, \text{kg} \times 4,130 = 66,080 \, \text{kg}

Step 2: Calculate Actual Quantity Used
Actual Quantity=Actual kg per unit×Actual units produced\text{Actual Quantity} = \text{Actual kg per unit} \times \text{Actual units produced}
Actual Quantity=14.4kg×4,130=59,472kg\text{Actual Quantity} = 14.4 \, \text{kg} \times 4,130 = 59,472 \, \text{kg}

Step 3: Standard Price per kg
Standard Price per kg=Standard Cost per Unit for MaterialsStandard kg per unit=67.2016=4.20per kg\text{Standard Price per kg} = \frac{\text{Standard Cost per Unit for Materials}}{\text{Standard kg per unit}} = \frac{67.20}{16} = 4.20 \, \text{per kg}

Step 4: Apply the Formula
Materials Usage Variance=(66,08059,472)×4.20\text{Materials Usage Variance} = (66,080 - 59,472) \times 4.20
Materials Usage Variance=6,608×4.20=27,753.60\text{Materials Usage Variance} = 6,608 \times 4.20 = 27,753.60

Result:
£27,753.60Favourable\boxed{£27,753.60 \, \text{Favourable}}


Would you like a detailed explanation of why this variance is favourable?

Related Questions:

  1. What is the materials price variance for the first quarter of 2024?
  2. How is the labour efficiency variance calculated in this scenario?
  3. What impact did the actual fixed overheads have on overall profitability?
  4. How does the contribution margin per unit differ between standard and actual results?
  5. What strategies could Muriel Ltd use to further improve material efficiency?

Tip:
A favourable usage variance suggests efficient use of materials, but it's essential to check if this efficiency affected product quality.

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Math Problem Analysis

Mathematical Concepts

Variance Analysis
Standard Costing
Cost Accounting

Formulas

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

Theorems

Standard Costing Principles

Suitable Grade Level

Undergraduate (Accounting/Finance) or Professional Certifications (e.g., ACCA, CIMA)