- 10 Marks
MA – L2 – Q51 – Decision Making Techniques
Question
Terra Works Limited is a company that is engaged in site clearance and site preparation work. Information about its operations is as follows:
(1) It is Terra Works Limited’s policy to hire all the plant and machinery it needs rather than to purchase its own plant and machinery.
(2) Terra Works Limited will enter into an advance hire agreement contract for the coming year at one of three levels – high, medium, or low – which correspond to the requirements of a high, medium, or low level of orders obtained.
(3) The level of orders obtained will not be known when the advance hire agreement contract is entered into. Probabilities have been estimated by management as to the likelihood of the orders being at a high, medium, or low level.
(4) Where the advance hire agreement entered into is lower than that required for the level of orders actually obtained, a premium rate must be paid to obtain the additional plant and machinery required.
(5) No refund is obtainable where the advance hire agreement for plant and machinery is at a level in excess of that required to satisfy the site clearance and preparation orders actually obtained.
A summary of the information relating to the above points is as follows:
| Level of Sales orders | Probability | Revenue GH¢000 | Variable costs GH¢000 | Plant and machinery hire costs | |
|---|---|---|---|---|---|
| Advance GH¢000 | Conversion GH¢000 | ||||
| High | 0.25 | 15,000 | 10,500 | 2,300 | 1,500 |
| Medium | 0.45 | 8,500 | 5,950 | 1,500 | 850 |
| Low | 0.30 | 4,000 | 2,800 | 1,000 | – |
| Low to medium | 850 | ||||
| Medium to high | 1,300 | ||||
| Low to high | 2,150 |
Required:
(a) Prepare a table showing the outcomes for each decision and outcome combination.
(b) Prepare a pay-off matrix and determine the advance hire contract that maximizes the expected value.
Answer
(a) Outcomes
| Decision | Outcome | Turnover GH¢000 | Variable cost GH¢000 | Advance hire GH¢000 | Conversion premium GH¢000 |
|---|---|---|---|---|---|
| Low | Low | 4,000 | 2,800 | 1,000 | 0 |
| Medium | 8,500 | 5,950 | 1,000 | 850 | |
| High | 15,000 | 10,500 | 1,000 | 2,150 | |
| Medium | Low | 4,000 | 2,800 | 1,500 | 0 |
| Medium | 8,500 | 5,950 | 1,500 | 0 | |
| High | 15,000 | 10,500 | 1,500 | 1,300 | |
| High | Low | 4,000 | 2,800 | 2,300 | 0 |
| Medium | 8,500 | 5,950 | 2,300 | 0 | |
| High | 15,000 | 10,500 | 2,300 | 0 |
(b) Pay-off matrix
| Decision | Low (x=) GH¢000 | Medium (x=) GH¢000 | High (x=) GH¢000 | Expected value (∑px) GH¢000 |
|---|---|---|---|---|
| Probability (p) | 0.30 | 0.45 | 0.25 | |
| Low | 200 | 700 | 1,350 | 712.5 |
| Medium | (300) | 1,050 | 1,700 | 807.5 |
| High | (1,100) | 250 | 2,200 | 332.5 |
The highest expected value is earned if the medium advance hire usage contract is signed.
- Topic: Decision making techniques
- Uploader: Salamat Hamid