How do you quantify the total flexibility value when a project has multiple embedded real options?

When a project contains multiple real options, the total flexibility value is generally less than the sum of individual option values computed in isolation. This is because options interact -- exercising one often affects the value or existence of others.\n\nTypes of Flexibility:\n\n- Timing option: Delay the investment until uncertainty resolves\n- Expansion option: Scale up if conditions are favorable\n- Contraction option: Scale down to reduce losses\n- Switching option: Change inputs, outputs, or processes\n- Abandonment option: Exit and recover salvage value\n\n`mermaid\ngraph TD\n A[\"Project with Multiple Options\"] --> B[\"Timing Option
Delay 1 year\"]\n A --> C[\"Expansion Option
Double capacity Year 3\"]\n A --> D[\"Abandonment Option
Exit for salvage\"]\n B --> E{\"Option Interactions\"}\n C --> E\n D --> E\n E -->|\"Expansion exercised\"| F[\"Abandonment option
less likely needed\"]\n E -->|\"Abandonment exercised\"| G[\"Expansion option
ceases to exist\"]\n E -->|\"Timing delayed\"| H[\"Both future options
may change value\"]\n F --> I[\"Total Value < Sum of Parts\"]\n G --> I\n H --> I\n`\n\nWorked Example:\n\nKensington Energy evaluates a wind farm with WACC = 10%.\n\nBase NPV (static): -$1.2M (reject under traditional analysis)\n\nIndividual option values (computed in isolation):\n- Timing option (delay 1 year): $0.9M\n- Expansion option (add turbines Year 4): $1.4M\n- Abandonment option (sell equipment): $0.7M\n\nNaive sum: $0.9M + $1.4M + $0.7M = $3.0M\nNaive Strategic NPV: -$1.2M + $3.0M = $1.8M\n\nBut the options interact:\n- If Kensington delays (timing option), the expansion and abandonment options shift by one year, changing their values\n- If demand is high enough to trigger expansion, abandonment becomes irrelevant (you don't abandon a successful project)\n- If demand is low enough to trigger abandonment, expansion becomes irrelevant\n\nProper valuation using a decision tree that accounts for interactions: Total flexibility value = $2.1M (not $3.0M)\n\nCorrected Strategic NPV: -$1.2M + $2.1M = +$0.9M\n\nRules for Interaction:\n1. Mutually exclusive options (expand OR abandon) cannot both be exercised -- their values are not additive\n2. Sequential options (delay THEN expand) require compound option valuation\n3. The more options a project has, the greater the gap between the naive sum and the true combined value\n\nCFA Exam Guidance:\n- Know that Strategic NPV = Base NPV + Total Option Value\n- Recognize that multiple options interact and are sub-additive\n- Decision trees are the primary exam tool for handling option interactions\n\nPractice multi-option valuation in our CFA Corporate Issuers question bank.