In Chapter 3, the NPV rule was introduced. The NPV rule states that when making an investment decision, take the alternative with the highest NPV. Choosing this alternative is equivalent to receiving its NPV in cash today. The NPV rule implies that individuals should accept positive NPV projects and reject negative NPV projects. The NPV isn't the only tool to evaluate investment decisions. We investigate several other rules that are commonly used to make investment decisions in this chapter.

Using the NPV Rule

The NPV tells us the present value of the benefits (positive cash flows) net of the costs (negative cash flows) of the project. It is important to note that the NPV is dependent on the project's cost of capital. Because the cost of capital won't always be certain, it is a good idea to calculate a NPV profile, which graphs the project's NPV over a range of discount rates. Keep in mind that the IRR of a project is the discount rate which makes the NPV of the project equal to 0. The difference between a project's cost of capital and its IRR is important. It tells us the amount of estimation error that can exist without altering the original decision on the project. As mentioned earlier, there are other investment decisions that can be used besides the NPV. As we begin to investigate this different rules, keep this in mind:

Sometimes other investment rules may give the same answer as the NPV rule. Othertimes, they may disagree. When different rules conflict, always base your decision on the NPV rule because it is the most accurate and reliable!

Alternative Decision Rules

The Payback Rule

The Payback Rule is by far the simplest investment rule. According to this rule, you should only accept a project if its cash flows pay back its initial investment within a pre-specified period. It implies that an opportunity that pays back its initial investment quickly is a good idea. The payback rule works as follows:

Calculate the payback period, which is the amount of time it takes to pay back the initial investment

Accept the project if the payback period is less than a pre-specified length of time

Reject the project if the payback period is greater than that pre-specified length of time

There are several reasons as to why the payback period isn't as reliable as the NPV decision rule. First, it ignores the TVM. Second, it ignores all cash flows that occur after the payback period, and lastly it lacks a decision criterion grounded in economics. Because of this, the payback period is best saved for small investment decisions.

The Internal Rate of Return

The Internal rate of return (IRR) investment rule states that you should take any investment opportunity where IRR exceeds the opportunity cost of capital and turn down any opportunity whose IRR is less than the opportunity cost of capital. In most situations, this rule will return the same decision as the NPV rule, but not always. The IRR works for projects if all of the project's negative cash flows precede its positive cash flows. The IRR rule tends to fail when there are delayed investments or multiple IRRs. To help overcome the fact that some projects may have more than one IRR, a modified internal rate of return (MIRR) can be calculated. This IRR is computed as the discount rate that sets the NPV of the modified cash flows of the project equal to zero. There are several ways to go about calculating an MIRR:

One option is to discount all of the negative cash flows to the present value and compound all of the positive cash flows to the end of the project

Another option is to discount all of the negative cash flows to the present value and leave the positive cash flows alone.

A third option would be to leave the initial cash flow alone and compound all of the remaining cash flows to the end of the project.

A problem with MIRR is that since the cash flows have been modified, the evaluation is no longer taking into consideration the true cash flows of the project. However, a decision to accept or reject the project based on the MIRR will be the same as the NPV decision.

Choosing Between Projects

So far, we have only been evaluating one project at a time. However, companies often have to choose which project to pursue among several different options. When choosing any one project excludes us from taking the other projects, we are facing mutually exclusive projects.When faced with mutually exclusive projects, we must choose the investment decision that yields the HIGHEST NPV... we cannot simply choose a project because it has a positive NPV. The IRR rule will not work when analyzing mutually exclusive projects. The IRR doesn't work because of differences in initial investments (scale) and when projects have different cash flow patterns.

The NPV rule is affected by the scale of a project. Going by the valuation principle which was introduced in Chapter 3, if you double the cash flows of an investment, it will be worth twice as much. The IRR doesn't have the same effect because it is not affect by scale. It measures the average return on an investment. For this reason, the IRR can't be used to compare projects that have different initial investments. When comparing mutually exclusive projects with different scales, NPV needs to be utilized because the dollar impact on value must be known.

Sensitivity to timing is another reason the IRR cannot be utilized when evaluating mutually exclusive projects. IRR represents the return on an investment, but a return depends on how long the return is earned.

Evaluating Projects with Different Lives

When it comes to analyzing and comparing investment opportunities that have different lives, it is best to compute the Equivalent Annual Annuity for each project which is the level annual cash flow with the same present value as the cash flows of the project. When considering the equivalent annual annuity of different projects, it is important to take into account the required life and replacement costs.

Choosing Among Projects When Resources Are Limited

All the investment opportunities talked about thus far have had no restraints whatsoever. Unfortunately, within the business world, managers are forced to operate within a tight budget. When there are limited resources to be used, picking projects with the highest NPV won't necessarily help you. For situations where you are faced with making decisions where resources are limited, it is best to use the Profitability Index. The profitability index helps identify the optimal combination of projects to undertake with limited resources so that you utilize as many of the resources as possible.

Profitability Index = Value Created / Resource Consumed = NPV / Resource Consumed

The profitability index measures the value created in terms of NPV per unit of resource consumed. When ranking projects with limited resources, you must start with the project that has the highest NPV. You then compute the profitability index for each project and rank them in descending order. You should take on each project until all resources are being consumed.

Putting It All Together

It is important to remember that the only decision making rule that will always be correct is the NPV. The NPV provides a dollar value measure of the impact of the project on shareholder wealth. The NPV is the only rule that is directly tied to the financial manager's goal of maximizing shareholder wealth.

## Chapter 7 - Investment Decision Rules

In Chapter 3, the NPV rule was introduced. The NPV rule states that when making an investment decision, take the alternative with the highest NPV. Choosing this alternative is equivalent to receiving its NPV in cash today. The NPV rule implies that individuals should accept positive NPV projects and reject negative NPV projects. The NPV isn't the only tool to evaluate investment decisions. We investigate several other rules that are commonly used to make investment decisions in this chapter.

Using the NPV Rule

The NPV tells us the present value of the benefits (positive cash flows) net of the costs (negative cash flows) of the project. It is important to note that the NPV is dependent on the project's cost of capital. Because the cost of capital won't always be certain, it is a good idea to calculate a

NPV profile,which graphs the project's NPV over a range of discount rates. Keep in mind that the IRR of a project is the discount rate which makes the NPV of the project equal to 0. The difference between a project's cost of capital and its IRR is important. It tells us the amount of estimation error that can exist without altering the original decision on the project. As mentioned earlier, there are other investment decisions that can be used besides the NPV. As we begin to investigate this different rules, keep this in mind:Sometimes other investment rules may give the same answer as the NPV rule. Othertimes, they may disagree. When different rules conflict, always base your decision on the NPV rule because it is the most accurate and reliable!Alternative Decision Rules

The Payback Rule

The

Payback Ruleis by far the simplest investment rule. According to this rule, you should only accept a project if its cash flows pay back its initial investment within a pre-specified period. It implies that an opportunity that pays back its initial investment quickly is a good idea. The payback rule works as follows:payback period,which is the amount of time it takes to pay back the initial investmentThere are several reasons as to why the payback period isn't as reliable as the NPV decision rule. First, it ignores the TVM. Second, it ignores all cash flows that occur after the payback period, and lastly it lacks a decision criterion grounded in economics. Because of this, the payback period is best saved for small investment decisions.

The Internal Rate of Return

The

Internal rate of return (IRR) investment rulestates that you should take any investment opportunity where IRR exceeds the opportunity cost of capital and turn down any opportunity whose IRR is less than the opportunity cost of capital. In most situations, this rule will return the same decision as the NPV rule, but not always. The IRR works for projects if all of the project's negative cash flows precede its positive cash flows. The IRR rule tends to fail when there are delayed investments or multiple IRRs. To help overcome the fact that some projects may have more than one IRR, amodified internal rate of return (MIRR)can be calculated. This IRR is computed as the discount rate that sets the NPV of the modified cash flows of the project equal to zero. There are several ways to go about calculating an MIRR:A problem with MIRR is that since the cash flows have been modified, the evaluation is no longer taking into consideration the true cash flows of the project. However, a decision to accept or reject the project based on the MIRR will be the same as the NPV decision.

Choosing Between Projects

So far, we have only been evaluating one project at a time. However, companies often have to choose which project to pursue among several different options. When choosing any one project excludes us from taking the other projects, we are facing

mutually exclusive projects.When faced with mutually exclusive projects, we must choose the investment decision that yields the HIGHEST NPV... we cannot simply choose a project because it has a positive NPV. The IRR rule will not work when analyzing mutually exclusive projects. The IRR doesn't work because of differences in initial investments (scale) and when projects have different cash flow patterns.The NPV rule is affected by the scale of a project. Going by the valuation principle which was introduced in Chapter 3, if you double the cash flows of an investment, it will be worth twice as much. The IRR doesn't have the same effect because it is not affect by scale. It measures the average return on an investment. For this reason, the IRR can't be used to compare projects that have different initial investments. When comparing mutually exclusive projects with different scales, NPV needs to be utilized because the dollar impact on value must be known.

Sensitivity to timing is another reason the IRR cannot be utilized when evaluating mutually exclusive projects. IRR represents the return on an investment, but a return depends on how long the return is earned.

Evaluating Projects with Different Lives

When it comes to analyzing and comparing investment opportunities that have different lives, it is best to compute the

Equivalent Annual Annuityfor each project which is the level annual cash flow with the same present value as the cash flows of the project. When considering the equivalent annual annuity of different projects, it is important to take into account the required life and replacement costs.Choosing Among Projects When Resources Are Limited

All the investment opportunities talked about thus far have had no restraints whatsoever. Unfortunately, within the business world, managers are forced to operate within a tight budget. When there are limited resources to be used, picking projects with the highest NPV won't necessarily help you. For situations where you are faced with making decisions where resources are limited, it is best to use the

Profitability Index.The profitability index helps identify the optimal combination of projects to undertake with limited resources so that you utilize as many of the resources as possible.Profitability Index = Value Created / Resource Consumed = NPV / Resource ConsumedThe profitability index measures the value created in terms of NPV per unit of resource consumed. When ranking projects with limited resources, you must start with the project that has the highest NPV. You then compute the profitability index for each project and rank them in descending order. You should take on each project until all resources are being consumed.

Putting It All Together

It is important to remember that the only decision making rule that will always be correct is the NPV. The NPV provides a dollar value measure of the impact of the project on shareholder wealth. The NPV is the only rule that is directly tied to the financial manager's goal of maximizing shareholder wealth.