Question Tag: Cost Function

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  • 12 Marks

QT – Nov 2017 – L1 – Q6b – Elements of Calculus

Calculate marginal cost, revenue, and profit for a company’s production of beverage cans.

Kyerewaa Ventures is a manufacturing company in the business of producing beverage cans for clients in the brewery industry. The weekly total cost to produce x cans is given by:

The demand function for the cans is given by:

The company has set a production limit to 10,000 cans and it sells all the cans that are produced.

Required:
i) Derive an expression for marginal cost, marginal revenue, and marginal profit. (4 marks)
ii) Determine the cost, revenue, and profit when the 2,501st can is produced and sold. (3 marks)
iii) Determine the cost, revenue, and profit when the 7,501st can is produced and sold. (3 marks)
iv) Advise the company whether to produce the 2,501st can or the 7,501st can. (2 marks)

  • 9 Marks

QT – May 2017 – L1 – Q3a – Elements of Calculus

Differentiate a cost function and determine how quickly the cost is changing at a specific production level.

The AXM manufacturing company has determined that the cost function for producing a particular type of pavement block is given by:

Where x is measured in number of units and  in GH¢.

Required:

i) Calculate the derivative of  with respect to .
(5 marks)

ii) Determine how quickly the cost is changing at x=1000
(4 marks)

  • 5 Marks

MA – May 2019 – L2 – Q2a – Cost-volume-profit (CVP) analysis

Determine the total variable cost per unit, total fixed overhead, and express the cost function based on given data.

Komosa Ltd is reviewing the selling price of its product for the coming year. A forecast of the annual costs that would be incurred by Komosa Ltd in respect of this product at differing activity levels is as follows:

Annual production (unit) 100,000 160,000 200,000
Direct materials (GH¢000) 200 320 400
Direct labour (GH¢000) 600 960 1,200
Overhead (GH¢000) 880 1,228 1,460

The cost behavior represented in the above forecast will apply for the whole range of output up to 300,000 units per annum of this product.

Required:
i) Calculate the total variable cost per unit and total fixed overhead. (4 marks)
ii) State the total cost function. (1 mark)

i) Total Variable Cost per Unit and Total Fixed Overhead:

  • Material Cost:
    GH¢ 200,000 / 100,000 units = GH¢ 2 per unit
  • Labour Cost:
    GH¢ 600,000 / 100,000 units = GH¢ 6 per unit
  • Variable overhead cost:
    Using high-low method:
    (GH¢ 1,460,000 – GH¢ 880,000) / (200,000 units – 100,000 units) = GH¢ 5.8 per unit
  • Total variable cost per unit:
    GH¢ 2 (materials) + GH¢ 6 (labour) + GH¢ 5.8 (overhead) = GH¢ 13.8 per unit
  • Fixed cost:
    Using the cost at 200,000 units:
    Total cost = GH¢ 1,460,000
    Variable cost = 200,000 units * GH¢ 13.8 = GH¢ 1,380,000
    Fixed cost = Total cost – Variable cost = GH¢ 1,460,000 – GH¢ 1,380,000 = GH¢ 300,000

(4 marks)

ii) Total Cost Function:

Total cost function: Y = GH¢ 300,000 + GH¢ 13.8x

  • 20 Marks

IMAC – AUG 2022 – L1 – Q5 – Costs and Cost Behaviour

Establishment of total cost function using high-low method, profit calculation for a specific production level, and identification of advantages and disadvantages of high-low method.

a) Takyi Carpentry makes twin-desk for local schools in the Daboase District. To facilitate control, the owner of the shop has asked you to assist him in analysing cost into fixed and variable elements.

Below is his six-year financial information:

Year No. of Twin-Desk Revenue (GH¢) Profit (GH¢)
2016 1,800 19,600 6,000
2017 1,700 22,000 6,200
2018 1,750 20,300 5,800
2019 2,100 26,200 8,000
2020 1,950 22,400 7,500
2021 2,050 21,800 6,800

Required: i) Establish total cost function using high-low method. (5 marks)

ii) Calculate profit for making 3,500 units of the twin-desk if the selling price is fixed at GH¢20. (3 marks)

iii) Identify TWO (2) advantages and TWO (2) disadvantages of using high-low method. (4 marks)

iv) Identify THREE (3) importance for classifying cost as fixed and variable. (3 marks)

b) For managers within a company, exercising control through standards and standard costing is a creative program aimed at determining whether the organisations’ resources are being used optimally. Standard costs are typically determined during the budgetary control process because it uses predetermined standard costs for direct material, direct labour and factory overheads.

Required: Explain THREE (3) benefits to a company that uses standard costing. (5 marks)

i) Establish total cost function using high-low method:

Year No. of Twin-Desk Total Cost (GH¢)
2016 1,800 13,600
2017 1,700 15,800
2018 1,750 14,500
2019 2,100 18,200
2020 1,950 14,900
2021 2,050 15,000

Using high and low points:

  • High point: 2,100 units and GH¢18,200
  • Low point: 1,700 units and GH¢13,600

iii) Advantages and disadvantages of using high-low method: Advantages:

  1. Simplicity: Easy to use and understand.
  2. Limited Data Requirement: Requires only two data points, making it useful when limited data is available.

Disadvantages:

  1. Inaccuracy: May result in high variances as it only uses two extreme points.
  2. Not Representative: May not represent the entire data set accurately if the high and low points are outliers.

iv) Importance for classifying cost as fixed and variable:

  1. Decision Making: Helps in making informed business decisions, such as pricing and budgeting.
  2. Break-even Analysis: Essential for calculating the break-even point and understanding cost behavior.
  3. Cost Control: Facilitates effective cost control and management by understanding cost behavior patterns.

b) Benefits of standard costing:

  1. Budgeting and Planning: Provides a basis for planning the use of organizational resources effectively.
  2. Performance Measurement: Allows for evaluation of managerial performance by comparing actual results with standard costs.
  3. Motivation: Acts as a motivating tool for managers and employees to achieve set targets.

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