6.4 Capital Budgeting, NPV, IRR, and Real Options

Capital allocation and project value

Capital budgeting decides which long-term projects deserve capital, a factory, software platform, distribution center, acquisition, or product launch. The decisions shape cash flows, risk, and strategic flexibility for years. The 2026 curriculum builds every decision rule on incremental after-tax cash flows: count only cash flows that occur because the project is accepted.

Four cash-flow rules drive most exam errors:

• Exclude sunk costs. Money already spent (a feasibility study, prior research) is irrelevant.
• Include opportunity costs. A factory built on land the firm could have sold has a real cost.
• Include externalities. Capture cannibalization of existing products and positive spillovers.
• Ignore financing costs in the cash flows. Interest is already captured in the discount rate; double-counting it understates NPV.

Also include incremental working-capital investment, capital expenditures, taxes, and terminal (salvage) cash flows.

NPV decision rule

Net present value (NPV) is the present value of expected incremental cash flows minus the initial outlay, discounted at a rate that reflects the project's risk, not blindly the firm's average. NPV = sum of discounted project cash flows - initial outlay.

• Positive NPV: project earns more than the required return and adds value. Accept.
• Zero NPV: project earns exactly the required return.
• Negative NPV: project destroys value (given the forecasts). Reject.

NPV is the strongest rule because it is in currency terms and assumes reinvestment at the required return. For mutually exclusive projects, choose the higher NPV.

IRR and ranking problems

The internal rate of return (IRR) is the discount rate that sets NPV to zero. For an independent project with conventional cash flows, accept if IRR exceeds the required return. But IRR has limits the exam exploits:

• A small project can show a high IRR yet add little value.
• Scale and timing differences make NPV and IRR rank mutually exclusive projects differently.
• Nonconventional cash flows (sign changes after the first outflow) can produce multiple IRRs or none.
• IRR implicitly assumes reinvestment at the IRR, often unrealistically high.

When NPV and IRR conflict, follow NPV.

Profitability and ROIC

Return on invested capital (ROIC) links operating profit to the capital that produced it: ROIC = NOPAT / invested capital, where NOPAT is net operating profit after tax. ROIC is value-relevant only against WACC (weighted average cost of capital). If ROIC exceeds WACC, growth creates value; if ROIC is below WACC, growth destroys value even while accounting earnings rise, a frequent exam trap.

Real options

A real option is managerial flexibility embedded in a real project, valuable because management can react as uncertainty resolves.

A pilot may carry a negative stand-alone NPV yet create a valuable option to expand into a large market; an abandonment option cuts downside by letting the firm exit before all losses occur. Real options can make a project worth more than a static NPV implies.

Capital budgeting workflow

1. Classify the project as independent or mutually exclusive.
2. Forecast incremental after-tax operating cash flows.
3. Add working capital, capex, opportunity costs, and terminal cash flows.
4. Exclude sunk costs and financing costs.
5. Discount at a risk-appropriate required return.
6. Accept positive-NPV independent projects; pick the highest NPV among exclusives.
7. Test sensitivity, scenarios, and embedded real options.

Other decision rules and their pitfalls

The curriculum also covers supporting criteria the exam contrasts with NPV. The profitability index (PI) equals the present value of future cash flows divided by the initial outlay; accept when PI exceeds 1.0, which is mathematically equivalent to a positive NPV and is useful for ranking under a capital constraint. Payback period counts the years to recover the initial outlay; it is simple and signals liquidity, but it ignores the time value of money and all cash flows after payback. Discounted payback fixes the time-value flaw but still ignores later cash flows.

None of these dominates NPV for value maximization, but each can break a tie or flag a liquidity concern.

A short worked NPV example

Suppose a project costs 1,000 today and returns 600 at the end of year 1 and 600 at the end of year 2, with a 10% required return. The present values are 600/1.10 = 545.5 and 600/1.21 = 495.9, summing to 1,041.4. NPV = 1,041.4 - 1,000 = 41.4, so the project adds value and should be accepted. The IRR here solves 1,000 = 600/(1+r) + 600/(1+r)^2, giving roughly 13.1%, comfortably above the 10% hurdle, so NPV and IRR agree for this independent conventional project. Conflicts arise only with mutually exclusive projects of different scale or timing, where NPV governs.

Mistakes that destroy capital-budgeting answers

The exam concentrates errors in a few places: discounting at the firm's average WACC when project risk differs, including financing cash flows that the discount rate already captures, treating a sunk cost as relevant, and forgetting the recovery of net working capital at project end. Catch these and most capital-budgeting items become routine.

Exam focus

If NPV and IRR conflict, prefer NPV. For "relevant cash flow" items, reject sunk costs, keep opportunity costs, and exclude interest. For real-option items, look for management flexibility under uncertainty. PI above 1.0 equals positive NPV; payback ignores both the time value of money and post-payback cash flows. Capital allocation is not pure math: limited capital is ranked by NPV, strategic fit, risk, and timing, but value still requires earning above the cost of capital over time.