**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

**of diameters are to be found.**

*range*

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)**

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