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Managerial Accounting Unit 10: Capital Budgeting (NPV, IRR, Payback)

Capital budgeting decides which long-term investments to make. This unit teaches payback, the simple rate of return, NPV, IRR and the profitability index, and how to build the cash flows they use.

Covers: Time value of money and present value factors, Payback period, Simple (accounting) rate of return, Net present value, Internal rate of return, Profitability index and capital rationing, Taxes, working capital and salvage in cash flows

Study guide

Capital budgeting is planning for long-term investments such as new equipment, plants or product lines. These decisions tie up large sums for years, so they use cash flows rather than accounting income, and they account for the time value of money: a dollar today is worth more than a dollar later because it can be invested. The present value of a single future amount is the amount × 1 ÷ (1 + r)^n, and the present value of an even stream (an annuity) is the payment × the annuity factor. Typical cash outflows are the initial investment, working capital and repairs; inflows are added revenues, cost savings, salvage and released working capital.

Two simple methods ignore discounting. The payback period is the time it takes for cash inflows to recover the investment: investment ÷ annual inflow for even flows, or a running total for uneven flows. It is easy and stresses liquidity, but it ignores the time value of money and everything after payback. The simple (accounting) rate of return is annual incremental net operating income ÷ initial investment. It uses accrual income, so depreciation is subtracted, and it also ignores discounting. Both are useful screens, but neither should decide a major investment on its own.

Net present value discounts every cash flow at the required rate of return (often the cost of capital) and subtracts the investment. If NPV is zero or positive, the project earns at least the required return and should be accepted. The internal rate of return is the rate that makes NPV exactly zero. With even cash flows, find it by dividing the investment by the annual inflow and locating that factor in the annuity table. Accept projects whose IRR is at least the required rate. For mutually exclusive projects, choose the higher NPV, because NPV measures dollar value and assumes reinvestment at the required rate, while IRR assumes reinvestment at the IRR itself.

When funds are limited, rank independent projects by the profitability index, the PV of cash inflows ÷ investment, which shows value created per dollar. Real analyses add details. Working capital invested at the start is an outflow and is usually recovered at the end. Salvage value is a single inflow at the end. With income taxes, after-tax cash flow = pretax cash flow × (1 - tax rate) + depreciation × tax rate, because depreciation lowers taxes even though it is not a cash flow. The book value of old equipment is sunk; only its resale value matters. When benefits are hard to measure, managers can ask how large they would need to be to make NPV zero.

Key ideas

• Capital budgeting uses cash flows and the time value of money, not accounting income.
• Payback = time to recover the investment; it ignores discounting and later cash flows.
• Simple rate of return = incremental net operating income ÷ investment.
• Accept a project if NPV ≥ 0, or if IRR ≥ the required rate of return.
• For mutually exclusive projects, prefer higher NPV over higher IRR.
• Profitability index ranks projects under capital rationing.
• Depreciation matters only through its tax shield; working capital and salvage are real cash flows.

Formulas and rules

Common mistakes

• Subtracting depreciation as a cash outflow in NPV analysis.
• Using the annuity factor for a single amount such as salvage or released working capital.
• Using average cash flow to compute payback when flows are uneven.
• Choosing the higher-IRR project when mutually exclusive projects conflict with NPV.
• Including the book value of old equipment instead of its resale value.

Before the test, make sure you can

• Compute present values of single amounts and annuities using factors.
• Calculate the payback period for even and uneven cash flows.
• Calculate the simple rate of return.
• Compute NPV, including salvage, working capital and mid-life outflows.
• Find the IRR for even cash flows and compare it with the required rate.
• Rank projects with the profitability index and choose between mutually exclusive projects.
• Compute after-tax cash flows and the depreciation tax shield.

Words to know

Capital budgeting

The process of planning significant long-term investments.

Time value of money

The idea that a dollar today is worth more than a dollar received later.

Required rate of return

The minimum return a project must earn; the discount rate in NPV, often the cost of capital.

Present value

The value today of a future cash flow, found by discounting.

Annuity

A series of equal cash flows at regular intervals.

Payback period

The time needed for a project's cash inflows to recover its investment.

Simple rate of return

Annual incremental net operating income divided by the initial investment.

Net present value (NPV)

The present value of cash inflows minus the present value of cash outflows.

Internal rate of return (IRR)

The discount rate at which a project's NPV equals zero.

Profitability index

PV of cash inflows divided by the investment; used to rank projects.

Capital rationing

A limit on the funds available for investment, forcing projects to be ranked.

Working capital

Current assets minus current liabilities; an investment in it is an outflow that is usually recovered.

Salvage value

Cash received from selling an asset at the end of its useful life.

Depreciation tax shield

The tax savings from depreciation: depreciation × tax rate.

Mutually exclusive projects

Projects where choosing one rules out the others.

Intangible benefits

Hard-to-measure benefits such as quality or flexibility that may justify an investment.

Sample practice questions

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