a) Draw up a decision (probability) tree diagram to represent the above information. A decision tree visually represents the decision points (squares), chance events (circles), probabilities, and outcomes. Decision Tree Diagram: $$ \begin{array}{ll} \textbf{Start (Decision Node)} & \\ \quad \text{1. Drill Immediately (No Tests)} & \\ \qquad \text{Chance Node (Drilling Outcome)} & \\ \qquad \quad \text{Success (P=0.55)} & \rightarrow \text{NPV } \text{N}120 \\ \qquad \quad \text{Failure (P=0.45)} & \rightarrow \text{NPV } \text{N}-40 \\ \quad \text{2. Undertake Tests} & \\ \qquad \text{Chance Node (Test Results)} & \\ \qquad \quad \text{Tests Show Success (P=0.7)} & \\ \qquad \qquad \text{Decision Node} & \\ \qquad \qquad \quad \text{a) Drill} & \\ \qquad \qquad \qquad \text{Chance Node (Drilling Outcome)} & \\ \qquad \qquad \qquad \quad \text{Success (P=0.8)} & \rightarrow \text{NPV } \text{N}100 \\ \qquad \qquad \qquad \quad \text{Failure (P=0.2)} & \rightarrow \text{NPV } \text{N}-50 \\ \qquad \qquad \quad \text{b) Sell Exploitation Rights} & \rightarrow \text{NPV } \text{N}65 \\ \qquad \quad \text{Tests Show Failure (P=0.3)} & \\ \qquad \qquad \text{Decision Node} & \\ \qquad \qquad \quad \text{a) Drill} & \\ \qquad \qquad \qquad \text{Chance Node (Drilling Outcome)} & \\ \qquad \qquad \qquad \quad \text{Success (P=0.2)} & \rightarrow \text{NPV } \text{N}100 \\ \qquad \qquad \qquad \quad \text{Failure (P=0.8)} & \rightarrow \text{NPV } \text{N}-50 \\ \qquad \qquad \quad \text{b) Sell Exploitation Rights} & \rightarrow \text{NPV } \text{N}15 \\ \quad \text{3. Sell Exploitation Rights Immediately (No Tests)} & \rightarrow \text{NPV } \text{N}45 \\ \end{array} $$ b) Evaluate the tree in order to advise the management of the company on its best course of action. We evaluate the tree by calculating the Expected Monetary Value (EMV) for each chance node and selecting the option with the highest EMV at each decision node, working backward from the end of the tree. Step 1: Calculate EMV for drilling after successful tests. $$ \text{EMV}_{\text{Drill | Test Success}} = (0.8 \times \text{N}100) + (0.2 \times \text{N}-50) = \text{N}80 - \text{N}10 = \text{N}70 $$ Comparing this to selling rights (N65), the best option if tests show success is to drill. Step 2: Calculate EMV for drilling after failed tests. $$ \text{EMV}_{\text{Drill | Test Failure}} = (0.2 \times \text{N}100) + (0.8 \times \text{N}-50) = \text{N}20 - \text{N}40 = \text{N}-20 $$ Comparing this to selling rights (N15), the best option if tests show failure is to sell exploitation rights. Step 3: Calculate EMV for undertaking tests. $$ \text{EMV}_{\text{Undertake Tests}} = (0.7 \times \text{EMV}_{\text{Drill | Test Success}}) + (0.3 \times \text{EMV}_{\text{Sell | Test Failure}}) $$ $$ \text{EMV}_{\text{Undertake Tests}} = (0.7 \times \text{N}70) + (0.3 \times \text{N}15) = \text{N}49 + \text{N}4.5 = \text{N}53.5 $$ Step 4: Calculate EMV for drilling immediately (no tests). $$ \text{EMV}_{\text{Drill Immediately}} = (0.55 \times \text{N}120) + (0.45 \times \text{N}-40) = \text{N}66 - \text{N}18 = \text{N}48 $$ Step 5: Compare the EMVs of the main decision options. Drill Immediately: N48 Undertake Tests: N53.5 Sell Exploitation Rights Immediately: N45 The highest EMV is N53.5, which corresponds to undertaking tests. Advice to Management: The company should undertake tests. If the tests show success, the company should then drill. If the tests show failure, the company should then sell the exploitation rights. c) Discuss the value of decision tree in providing management with guidance for decision making. Decision trees are valuable tools for management because they provide a structured and visual framework for analyzing complex decisions