THE FOLLOWING LEARNING OUTCOMES
an understanding of:
Modern manufacturing economics, systems and organisation Skills and the ability to:
Undertake a costing analysis for a range of product types.
Apply the basic principles of quality control
IMPORTANT INFORMATION
You are required to submit your work within the bounds of the University Infringement of Assessment Regulations (see your Programme Guide). Plagiarism, paraphrasing and downloading large amounts of information from external sources, will not be tolerated and will be dealt with severely. Although you should make full use of any source material, which would normally be an occasional sentence and/or paragraph (referenced) followed by your own critical analysis/evaluation. You will receive no marks for work that is not your own. Your work may be subject to checks for originality which can include use of an electronic plagiarism detection service.
Where you are asked to submit an individual piece of work, the work must be entirely your own. The safety of your assessments is your responsibility. You must not permit another student access to your work. Where referencing is required, unless otherwise stated, the Harvard referencing system must be used (see your Programme Guide).
PART A: Quantitative Analysis
1. A company wishes to introduce a new product. In order to do this, it must invest in some new manufacturing equipment. The choice is between Machine A and Machine B. Costs and income associated with each machine are as follows.
|
Costs / Income
|
Machine A
|
Machine B
|
|
Fixed Costs
|
£75,000
|
£87,000
|
|
Variable Cost per Product Produced
|
£13
|
£10.50
|
|
Selling Price for each Product
|
£25
|
£25
|
Plot separate break-even graphs (Costs/Income -v- No of Products) for Machine A and Machine B. Which machine would you recommend for purchase? Why?
2 A batch of 2500 components is manufactured by an operator. Each of these components takes 4 minutes to make. The direct materials costs are £2 per component. The operator is paid £15 per hour (direct labour costs). If the total overheads in this company are calculated at 350% of direct labour costs, what is the true cost of manufacturing each component?
3 (a) A potential 6-year manufacturing project requires the purchase of a new piece of machinery. You are the project manager and you must choose between two potential machines (Machine A and Machine B), either of which would be suitable. The cost of each machine is identical at £80,000. However, they differ in performance such that the projected future cash flows are different for each machine. Projected cash flows over the 6 years of the project are as follows in Table ()A3:
|
Year
|
Cash Flow: Machine A
|
Cash Flow: Machine B
|
|
0
|
£80,000
|
£80,000
|
|
1
|
£5,000
|
£35,000
|
|
2
|
£8,000
|
£25,000
|
|
3
|
£12,000
|
£18,000
|
|
4
|
£20,000
|
£10,000
|
|
5
|
£25,000
|
£7.000
|
|
6
|
£30,000
|
£5,000
|
Table QA3: Six year cash flow figures for Machine A and Machine B.
(i) By simple inspection of the cash flow figures, estimate the payback period for each
machine and thereby state which machine you would choose and justify your choice.
(ii) Your colleague disagrees with your choice. Suggest one valid reason why your colleague's choice may be justified?
(b) Calculate the total NPV for each machine after 6 years assuming a discount (inflation) rate of 7% for each year of the project. Table B3b provides a list of discount factors for a range of discount/inflation rates.
(c) Calculate the total NPV for Machine A only assuming a discount (inflation) rate of 4% for each year of the project. Hence calculate the Internal Rate of Return (IRR) for Machine A over the 6 year period by a graphical method.
|
|
Discount Factors for given discount (inflation) rates over a 6-year project
|
|
Years
|
1%
|
2%
|
3%
|
4%
|
5%
|
6%
|
7%
|
8%
|
9%
|
10%
|
|
1
|
0.9901
|
0.9804
|
0.9709
|
0.9615
|
0.9524
|
0.9434
|
0.9346
|
0.9259
|
0.9174
|
0.9091
|
|
2
|
0.9803
|
0.9612
|
0.9426
|
0.9246
|
0.9070
|
0.8900
|
0.8734
|
0.8573
|
0.8417
|
0.8264
|
|
3
|
0.9706
|
0.9423
|
0.9151
|
0.8890
|
0.8638
|
0.8396
|
0.8163
|
0.7938
|
0.7722
|
0.7513
|
|
4
|
0.9610
|
0.9238
|
0.8885
|
0.8548
|
0.8227
|
0.7921
|
0.7629
|
0.7350
|
0/084
|
0.6830
|
|
5
|
0.9515
|
0.9057
|
0.8626
|
0.8219
|
0.7835
|
0.7473
|
0.7130
|
0.6806
|
0.6499
|
0.6209
|
|
6
|
0.9420
|
0.8880
|
0.8375
|
0.7903
|
0.7462
|
0.7050
|
0.6663
|
0.6302
|
0.5963
|
0.5645
|
A4. A PVC pipe for water transport is manufactured by Company A. This extruded pipe has a nominal outer diameter of 25 cm and the drawing specifications state that this diameter should be 25cm ± 0.4cm. As part of a Quality Control regime, the pipe is regularly inspected for compliance to this requirement. Inspections involve diameter measurements on sample batches of 10 pipes. For each sample batch, the average diameter and range of diameters are to be found.
Table 0A4 gives details of the measurements for 8 successive sample batches.
|
Sample Batch
|
10 x DIAMETER (cm)
|
|
1
|
24.7
|
25
|
24.7
|
24.9
|
24.9
|
24.8
|
24.9
|
24.9
|
24.6
|
24.9
|
|
2
|
25
|
24.9
|
24.9
|
25
|
25
|
25.1
|
25
|
24.9
|
24.8
|
24.7
|
|
3
|
24.6
|
24.6
|
24.7
|
25
|
24.9
|
24.9
|
25
|
24.7
|
25
|
25.1
|
|
4
|
25
|
24.6
|
24.8
|
25
|
25
|
24.7
|
24.8
|
25
|
25
|
24.9
|
|
5
|
25.4
|
25.5
|
25.4
|
25.5
|
25.6
|
25.5
|
25.7
|
25.7
|
25.6
|
25.4
|
|
6
|
25.3
|
25.4
|
25.5
|
25.6
|
25.6
|
25.5
|
25.6
|
25.6
|
25.4
|
25.4
|
|
7
|
25.6
|
25.7
|
25.6
|
25.7
|
25.6
|
25.6
|
25.4
|
25.3
|
25.2
|
25.6
|
|
8
|
25.5
|
25.6
|
25.3
|
25.5
|
25.5
|
25.5
|
25.4
|
25.5
|
25.6
|
25.6
|
For the "Average Control Chart", the Control Limits are 25cm ± 0.2cm and the Drawing Limits are 25cm ± 0.4cm.
For the "Range Control Chart", the Control Limit is 5mm and the Action Limit is 8mm.
(a) Calculate (i) the average and (ii) the range for each sample batch. (10 marks)
(b) Plot the average and range control charts showing the appropriate limits on each. (10 marks)
(c) Comment on the Quality implications of the data you have analysed. (10 marks)
A5 The "Economies of Scale" equation may be written as:
C2 = Cl x (02 Q1)n
where Ci is the known cost of a previous project, C2 is the cost of a new (larger) project, Q1 is the SIZE of the first project and Q2 is the SIZE of the new project. The index, n, is a term which governs how economies of scale apply.
If your original manufacturing project cost £1.034,564, how much would a new manufacturing project 3 times the size cost if n = 0.6?
PART B: CES Exercises on Manufacturing
Bl. Compare the manufacturing processes of (i) manual green sand casting and (ii) gravity die casting in terms of their respective economics. The component to be manufactured is 20cm in length and possesses a mass of 500g. It is to be manufactured from a cast aluminium alloy of price £1.75 per kg.
Use CES (Edu Level 3) to generate plots of Cost per Unit (£) -v- Batch size (No of units produced) for each process similar to that shown below:
|
Use the UPPER
bound as your line for the basis of comparison. This
helps avoid ambiguity in data analysis and interpretation.
|
The full set of assumptions on which you should base your plots is as follows:
|
Economic Factor
|
Value
|
|
Capital Write-Off Time (yr)
|
5
|
|
Component Length (m)
|
0.2
|
|
Component Mass (kg)
|
0.5
|
|
Discount Rate (%)
|
5
|
|
Load Factor
|
0.5
|
|
Materials Price (Efkg)
|
1.75
|
|
Overhead Rate (£lhi-)
|
75
|
Tasks:
(i) Manually extract sufficient data points from your CES-generated plots (remember to use the UPPER line of each plot for your own data set to avoid ambiguity).
(ii) Enter the data into Excel in the following format, or similar:
|
Batch Size
|
Cost per Unit (£)
|
|
Die Casting
|
Sand Casting
|
|
|
?
|
?
|
|
10
|
?
|
?
|
|
100
|
?
|
?
|
|
1000
|
?
|
?
|
|
10000
|
?
|
?
|
|
100000
|
?
|
?
|
|
1000000
|
?
|
?
|
|
10000000
|
?
|
?
|
(iii) Using Excel, plot Cost per Unit (y-axis) -v- Batch Size (x-axis) showing both die casting and sand casting on the same graph. Use LOG scales for both sets of axes. Label and title all graphs appropriately.
(iv) Report on your results. Discuss the comparative economics of the two competing processes in terms of:
(a) the SHAPE of the graph (i.e. why is it this shape?)
(b) Determine the batch size at which the cost per unit is identical for both processes.
(c) Explain why the unit component cost is cheaper for one process at low batch sizes while cheaper for the other process at larger batch sizes. Use as many of the economic factors used (in the assumption table above) as necessary to help your explanation.
Tasks
(i) The process economics for hot metal extrusion and filament winding have been calculated as follows:
|
Batch Size (n)
|
Unit Cost (E)
|
Unit Cost (f)
|
|
|
Hot Metal Extrusion
|
Filament Winding
|
|
1
|
10021.6
|
1021.7
|
|
10
|
1021,6
|
121.7
|
|
100
|
121.6
|
31.7
|
|
1000
|
31.6
|
22.7
|
|
10000
|
22.6
|
21.8
|
|
100000
|
21.7
|
21.7
|
|
1000000
|
21.6
|
21.7
|
|
10000000
|
21.6
|
21.7
|
Plot these data on a single set of axes (use log axes) of Unit Cost (y-axis) -v- Batch size (x-axis).
Which process would you choose for small (<1000 shafts) production runs? Which process would you choose for large (>10,000 shafts) production runs? Comment on your choices.
(ii) Your planned production run is ? 10,000 shafts. You have been instructed to take environmental impact issues of your choice into account as well as the process economics. Use the "Eco-Audit" tool in CES to compare the energy and CO2 impacts of the 2 possible material / process choices.