Allocate capital using incremental cash flows

Learning goals

• Separate maintenance, expansion, regulatory and strategic investment purposes.
• Compare NPV, IRR and ROIC while recognizing estimation and option limits.

Draft · approximately 45 minutes, excluding further revision.

Specify the cash flows the decision changes

Capital allocation begins with strategy, feasible alternatives, a decision rule and later review. Include incremental after-tax cash flows, working-capital changes, opportunity costs, cannibalization and terminal effects. Exclude sunk costs that do not change with the decision. If discounting operating cash flows at WACC, do not subtract financing interest again in the same cash flows. Match nominal cash flows with nominal rates, currency with currency and project risk with an appropriate required return.

Maintenance preserves capability, expansion adds capacity, and compliance investments may be necessary even without a stand-alone revenue increase. Mutually exclusive choices, capital limits and execution capacity can change which positive-NPV projects can be selected. Challenge overly optimistic forecasts, unsupported terminal values and incentives to preserve a failing project.

Measures and flexibility answer different questions

NPV discounts all signed cash flows and measures modeled value above the required return. IRR is a rate setting NPV to zero; scale, timing and unconventional sign patterns can make IRR rankings conflict with value or create multiple roots. ROIC=NOPAT/average invested capital is a period measure whose accounting base and timing matter; ROIC above cost of capital is useful evidence, not a substitute for a full forecast valuation.

A real option is managerial flexibility to delay, expand, contract, switch or abandon under future information. Flexibility can have value but has exercise costs and operational constraints. Do not simply add an option premium if the base-case cash flows already incorporate the same flexibility. Sensitivity and scenarios reveal dependence on assumptions; they do not validate the forecast by themselves.

Formula and assumptions

NPV=ΣCFₜ/(1+r)^t; IRR solves NPV=0; ROIC=NOPAT/average invested capital

A two-year investment

1. Invest 100 today and receive 60 at each of years 1 and 2. At 10%, NPV=−100+60/1.10+60/1.10²=4.1322.
2. With x=1+IRR, 100x²−60x−60=0 gives IRR≈13.0662%. Both measures support value creation under these assumed flows and rate, not certainty of realization.
3. If NOPAT is 12 and average invested capital 100, ROIC=12%. At a 10% capital cost, the period spread is 2 percentage points; retain the distinction between this accounting spread and the 4.1322 NPV.

Calculation lab

Errors to catch

• Counting sunk research cost as an incremental future outflow.
• Double-counting financing costs or real-option flexibility.

Original knowledge check

Answer every question before checking. Review explanations after submitting; retry starts a new attempt.

Sources and coverage status

These original lessons are drafts. Public outlines are used to check scope; the official learning-outcome text and proprietary question banks are not reproduced here. Follow the source for exam-year requirements and updates.

• Reference · www.cfainstitute.org
• Reference · www.investor.gov