Capital budgeting: NPV, IRR, and capital rationing

Learning goals

• Build an incremental after-tax cash-flow timeline without including sunk costs.
• Calculate and interpret net present value, profitability index, and payback.
• Explain what internal rate of return measures and when it can mislead.
• Choose projects under capital rationing while stating non-financial constraints.

Prerequisite check

You should be able to distinguish relevant future cash flows from accounting profit and use present-value factors. A depreciation expense is not itself a cash outflow; its tax effect matters only when the case supplies enough tax information. If a question gives after-tax operating cash flows, do not deduct tax a second time.

Vocabulary

• Capital budgeting: evaluating long-lived investments such as equipment, systems, facilities, or product capacity.
• Net present value (NPV): present value of future incremental cash inflows less the present value of incremental cash outflows.
• Internal rate of return (IRR): discount rate that makes a project's NPV zero.
• Profitability index (PI): present value of future inflows divided by the magnitude of the initial investment.
• Capital rationing: a limit on funds available for otherwise acceptable projects.
• Terminal cash flow: end-of-project cash flow such as disposal proceeds and recovery of working capital.
• Sunk cost: a past cost that cannot be changed by the decision.

Core idea

A long-term project creates value only when the present value of its incremental, risk-adjusted cash benefits exceeds the resources committed. NPV answers that value question directly in dollars. Payback describes liquidity exposure, PI describes value per invested dollar, and IRR expresses return as a rate; none replaces a clear cash-flow timeline and a defensible discount rate.

Capital budgeting is often taught in finance, but accountants are central to it. They reconcile forecasts to operational evidence, separate cash from accruals, challenge bias, document assumptions, and compare actual results with the approved business case.

Why this treatment makes sense

A dollar received four years from now cannot be compared directly with a dollar committed today because today’s dollar can earn a return and future cash is uncertain. Discounting puts each cash flow at a common date. Using only incremental cash flows prevents unrelated allocated overhead or already-spent research from distorting the choice. Recoverable working capital is an initial outflow and a terminal inflow, not an expense that disappears.

A repeatable method

1. Define the decision, project life, alternatives, and time zero.
2. Build a timeline for equipment, installation, opportunity cost, and working capital.
3. Forecast incremental after-tax operating cash flows; use case-supplied tax facts.
4. Add disposal proceeds, cleanup costs, and working-capital recovery at the end.
5. Select the required return that matches project risk and the question's policy.
6. Discount every cash flow and calculate NPV; accept an independent project if NPV is positive, subject to strategy, capacity, risk, and ethics.
7. Calculate payback, PI, or IRR only as supporting measures and explain their limits.
8. Stress-test the most uncertain volume, price, cost, timing, and residual assumptions.
9. Record approval conditions and create a post-completion review plan.

Worked example

Northern Print Co. is considering an automated finishing system. Equipment costs $180,000 and installation costs $12,000. The project also requires $18,000 of working capital at time zero. Management expects four annual after-tax cash savings of $65,000. At the end of year 4, the system should produce $20,000 disposal proceeds, and the $18,000 working capital should be recovered. The required return is 9%.

The time-zero outflow is $180,000 + $12,000 + $18,000 = $210,000. The four-year 9% annuity factor is approximately 3.23972, so the operating cash flows have present value $65,000 × 3.23972 = $210,582. The terminal $38,000 has present value about $38,000 ÷ 1.09⁴ = $26,920.

NPV = $210,582 + $26,920 − $210,000 = $27,502 positive.

The PI is $237,502 ÷ $210,000 = 1.13. Simple payback is about $210,000 ÷ $65,000 = 3.23 years, although that shortcut ignores the terminal cash and time value. The IRR is approximately 14.4%, which is above 9% and agrees with the positive NPV. Recommend proceeding only if the forecast, implementation capacity, controls, and strategic fit survive sensitivity review.

Journal, ledger, and statement connection

The capital-budgeting model does not create an entry merely because a project is recommended. On acquisition, supported costs flow to the appropriate asset and working-capital accounts; later depreciation, impairment, disposal, and operating results follow the applicable reporting framework. The approved model should link to purchase orders, the fixed-asset register, cash forecasts, and post-completion reports. Differences between forecast and actual cash flows are management-learning evidence, not amounts to hide by changing the original baseline.

Common mistakes

• Including a sunk feasibility study because it appears in the project spreadsheet.
• Omitting installation, training needed to make the asset ready, opportunity cost, working capital, cleanup, or terminal recovery when the facts make them relevant.
• Discounting accounting profit rather than incremental cash flow.
• Deducting tax again from cash flows already labelled after-tax.
• Choosing the highest IRR when mutually exclusive projects differ in scale or timing; NPV normally gives the direct value comparison at the required return.
• Treating positive NPV as permission to ignore privacy, safety, labour, environmental, implementation, or forecast-bias risks.

Guided practice

A machine costs $90,000 and requires $10,000 working capital. It provides three annual after-tax cash inflows of $38,000. At the end of year 3, $8,000 disposal proceeds and the $10,000 working capital are recovered. At 8%, use the three-year annuity factor 2.57710 and year-3 present-value factor 0.79383.

Operating cash-flow PV = $38,000 × 2.57710 = $97,930. Terminal PV = $18,000 × 0.79383 = $14,289. NPV = $97,930 + $14,289 − $100,000 = $12,219 positive.

Independent practice

Level 1 — calculate: Equipment and installation cost $125,000, working capital is $15,000, four annual after-tax inflows are $42,000, and year-4 disposal plus working- capital recovery is $25,000. At 10%, use annuity factor 3.16987 and year-4 factor 0.68301. Calculate NPV and state the independent-project decision.

Level 2 — compare: Project A requires $100,000 and has PV of future inflows $125,000. Project B requires $180,000 and has PV of future inflows $215,000. Compare NPV and PI. Which would you choose if they are mutually exclusive and have comparable risk and lives? How could strict capital rationing change the discussion?

Level 3 — ration: A $250,000 capital limit applies to indivisible projects. X requires $120,000 and has NPV $30,000; Y requires $100,000 and has NPV $22,000; Z requires $70,000 and has NPV $17,000. Choose the feasible combination with the highest total NPV, then identify two facts the numeric ranking does not capture.

Self-check and solutions

Level 1: Operating PV = $42,000 × 3.16987 = $133,135. Terminal PV = $25,000 × 0.68301 = $17,075. Total PV is $150,210; initial outflow is $140,000; NPV is $10,210 positive, so accept if the qualitative and risk review is satisfactory.

Level 2: A has NPV $25,000 and PI 1.25. B has NPV $35,000 and PI about 1.19. If only one can be chosen and risk/life are comparable, B creates $10,000 more value and NPV supports B. Under a hard funding limit with other projects available, A's higher value per invested dollar may help form a better portfolio; enumerate feasible combinations rather than ranking by PI alone.

Level 3: X + Y costs $220,000 and produces NPV $52,000. X + Z costs $190,000 and produces $47,000; Y + Z costs $170,000 and produces $39,000. Choose X + Y from the given independent combinations. Before approval, investigate dependencies, staffing, timing, risk, safety, privacy, environmental effects, and whether forecasts share an overly optimistic assumption.

Retrieval practice

1. What decision rule does positive NPV support for an independent project?
2. Why is working capital usually both a time-zero outflow and a terminal inflow?
3. Name one reason IRR can rank mutually exclusive projects poorly.
4. Is a sunk cost relevant merely because it appears in the original proposal?

Answers: accept subject to qualitative constraints; cash is tied up then released; scale, timing, or multiple-sign-change problems; no.

Exam-style application

Write a one-page recommendation for a warehouse system using a supplied cash-flow forecast. Show the timeline and NPV, identify a sunk cost, repair one missing working- capital cash flow, compare NPV with payback, test a 10% decline in annual savings, and name the evidence owner for the post-completion review. A strong answer separates the calculation, decision, uncertainty, controls, and information still required.

Lesson summary

Capital budgeting converts incremental long-term cash flows into a present-value decision. NPV is the primary value measure; IRR, PI, and payback provide supporting views. Accountants protect the decision by tracing assumptions, testing risk, and comparing actual outcomes with the approved case.