Capital Budgeting Techniques

Ribbon

GLOSSARY

Capital Budget:  (1) The amount of money set aside for the purchase of fixed assets (e.g., equipment, buildings, etc.).  Also, (2) a request for authorization to purchase new fixed assets.

Mutually Exclusive Proposals:  Consideration of two or more assets that perform the same function.  If one is chosen for purchase, the others are automatically rejected.

Profitability Index:  A ratio of the present value of the benefits (PVB) to the present value of the costs (PVC).  The index is used instead of Net Present Value (i.e., PVB - PVC) when evaluating mutually exclusive proposals that have different costs.


As the picture above illustrates, the capital budgeting decision may be thought of as a cost-benefit analysis.  We are asking a very simple question: "If I purchase this fixed asset, will the benefits to the company be greater than the cost of the asset?"  In essence, we are placing the cash inflows and outflows on a scale (similar to the one above) to see which is greater.

A complicating factor is that the inflows and outflows may not be comparable: cash outflows (costs) are typically concentrated at the time of the purchase, while cash inflows (benefits) may be spread over many years.  The time value of money principle states that dollars today are not the same as dollars in the future (because we would all prefer possessing dollars today to receiving the same amount of dollars in the future).  Therefore, before we can place the costs and benefits on the scale, we must make sure that they are comparable.  We do this by taking the present value of each, which restates all of the cash flows into "today's dollars."  Once all of the cash flows are on a comparable basis, they may be placed onto the scale to see if the benefits exceed the costs.

The Major Capital Budgeting Techniques

A variety of measures have evolved over time to analyze capital budgeting requests.  The better methods use time value of money concepts.  Older methods, like the payback period, have the deficiency of not using time value techniques and will eventually fall by the wayside and be replaced in companies by the newer, superior methods of evaluation.

Very Important:  A capital budgeting analysis conducts a test to see if the benefits (i.e., cash inflows) are large enough to repay the company for three things:  (1) the cost of the asset, (2) the cost of financing the asset (e.g., interest, etc.), and (3) a rate of return (called a risk premium) that compensates the company for potential errors made when estimating cash flows that will occur in the distant future.

Let's take a look at the most popular techniques for analyzing a capital budgeting proposal.

1. Payback Period

Alright, let's get this out of the way up front: the Payback Period isn't a very good method. After all, it doesn't use the time value of money principle, making it the weakest of the methods that we will discuss here. However, it is still used by a large number of companies, so we'll include it in our list of popular methods.

What is the payback period? By definition, it is the length of time that it takes to recover your investment.

For example, to recover $30,000 at the rate of $10,000 per year would take 3.0 years.  Companies that use this method will set some arbitrary payback period for all capital budgeting projects, such as a rule that only projects with a payback period of 2.5 years or less will be accepted.  (At a payback period of 3 years in the example above, that project would be rejected.)

The payback period method is decreasing in use every year and doesn't deserve extensive coverage here.

2. Net Present Value

Using a minimum rate of return known as the hurdle rate, the net present value of an investment is the present value of the cash inflows minus the present value of the cash outflows.  A more common way of expressing this is to say that the net present value (NPV) is the present value of the benefits (PVB) minus the present value of the costs (PVC)

NPV = PVB - PVC

By using the hurdle rate as the discount rate, we are conducting a test to see if the project is expected to earn our minimum desired rate of return.  Here are our decision rules:

If the NPV is: Benefits vs. Costs Should we expect to earn at least
our minimum rate of return?
Accept the
investment?
Positive Benefits > Costs Yes, more than Accept
Zero Benefits = Costs Exactly equal to Indifferent
Negative Benefits < Costs No, less than Reject

Remember that we said above that the purpose of the capital budgeting analysis is to see if the project's benefits are large enough to repay the company for (1) the asset's cost, (2) the cost of financing the project, and (3) a rate of return that adequately compensates the company for the risk found in the cash flow estimates.

Therefore, if the NPV is:

3. Internal Rate of Return

The Internal Rate of Return (IRR) is the rate of return that an investor can expect to earn on the investment.  Technically, it is the discount rate that causes the present value of the benefits to equal the present value of the costs.  According to surveys of businesses, the IRR method is actually the most commonly used method for evaluating capital budgeting proposals.  This is probably because the IRR is a very easy number to understand because it can be compared easily to the expected return on other types of investments (savings accounts, bonds, etc.). If the internal rate of return is greater than the project's minimum rate of return, we would tend to accept the project.

The calculation of the IRR, however, cannot be determined using a formula; it must be determined using a trial-and-error technique.  This process is explained in the following link.

Calculation of the Internal Rate of Return


Which Method Is Better:  the NPV or the IRR?

Ignoring the payback period, let's ask the question: Which method is better - the NPV or the IRR? Answer: The NPV is better than the IRR. It is superior to the IRR method for at least two reasons:

  1. Reinvestment of Cash Flows:  The NPV method assumes that the project's cash inflows are reinvested to earn the hurdle rate; the IRR assumes that the cash inflows are reinvested to earn the IRR.  Of the two, the NPV's assumption is more realistic in most situations since the IRR can be very high on some projects.
  1. Multiple Solutions for the IRR:  It is possible for the IRR to have more than one solution.  If the cash flows experience a sign change (e.g., positive cash flow in one year, negative in the next), the IRR method will have more than one solution.  In other words, there will be more than one percentage number that will cause the PVB to equal the PVC.

When this occurs, we simply don't use the IRR method to evaluate the project, since no one value of the IRR is theoretically superior to the others.  The NPV method does not have this problem.

Is there any way that we can improve the performance of the IRR? Fortunately, yes. Let's take a look at how we can do this, with another technique called the modified internal rate of return.


4. Modified Internal Rate of Return

The Modified Internal Rate of Return (MIRR) is an attempt to overcome the above two deficiencies in the IRR method.  The person conducting the analysis can choose whatever rate he or she wants for investing the cash inflows for the remainder of the project's life.

For example, if the analyst chooses to use the hurdle rate for reinvestment purposes, the MIRR technique calculates the present value of the cash outflows (i.e., the PVC), the future value of the cash inflows (to the end of the project's life), and then solves for the discount rate that will equate the PVC and the future value of the benefits.  In this way, the two problems mentioned previously are overcome:

  1. the cash inflows are assumed to be reinvested at a reasonable rate chosen by the analyst, and
  2. there is only one solution to the technique.

To see how the MIRR is calculated, click on the link below:

Calculation of the Modified Internal Rate of Return


A Sample Capital Budgeting Request and Evaluation Form

What does an capital budgeting analysis look like? To see an example of an actual capital budgeting request and evaluation form, go to this page of a mining company's request for the replacement of 17 dump trucks.


Removing Potential Biases When Evaluating Mutually Exclusive Proposals

Unfortunately, some potential biases creep into our standard methods of analyzing capital budgeting projects. In other words, some of the methods have a tendency to make some projects look better than others, e.g., small vs. large projects, short-lived vs. long-lived projects. Let's look at these in more detail.

  1. Scale Effect - If we are considering mutually exclusive proposals and the assets (e.g., machines) cost different amounts, there is a potential bias in favor of accepting the more expensive asset, simply because of the larger size of the price tag.  For example, we may consider investing in either:

If we make our decision based solely on the NPV's dollar amount, we would choose asset B since it has the higher NPV.  However, per dollar invested, asset A obviously has the higher return.  If the cost of the two assets differ by a considerable amount, we should use the profitability index instead of the NPV to make our decision.

The profitability index, by definition, is the ratio of the present value of the benefits (PVB) to the present value of the cost (PVC).  This simple benefits-to-costs ratio will remove the scale effect's bias.  We obviously prefer to invest in the asset that has the higher value for the profitability index.

  1. Unequal Lives - If we are comparing mutually exclusive proposals and the assets (e.g., machines) have different lives, there is a bias in favor of accepting the longer-lived asset.  For example, assume that you are evaluating two machines but will only purchase one of them because they compete for the same job (i.e., they are mutually exclusive).  Assume that one of the machines has an expected life of 3 years and the other has an expected lifetime of 5 years before it wears out.  Everything else being the same, the 5-year machine will have the higher Net Present Value.  (It has to do with the amount of interest earned on the reinvestment of the cash inflows over a longer period of time.)

To see how to eliminate this bias, read this coverage of replacement chains.


Risk Management Techniques

How accurate will our estimates of cash flows be? After all, these are estimates of cash flows, not guarantees. There is a certainty that our cash flow estimates will be wrong to some degree.  After all, we are making certain assumptions (about future prices of raw materials, labor costs, operating schedules, etc.) to come up with these estimates of future savings and benefits.  Some of these assumptions will prove to be faulty.

Our goal is to avoid what we might call a Type II error - in this case, accepting a project that will lose money.  (As opposed to a Type I error of not accepting a project that will eventually prove to be profitable.)  Most people would consider the Type II error the more serious of the two since it leads to an actual, realized loss (as opposed to an opportunity loss).  Fortunately, there are several procedures available for assessing this risk and managing it.

For more details, read this section on managing the risk inherent in cash flow estimates.


Some Sample Capital Budgeting Problems

Here are some sample problems, with solutions:

  1. Shenandoah
  2. Seal-A-Deal
  3. Tantalize, Inc.
  4. Falcon Airlines
  5. Princess Cruise Lines

Here are some sample problems for practice:

  1.  Three Practice Problems
  2. Williamette Wireless (Sunk Costs)

Work the problems on your own before looking at the Answers to the Practice Problems shown above.

If you want to see the details of the solution, you can enter each problem's data into the spreadsheet below.


A Capital Budgeting Spreadsheet

For data that you enter, the Excel spreadsheet below will calculate each of the following:

  1. net present value
  2. internal rate of return
  3. modified internal rate of return
  4. payback period

The spreadsheet also performs a "replacement chain" analysis for comparing assets with unequal lives.

The spreadsheet contains a "front-end" menu page.  The program will work fine if you don't use the menu.  However, if you want to use it to simplify your use, you will need to do the following:

  1. If you are using Excel 2007 or Excel 2010, you will see a Security Warning bar that says, "Macros have been disabled" with an "Options" button that follows.  Click the Options button and choose "Enable this content" in the dialog box.
  2. If you are using Excel 2003, set your Excel macro security protection to "Medium".  Use the Excel menu to select Tools, Macro, Security, Medium.  Open the spreadsheet file in Excel.  When the file opens, you will be asked to choose either "Disable macros" or "Enable macros".  The file is virus-free, so it should be safe to click on "Enable Macros".

Also, the display is set for a 19-inch monitor.  If you have a different size monitor, you may want to use Excel's "Zoom" feature (i.e., Edit, Zoom) to change the size of the display for each screen.

Capital Budgeting.xls


Related Topics

Hurdle Rate

Managing Risk of Cash Flow Estimates in Capital Budgeting Decisions

Treatment of Inflation in Analysis of Capital Budgeting Projects

Replacement Chains (Adjusting for Unequal Lives)

MACRS Depreciation Table

Present Value Table (MS Word format)

Future Value Table (MS Word format)