B1. 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?
(10 marks)
B2. 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. If the total overheads in this company are calculated at 350% of direct labour costs, what is the true cost of manufacturing each component?
(5 marks)
B3. (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 B3a:
| 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 B3a: Six year cash flow figures for Machine A and Machine B.
- 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.
- Your colleague disagrees with your choice. Suggest one valid reason why your colleague’s choice may be justified?
(6 marks)
(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.
(10 marks)
(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.
(9 marks)
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 | 0.7084 | 0.6830 |
| 5 | 0.9515 | 0.9057 | 0.8626 | 0.8219 | 0.7835 | 0.7473 | 0.7130 | 0.6806 | 0.6499 | 0.6209 |
| 6Table | B3b0.9420.Discount0.8880Factors0.8375over | 6 years0.7903 for various0.7462 | inflation/discount0.70500.6663 | rates0.6302. | 0.5963 | 0.5645 | ||||
B4. 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 B4 gives details of the measurements for 8 successive sample batches.
| Sample | Range | ||
| Batch | 10 x Diameter (cm) | Average (cm) | (mm) |
| 1 | 25.0, 25.1, 24.8, 25.1, 25.1, 24.9, 25.0, 25.0, 24.9, 25.1 | ||
| 2 | 25.2, 24.9, 24.9, 25.0, 25.0, 25.1, 25.1, 24.9, 25.1, 25.1 | ||
| 3 | 25.0, 25.1, 25.2, 25.2, 25.3, 25.1, 25.0, 25.4, 25.0, 25.1 | ||
| 4 | 25.2, 25.4, 25.4, 25.5, 25.4, 25.5, 25.3, 25.2, 25.2, 25.4 | ||
| 5 | 25.3, 25.4, 25.3, 25.5, 25.6, 25.2, 25.3, 25.5, 25.5, 25.4 | ||
| 6 | 25.2, 25.4, 25.3, 25.6, 25.6, 25.5, 25.6, 25.6, 25.4, 25.4 | ||
| 7 | 25.4, 25.5, 25.6, 25.7, 25.6, 25.6, 25.7, 25.6, 25.7, 25.4 | ||
| 8 | 25.7, 25.6, 25.7, 25.6, 25.6, 25,6, 25.4, 25.7, 25.6, 25.8 |
Table B4. QC data for extruded pipe.
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.
(4 marks)
(b) Plot the average and range control charts showing the appropriate limits on each.
(8 marks)
(c) Comment on the Quality implications of the data you have analysed.
(8 marks)
