Capital budgeting

Internal rate of return (IRR)

For a project with one investment outlay, made initially, the IRR is the discount rate that makes the present value of the future after-tax cash flows equal that investment outlay. Discounted at the IRR, the NPV is equal to zero. The decision rule for the IRR is to invest if the IRR exceeds the required rate of return for a project.

Multiple IRR Problem

For nonconventional projects the multiple IRR problem can occur. For example, a project with two sign changes could have zero, one, or two IRRs. Having two sign changes does not mean that you will have multiple IRRs; it just means that you might. The "multiple IRR problem" and the "no IRR problem" can arise for a project with nonconventional cash flows—cash flows that change signs more than once during the project's life.

Crossover rate

The crossover rate is the discount rate at which the NPV profiles for two projects cross; it is the only point where the NPVs of the projects are the same.

Discounted payback period

The discounted payback period is the number of years it takes for the cumulative discounted cash flows from a project to equal the original investment. The discounted payback period partially addresses the weaknesses of the payback period.

Payback period

The payback period is the number of years required to recover the original investment in a project. The payback is based on cash flows. The payback period ignores the time value of money and the risk of the project. Additionally, the payback period ignores cash flows after the payback period is reached. Can be used as a measure of liquidity.

Profitability Index

The profitability index (PI) is the present value of a project's future cash flows divided by the initial investment. Decision rule is to invest if PI>1.0 and don't if otherwise.

Choosing between NPV and IRR

Whenever the NPV and IRR rank two mutually exclusive projects differently, you should choose the project based on the NPV.

Conventional vs Nonconventional cash flows

An investment that involved outlays (negative cash flows) for the first couple of years that were then followed by positive cash flows would be considered to have a conventional pattern. If cash flows change signs once, the pattern is conventional. If cash flows change signs two or more times, the pattern is nonconventional.

Unlimited funds versus capital rationing

An unlimited funds environment assumes that the company can raise the funds it wants for all profitable projects simply by paying the required rate of return. Capital rationing exists when the company has a fixed amount of funds to invest.

Cannibalization

Cannibalization occurs when an investment takes customers and sales away from another part of the company.

Capital budgeting

Capital budgeting is the process that companies use for decision making on capital projects—those projects with a life of a year or more.

Opportunity cost

If you replace an old machine with a new one, what is the opportunity cost? If you invest $10 million, what is the opportunity cost? The answers to these twp questions are, respectively: the cash flows the old machine would generate, and $10 million (which you could invest elsewhere).

NPV profiles

The NPV profile is a graph that shows a project's NPV graphed as a function of various discount rates. The vertical axis represents a discount rate of zero. The point where the profile crosses the vertical axis is simply the sum of the cash flows. The horizontal axis represents an NPV of zero. By definition, the project's IRR equals an NPV of zero.

Incremental cash flow

The cash flow that is realized because of a decision; the changes or increments to cash flows resulting from a decision or action.