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Corporate Finance Unit 8: Capital Budgeting: NPV, IRR, Payback

Capital budgeting decides which long-term projects a firm should take. This unit compares the main decision rules and shows how to build a project's incremental after-tax cash flows.

Covers: Net present value, Payback and discounted payback, IRR, MIRR and their problems, Profitability index and capital rationing, Incremental cash flows: sunk, opportunity and side-effect costs, Operating cash flow, NWC, depreciation and salvage, Unequal lives and equivalent annual cost

Study guide

Net present value is the core rule: NPV = −C₀ + Σ CFₜ ÷ (1 + r)ᵗ, where r is the project's risk-adjusted required return. A positive NPV means the project is worth more than it costs, so taking it raises shareholder wealth by exactly that amount. NPV uses all cash flows, accounts for timing and risk, and adds across projects. The payback period, the time until cumulative cash flows recover the cost, is simple but ignores the time value of money and everything after the cutoff. Discounted payback fixes the first problem but not the second. Both bias firms toward short-lived projects.

The internal rate of return is the discount rate that makes NPV zero. For a conventional project (an outflow followed by inflows), accepting when IRR > r gives the same answer as NPV. IRR has problems. With mutually exclusive projects, IRR can rank them wrongly when their sizes or cash flow timing differ; the crossover rate, the IRR of the difference in cash flows, shows where the NPV ranking flips. Projects whose cash flows change sign more than once can have several IRRs or none. The modified IRR (MIRR) compounds inflows at the required return, giving a single rate that avoids the reinvestment assumption of the IRR.

The profitability index, PI = PV of future cash flows ÷ initial cost, accepts projects with PI > 1, which is the same as NPV > 0. PI is most useful under capital rationing, when the budget is limited: ranking by PI picks projects with the most value per dollar. When projects cannot be split, though, check feasible combinations and pick the set with the highest total NPV. For mutually exclusive projects with different lives that will be repeated, compare equivalent annual annuities (EAA = NPV ÷ annuity factor) or, for cost-only choices, equivalent annual costs.

Good decisions require the right cash flows. Include only incremental cash flows: those that change because the project is accepted. Ignore sunk costs, such as research already done. Include opportunity costs, such as the market value of land the firm already owns. Include side effects: erosion of sales of existing products is a cost, and spillover gains are a benefit. Include investment in net working capital, which is an outflow at the start and is usually recovered at the end. Exclude financing costs such as interest, because the discount rate already accounts for the cost of capital.

Operating cash flow is OCF = (Sales − Costs)(1 − t) + Depreciation × t. The second term is the depreciation tax shield: depreciation is not a cash expense, but it lowers taxes. Faster methods such as MACRS move tax savings earlier and raise their present value. When an asset is sold at the end, the after-tax salvage value equals the sale price minus the tax on any gain over book value (or plus the tax saved on a loss). A full project analysis lists, year by year, capital spending, OCF, NWC changes and after-tax salvage, then discounts the totals.

Key ideas

• Accept projects with positive NPV; NPV measures the value added to the firm.
• Payback ignores the time value of money and all cash flows after the cutoff.
• IRR agrees with NPV for single conventional projects but can mislead for mutually exclusive or nonconventional projects.
• Use only incremental cash flows: ignore sunk costs, include opportunity costs and side effects.
• Investment in NWC is a cash outflow at the start and an inflow when recovered.
• Depreciation matters only through its tax shield, D × t.
• Compare repeatable projects with unequal lives using equivalent annual annuities or costs.

Formulas and rules

Common mistakes

• Including sunk costs or interest expense in project cash flows.
• Forgetting to recover net working capital at the end of the project.
• Taxing the full salvage price instead of only the gain over book value.
• Choosing between mutually exclusive projects by IRR instead of NPV.
• Comparing total NPVs of projects with different lives that will be repeated.

Before the test, make sure you can

• Calculate NPV, IRR, MIRR and the profitability index.
• Calculate payback and discounted payback periods.
• Explain when IRR and NPV conflict and find the crossover rate.
• Identify relevant incremental cash flows, sunk costs, opportunity costs and erosion.
• Calculate OCF using the tax-shield approach and after-tax salvage.
• Build a full project cash flow schedule including NWC.
• Choose among projects under capital rationing.
• Compare unequal-life projects with EAC or EAA.

Words to know

Net present value

PV of a project's future cash flows minus its cost; the value it adds.

Internal rate of return

The discount rate that makes a project's NPV equal zero.

Payback period

Time needed for cumulative cash flows to recover the initial cost.

Discounted payback

Time needed for cumulative discounted cash flows to recover the cost.

Profitability index

PV of future cash flows divided by the initial investment.

Modified IRR

A rate that compounds inflows at the required return, avoiding multiple IRRs.

Mutually exclusive projects

Projects where accepting one means rejecting the others.

Crossover rate

The discount rate at which two projects have equal NPVs.

Incremental cash flows

Changes in the firm's cash flows caused directly by taking a project.

Sunk cost

A cost already incurred that cannot be recovered; irrelevant to the decision.

Opportunity cost

The most valuable alternative given up by using an asset in the project.

Erosion

Lost cash flows from existing products caused by a new project (cannibalization).

Depreciation tax shield

Tax savings from depreciation: D × t.

After-tax salvage value

Sale price of an asset minus taxes on any gain over book value.

MACRS

The U.S. accelerated depreciation system that front-loads depreciation deductions.

Capital rationing

A limit on the total capital available for new projects.

Equivalent annual cost

PV of costs converted to a level annual amount over the asset's life.

Sample practice questions

30 more questions like these, from level 1 to 5, are in the practice set.