1. **State the problem:** Makutano Company must decide whether to develop a new product with a research and development (R&D) cost of 500000. There is a 70% chance the product launch will be successful and a 30% chance it will fail. If successful, profits depend on product popularity (high, medium, low) with given probabilities and profits over two years. If failure, there is a chance to sell the R&D work or it becomes worthless. 2. **Decision tree components:** - Decision node: Develop Product (cost = 500000) - Success branch (probability 0.7) leads to a chance node with three outcomes: - High popularity (0.2) with profits 550000 per annum for 2 years - Medium popularity (0.5) with profits 450000 per annum for 2 years - Low popularity (0.3) with profits 350000 per annum for 2 years - Failure branch (probability 0.3) leads to a chance node with two outcomes: - Sell R&D (0.6) for 100000 - Worth nothing (0.4) for 0 3. **Calculate total profits for each popularity level:** Since profits are per annum for 2 years, total profit = profit per annum \times 2 - High: $$550000 \times 2 = 1100000$$ - Medium: $$450000 \times 2 = 900000$$ - Low: $$350000 \times 2 = 700000$$ 4. **Calculate expected profit if successful:** Expected profit = $$0.2 \times 1100000 + 0.5 \times 900000 + 0.3 \times 700000$$ Calculate each term: - $$0.2 \times 1100000 = 220000$$ - $$0.5 \times 900000 = 450000$$ - $$0.3 \times 700000 = 210000$$ Sum: $$220000 + 450000 + 210000 = 880000$$ 5. **Calculate expected value if failure:** Expected value = $$0.6 \times 100000 + 0.4 \times 0 = 60000$$ 6. **Calculate overall expected value of developing the product:** Expected value = $$0.7 \times 880000 + 0.3 \times 60000 - 500000$$ Calculate each term: - $$0.7 \times 880000 = 616000$$ - $$0.3 \times 60000 = 18000$$ Sum and subtract cost: $$616000 + 18000 - 500000 = 134000$$ 7. **Interpretation:** The expected net profit from developing the product is Shs. 134000. Since this is positive, it suggests that developing the product is a financially favorable decision. **Summary:** - Decision node: Develop Product (cost 500000) - Success (0.7): Expected profit 880000 - Failure (0.3): Expected value 60000 - Overall expected value: 134000 This decision tree helps visualize probabilities, outcomes, and expected values to guide the decision.