Let's solve the problem step by step as requested. --- ## **Given Information** - **Investment Amount:** 1,000,000 SAR - **Investment Options:** - **High-risk Investment:** - Profit: 100% (i.e., gain 1,000,000 SAR, total = 2,000,000 SAR) with probability .7 - Loss: Lose 50% (lose 500,000 SAR, total = 500,000 SAR) with probability .3 - **Low-risk Investment:** - Profit: 5% (gain 50,000 SAR, total = 1,050,000 SAR) with probability 1. - Loss: Lose 1/3 (lose 333,333 SAR, total ≈ 666,667 SAR) if withdrawn early (assume probability of early withdrawal is . unless otherwise specified) - **Expected value decrease due to inflation:** 2% per year (over 10 years, but for decision, just subtract 20% of final value) - **Inflation scenario for (c):** 3% per year (so subtract 30% of final value in this part) --- ## **a) Construct a Decision Tree** **Structure:** - **Start** - High-risk Investment - Success (.7): 2,000,000 SAR (before inflation) - Failure (.3): 500,000 SAR (before inflation) - Low-risk Investment - Success (1.): 1,050,000 SAR (before inflation) - Early Withdrawal (if any): 666,667 SAR (before inflation, probability not given so ignore for now) **Adjust for 2% inflation per year over 10 years:** - **Total decrease = 20%** - Multiply each outcome by .8 ### **Decision Tree Table** | Option | Outcome | Probability | Value before inflation | Value after inflation | |-------------------|----------------|-------------|-----------------------|----------------------| | High-risk | Success | .7 | 2,000,000 | 1,600,000 | | High-risk | Failure | .3 | 500,000 | 400,000 | | Low-risk | Success | 1. | 1,050,000 | 840,000 | --- ## **b) Determine the Best Decision Using EMV** **EMV (Expected Monetary Value) Calculations:** 1. **High-risk Investment:** \[ EMV = (.7 \times 1,600,000) + (.3 \times 400,000) = 1,120,000 + 120,000 = 1,240,000 \text{ SAR} \] 2. **Low-risk Investment:** \[ EMV = 1. \times 840,000 = 840,000 \text{ SAR} \] **Conclusion:** **Best decision is to choose the High-risk investment** (EMV = 1,240,000 SAR). --- ## **c) If the inflation rate is about 3%, what is the second-best option?** - 3% per year over 10 years = 30% total decrease - Multiply each outcome by .7 ### **Recalculate Outcomes** | Option | Outcome | Probability | Value after 3% inflation | |-------------------|----------------|-------------|-------------------------| | High-risk | Success | .7 | 2,000,000 × .7 = 1,400,000 | | High-risk | Failure | .3 | 500,000 × .7 = 350,000 | | Low-risk | Success | 1. | 1,050,000 × .7 = 735,000 | **New EMVs:** 1. **High-risk:** \[ EMV = (.7 \times 1,400,000) + (.3 \times 350,000) = 980,000 + 105,000 = 1,085,000 \text{ SAR} \] 2. **Low-risk:** \[ EMV = 1. \times 735,000 = 735,000 \text{ SAR} \] **Second-best option:** **Low-risk investment** (since EMV is lower than high-risk, but higher than the early withdrawal scenario). --- ## **Summary Table** | Scenario | High-risk EMV | Low-risk EMV | Best Option | Second-best Option | |------------------------------|---------------|--------------|---------------------|--------------------| | 2% inflation (10 yrs, 20%) | 1,240,000 | 840,000 | High-risk | Low-risk | | 3% inflation (10 yrs, 30%) | 1,085,000 | 735,000 | High-risk | Low-risk | --- ## **Final Answers** ### **a) Decision Tree:** - Already provided above. ### **b) Best Decision (EMV):** - **High-risk investment** (EMV = **1,240,000 SAR** after 2% inflation). ### **c) Second-best Option (3% inflation):** - **Low-risk investment** (EMV = **735,000 SAR** after 3% inflation). --- If you need the tree diagram visualized, let me know!