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- 20 Marks
Question
Jodoo Company Ltd had a new, large order for its product and thinks this may herald an expansion of the market and thus its sales and profits. Jodoo Ltd could move the factory to a new and larger site (cost: GHS 1 million), expand the existing factory (cost: GHS 0.25 million), or meet the new order by overtime (cost: GHS 0.08 million).
Three likely sales increase scenarios were proposed:
- 40% increase in sales with a probability of 0.2
- 10% increase in sales with a probability of 0.6
- 0% increase in sales with a probability of 0.2
The expected profits under each option are:
| Sales Increase % | New Factory (GHS million) | Expanded Factory (GHS million) | Overtime (GHS million) |
|---|---|---|---|
| 40% | 6 | 3.5 | 1.5 |
| 10% | 2.5 | 2.5 | 1.5 |
| 0% | 0 | 0 | 0 |
Required:
(i) Construct a decision tree to represent the various scenarios of expansion. (6 Marks)
(ii) Calculate the expected monetary value (EMV) of each node of your tree. (8 Marks)
(iii) Advise the company on how to react to this opportunity. (6 Marks)
Answer
(i) Decision Tree for Jodoo Company Ltd’s Expansion Scenarios:
The decision tree should represent the three potential decisions: moving to a new factory, expanding the current factory, or using overtime. Each decision branches into three possible sales increase outcomes (40%, 10%, 0%), with corresponding profits.
(ii) Expected Monetary Value (EMV) Calculation:
- EMV (Move to new factory) = (0.2 × 6) + (0.6 × 2.5) + (0.2 × 0) = 1.2 + 1.5 + 0 = GHS 2.7 million
- EMV (Expand existing factory) = (0.2 × 3.5) + (0.6 × 2.5) + (0.2 × 0) = 0.7 + 1.5 + 0 = GHS 2.2 million
- EMV (Overtime) = (0.2 × 1.5) + (0.6 × 1.5) + (0.2 × 0) = 0.3 + 0.9 + 0 = GHS 1.2 million
(iii) Advice to Jodoo Company Ltd:
Based on the EMV calculations:
- The move to a new factory results in an EMV of GHS 2.7 million, which is the highest EMV but requires a large initial investment of GHS 1 million.
- The expanded factory has a slightly lower EMV of GHS 2.2 million, with a lower initial investment of GHS 0.25 million, leading to a higher net profit.
- Overtime has the lowest EMV at GHS 1.2 million, and while it has minimal initial costs (GHS 0.08 million), it restricts future growth potential.
The company should choose to expand the existing factory, as it provides the highest net expected profit after costs (EMV of GHS 2.2 million with only GHS 0.25 million investment, yielding a net profit of GHS 1.95 million). This option balances profitability and cost-effectiveness while providing room for moderate growth.
- Tags: Business decision, Decision tree, Expected Monetary Value, Payoff table, Probability
- Level: Level 1
- Topic: Probability
- Series: NOV 2015
- Uploader: Joseph