chapter7

NPV profile

A graph of the project's NPV over a range of discount rates.

independent project

A project whose acceptance or rejection is independent of the acceptance or rejection of other projects.

payback investment rule

Accept a project if the project cash flows pay back the initial investment within a specified period of time.

PI decision rule

Accept projects with a positive PI greater than 1 or some specified number.

Basic IRR Rule

Accept the project if IRR is greater than the discount rate. Reject the project if IRR is less than the discount rate

If a project with conventional cash glows has a payback period less than the project's life, can you definitively state the algebraic sign of the NPV? If you know the discounted payback period is less than the project's life, what can you say about the NPV?

Assuming conventional cash flows, a payback period less than the project's life means that the NPV is positive for a zero discount rate, but nothing more definitive can be said. For discount rates greater than zero, the payback period will still be less than the project's life, but the NPV may be positive, zero, or negative, depending on whether the discount rate is less than, equal to, or greater than the IRR. The discounted payback includes the effect of the relevant discount rate. If a project's discounted payback period is less than the project's life, it must be the case that NPV is positive.

NPV Rule

accept a project if NPV > 0 reject a project of NPV < 0

payback method

alternative to NPV; how long it takes a firm to cover the initial cost of a project

Why would multiple foreign companies all come to the same conclusion that it is better to build factories in the United States?

assumption of homogenous information, everyone know the same things about a market

Internal Rate of Return (IRR)

capital budgeting method that is the rate that causes the NPV of a project to equal zero; The per- period rate earned on the project.

discounted payback period method

first discount the cash flows, then see how long it takes for the discounted cash flows to equal the initial investment; still has the flaws of the normal payback period

Capital Budgeting

The decision process for accepting or rejecting projects

Modified IRR (MIRR)

Combines the cash flows until only one change in sign remains.

NPV can be used in these situations, but not IRR:

1. Multiple internal rates of return 2. Multiple changes in cash flow signs

3 Attributes of NPV

1. NPV uses cash flows 2. NPV uses a;; the cash flows of a project 3. NPV discounts the cash flows properly `

Issues with the payback period method

1. Timing of cash flows can mean improper discounting 2. Ignores all cash flows AFTER the payback period; could lead to valuable long-term projects being rejected if taken too seriously 3. Arbitrary standard for the payback period: no comparable guide for using a payback cutoff date

3 assumptions

1. Wealth is created through good project decisions 2. Corporations operate in competitive markets 3. the value of a firm is a sum of the value of its productive projects

Steps of the discounted payback period

1. discount the cash flows using the discount rate 2. add the discounted cash flows 3. accept if the discounted payback period is less than some pre-specified number of years

NPV is....

1. equal to zero when the discount rate equals the IRR 2. positive for discount rates below the IRR 3. negative for discount rates above the IRR

issues with the average accounting return method

1. uses accounting instead of financial numbers, which are subject to an accountant's judgement 2. Does not take timing into account 3. offers no guidance on what the right targeted rate of return should be either

Relationship between a project's payback and its IRR?

For long-lived projects with relatively constant cash flows, the sooner the project pays back, the greater is the IRR, and the IRR is approximately equal to the reciprocal of the payback period.

Why use NPV?

NPV measures the wealth created by a project: the difference between the benefits of the project and the cost of the project. The NPV profile shows the relationship between NPV, IRR and the discount rate.

Suppose a project has conventional cash flows and a positive NPV. What do you know about its payback? Discounted Payback? Profitability Index? IRR?

Payback: less than the project's life Discounted Payback: less than the project's life Profitability Index: greater than 1 IRR: greater than the required return

NPV =

Present Value (inflows) - Present Value (outflows)

You are evaluating two projects, A and B. A has a short period of future cash flows, while Project B has relatively long future cash flows. Which project will be more sensitive to changes in the required return? Why?

Project B's NPV would be more sensitive to changes in the discount rate. The reason is the time value of money. Cash flows that occur further out in the future are always more sensitive to changes in the interest rate. This sensitivity is similar to the interest rate risk of a bond.

mutually exclusive projects

Projects in which the acceptance of one excludes accepting the other projects.

Indivisibilities

Projects must be taken in their entirety, which means that a company cannot invest in a fraction of the project.

Incremental IRR

The IRR of the incremental cash flows that would result from replacing one project with another.

One of the less flattering interpretations of the acronym MIRR is "meaningless internal rate of return." Why do you think people say this?

The MIRR is calculated by finding the present value of all cash outflows, the future value of all cash inflows to the end of the project, and then calculating the IRR of the two cash flows. As a result, the cash flows have been discounted or compounded by one interest rate (the required return), and then the interest rate between the two remaining cash flows is calculated. As such, the MIRR is not a true interest rate. In contrast, consider the IRR. If you take the initial investment, and calculate the future value at the IRR, you can replicate the future cash flows of the project exactly.

Average accounting return method

The average project earnings after taxes and depreciation, divided by the average book value of the investment during its life; another flawed capital budgeting method used often in the real world

capital rationing

The case where funds are limited to a fixed dollar amount and must be allocated among competing projects.

profitability index (PI)

The ratio of the present value of the future expected cash flows after initial investment divided by the amount of the initial investment.; wealth created by each dollar invested into the project

Difficulties that might appear in actual applications of the various criteria associated with capital budgeting? Which method is the easiest to implement in real life, and which is the most difficult?

The single biggest difficulty, by far, is coming up with reliable cash flow estimates. Determining an appropriate discount rate is also not a simple task. Simplest: payback approach, followed by AAR, but even these require revenue and cost projections. The discounted cash flow measures (discounted payback, NPV, IRR, and profitability index) are really only slightly more difficult in practice.

A criticism of the IRR is that there is an implicit assumption that the intermediate cash flows of the project are reinvested at the internal rate of return. How would you evaluate this criticism?

The statement is incorrect. It is true that if you calculate the future value of all intermediate cash flows to the end of the project at the IRR, then calculate the IRR of this future value and the initial investment, you will get the same IRR. However, as in the previous question, what is done with the cash flows once they are generated does not affect the IRR.

A criticism of NPV is that there is an implicit assumption that the intermediate cash flows of the project are reinvested at the required rate of return. How would you evaluate this criticism?

The statement is incorrect. It is true that if you calculate the future value of all intermediate cash flows to the end of the project at the required return, then calculate the NPV of this future value and the initial investment, you will get the same NPV. However, NPV says nothing about reinvestment of intermediate cash flows. The NPV is the present value of the project cash flows. What is actually done with those cash flows once they are generated is not relevant. Put differently, the value of a project depends on the cash flows generated by the project, not on the future value of those cash flows. The fact that the reinvestment "works" only if you use the required return as the reinvestment rate is also irrelevant because reinvestment is not relevant in the first place to the value of the project. One caveat: Our discussion here assumes that the cash flows are truly available once they are generated, meaning that it is up to firm management to decide what to do with the cash flows. In certain cases, there may be a requirement that the cash flows be reinvested. For example, in international investing, a company may be required to reinvest the cash flows in the country in which they are generated and not "repatriate" the money. Such funds are said to be "blocked" and reinvestment becomes relevant because the cash flows are not truly available.

NPV Investment Rule

When making an investment decision, take the alternative with the highest NPV. Choosing this alternative is equivalent to receiving its NPV in cash today.

Are the capital budgeting criteria we discussed applicable to nonprofit corporations? How should such entities make capital budgeting decisions? What about the US gov?

Yes, they are. Such entities generally need to allocate available capital efficiently, just as for-profits do. However, it is frequently the case that the "revenues" from not-for-profit ventures are not tangible. For example, charitable giving has real opportunity costs, but the benefits are generally hard to measure. To the extent that benefits are measurable, the question of an appropriate required return remains. Payback rules are commonly used in such cases. Finally, realistic cost/benefit analysis along the lines indicated should definitely be used by the U.S. government and would go a long way toward balancing the budget!

incremental IRR is used to account for the ______ issue when evaluating project cash flows

scale

When cash flows come at the end of the project, then they are more.....

sensitive to the market

value additivity

the value of a firm is simply the sum of the values of the different projects, divisions, or other entities within a firm; value of a firm raises by the amount of NPV within a project