Choosing Among Projects When Resources Are Limited
Key Terms
Using the NPV Rule Net Present Value is defined as the difference between the present value of the future cash flows from an investment and the amount of investment. Present value of the expected cash flows is computed by discounting them at the required rate of return.
Example: An investment of $1,000 today at 10% will yield $1,100 at the end of the year; therefore, the present value of $1,100 at the desired rate of return (10 %) is $1,000. The amount of investment ($1,000 in this example) is deducted from this figure to arrive at NPV which here is zero ($1,000-$1,000). ^{[1]}
Rules:
--A zero NPV means the project repays the original investment plus the required rate of return.
--A positive NPV means a better return
--A negative NPV means a worse return, than the return from zero NPV.
The NPV Profile
Sometimes it is useful to compute an NPV Profile, which graphs the project's NPV over a range of discount rates. It is easy to prepare one using a spreadsheet such as Excel. Here is an example of an NPV Profile with instructions on how to use it.
Alternative Decision Rules Even though the NPV rule is the most accurate and reliable rule, in practice there are a wide variety of rules that are applied. Exactly why other capital budgeting techniques are used in practice is not always clear, but it is always good to know that they are out there and you should know what they are, how they are used, and how they compare to NPV. The two rules we’ll examine here are the Payback Rule and the Internal Rate of Return (IRR) Rule.
Payback Rule This investment rule suggests that you should only accept a project if its cash flows pay back its initial investment within a pre-specified period. In other words, an investment is acceptable if the Payback that results from it falls under a pre-determined # of years. The following example illustrates this idea well:
This is a financial timeline with cash flows of $50,000 (initial investment), 30 thousand in Year 1, 20 thousand in Year 2, 10 thousand in Year 3 and 5000 in Year 4.
Question: What is the payback period in this case? Well the company initially invests $50,000 and recovers $30,000 of it in the 1st year. This means it has $20,000 more left to recover (50,000 - 30,000). In the 2nd year, the company has a cash flow of $20,000 and this is the point where the company BREAK EVENS. Thus, the Payback Period is exactly 2 years.
In most instances, the numbers and cash flows won't be as good as in this example.^{[2]} It is important to note that the payback rule is not as reliable as the NPV rule because it (1) ignores the time value of money, (2) ignores cash-flows after the payback period and (3) lacks a decision criterion groudned in economics.
IRR Rule Basically, the IRR states the following: Take any investment opportunity where IRR exceeds the opportunity cost of capital. Turn down any opportunity whose IRR is less than the opportunity cost of capital.
Just like the NPV rule, IRR is based on the concept that if the return on the investment opportunity you are considering is greater than the return on other alternatives in the market with equivalent risk and maturity, you should undertake the investment opportunity.
IRR can be calculated by trial and error, financial calculators and Excel spreadsheets.
Choosing Between Projects When choosing any one project excludes us from taking the other project,we are facing mutually exclusive projects. With mutually exclusive projects, the manager's goal is to rank the projects and choose only the best one. The NPV rule, in situations like these, help managers with this decision. The NPV rule says : Pick the project with the highest NPV. Applying the IRR rule would not be very effective when making these decisions as it could lead to mistakes. Problems arise when the mutually exclusive investment have differeces in scale (require different initial investments) and when they have different cash flow patterns. It is adviced that one always rely on Net Present Value (NPV) to help us determine which option is truly more valuable.
Evaluating Projects with Different Lives Sometimes a company will have to choose between two solutions to the same problem. Often these solutions have different time lengths associated with them. One solution that financial managers can choose to best evaluate the proposed solutions is using the Equivalent Annual Annuity. Using this, decisions with different life spans can be compared on the basis of constant annual cost. In order to do this, you need to have the following information: Present Value, number of years and the discount rate. The formula is in the document below.
When you have compared the choices in similar terms, the decision is easier to make. You must also take into consideration the required life of the solution, because you don't want to pay for something you will not use past its useful life. You should also take into consideration the replacement cost. Over time technology will often be reduced in cost and can make replacing a solution a better idea down the road.
Choosing Among Projects When Resources Are Limited
When choosing projects, you also have to determine your resource needs. People, equipment, time and money are often limited resources. A helpful tool is to use the Profitability Index for these projects. The profitability index measures value created in terms of NPV per unit of resource consumed. When there are multiple projects to consider. It is helpful to compute the profitabilty index of each project, sort them according to rank (highest is best) and then select projects beginning at the top of the list, until your resource is consumed. The profiability index has some limitations however, it breaks down when there is more than one constraint and it requires scrutiny to ensure that all constrained resources are used.
Key Terms Equivalent Annual Annuity
The level annual cash flow that has the same present value as the cash flows of a project.
Use to evaluate alternative projects with different lives.
Internal Rate of Return (IRR) Investment Rule
A decision rule that accepts any investment opportunity where the IRR exceeds the opportunity cost of capital and otherwise rejects the opportunity.
Modified Internal Rate of Return
The discount rate that sets the NPV of modified cash flows of a project equal to zero. Cash flows are modified so there is only one negative cash flow (and one sign change) to ensure that only one IRR exists.
Mutually Exclusive Projects
Projects that compete with one another; by accepting one, and exclude the others.
NPV Profile A grah of a projects NPV over a range of discount rates.
Payback Investment Only Projects that pay back their initial investment within the payback period are undertaken.
Payback Period The amount of time until the cash flows from a project offset the initial investment. The time it takes to pay back the initial investment.
Profitability Index Measures the NPV per unit of resource consumed.
REFERENCES Berk, Jonathan, Et Al. “Investment Decision Rules.” Fundamentals of Corporate Finance. Boston, MA: Prentice Hall, 2008. 204-233. Print.
Contents
Using the NPV Rule
Net Present Value is defined as the difference between the present value of the future cash flows from an investment and the amount of investment. Present value of the expected cash flows is computed by discounting them at the required rate of return.
Example:
An investment of $1,000 today at 10% will yield $1,100 at the end of the year; therefore, the present value of $1,100 at the desired rate of return (10 %) is $1,000. The amount of investment ($1,000 in this example) is deducted from this figure to arrive at NPV which here is zero ($1,000-$1,000). ^{[1]}
Rules:
--A zero NPV means the project repays the original investment plus the required rate of return.
--A positive NPV means a better return
--A negative NPV means a worse return, than the return from zero NPV.
The NPV Profile
Sometimes it is useful to compute an NPV Profile, which graphs the project's NPV over a range of discount rates. It is easy to prepare one using a spreadsheet such as Excel. Here is an example of an NPV Profile with instructions on how to use it.
Alternative Decision Rules
Even though the NPV rule is the most accurate and reliable rule, in practice there are a wide variety of rules that are applied. Exactly why other capital budgeting techniques are used in practice is not always clear, but it is always good to know that they are out there and you should know what they are, how they are used, and how they compare to NPV. The two rules we’ll examine here are the Payback Rule and the Internal Rate of Return (IRR) Rule.
Payback Rule
This investment rule suggests that you should only accept a project if its cash flows pay back its initial investment within a pre-specified period. In other words, an investment is acceptable if the Payback that results from it falls under a pre-determined # of years. The following example illustrates this idea well:
|Year 0 . |Year 1 .|Year 2 . |Year 3 . |Year 4 . |
- $50,000 $30,000 $20,000 $10,000 $5,000
This is a financial timeline with cash flows of $50,000 (initial investment), 30 thousand in Year 1, 20 thousand in Year 2, 10 thousand in Year 3 and 5000 in Year 4.
Question: What is the payback period in this case? Well the company initially invests $50,000 and recovers $30,000 of it in the 1st year. This means it has $20,000 more left to recover (50,000 - 30,000). In the 2nd year, the company has a cash flow of $20,000 and this is the point where the company BREAK EVENS. Thus, the Payback Period is exactly 2 years.
In most instances, the numbers and cash flows won't be as good as in this example.^{[2]}
It is important to note that the payback rule is not as reliable as the NPV rule because it (1) ignores the time value of money, (2) ignores cash-flows after the payback period and (3) lacks a decision criterion groudned in economics.
IRR Rule
Basically, the IRR states the following: Take any investment opportunity where IRR exceeds the opportunity cost of capital. Turn down any opportunity whose IRR is less than the opportunity cost of capital.
Just like the NPV rule, IRR is based on the concept that if the return on the investment opportunity you are considering is greater than the return on other alternatives in the market with equivalent risk and maturity, you should undertake the investment opportunity.
IRR can be calculated by trial and error, financial calculators and Excel spreadsheets.
Choosing Between Projects
When choosing any one project excludes us from taking the other project,we are facing mutually exclusive projects. With mutually exclusive projects, the manager's goal is to rank the projects and choose only the best one. The NPV rule, in situations like these, help managers with this decision. The NPV rule says : Pick the project with the highest NPV. Applying the IRR rule would not be very effective when making these decisions as it could lead to mistakes. Problems arise when the mutually exclusive investment have differeces in scale (require different initial investments) and when they have different cash flow patterns. It is adviced that one always rely on Net Present Value (NPV) to help us determine which option is truly more valuable.
Evaluating Projects with Different Lives
Sometimes a company will have to choose between two solutions to the same problem. Often these solutions have different time lengths associated with them. One solution that financial managers can choose to best evaluate the proposed solutions is using the Equivalent Annual Annuity. Using this, decisions with different life spans can be compared on the basis of constant annual cost. In order to do this, you need to have the following information: Present Value, number of years and the discount rate. The formula is in the document below.
When you have compared the choices in similar terms, the decision is easier to make. You must also take into consideration the required life of the solution, because you don't want to pay for something you will not use past its useful life. You should also take into consideration the replacement cost. Over time technology will often be reduced in cost and can make replacing a solution a better idea down the road.
Choosing Among Projects When Resources Are Limited
When choosing projects, you also have to determine your resource needs. People, equipment, time and money are often limited resources. A helpful tool is to use the Profitability Index for these projects. The profitability index measures value created in terms of NPV per unit of resource consumed. When there are multiple projects to consider. It is helpful to compute the profitabilty index of each project, sort them according to rank (highest is best) and then select projects beginning at the top of the list, until your resource is consumed. The profiability index has some limitations however, it breaks down when there is more than one constraint and it requires scrutiny to ensure that all constrained resources are used.
Key Terms
Equivalent Annual Annuity
The level annual cash flow that has the same present value as the cash flows of a project.
Use to evaluate alternative projects with different lives.
Internal Rate of Return (IRR) Investment Rule
A decision rule that accepts any investment opportunity where the IRR exceeds the opportunity cost of capital and otherwise rejects the opportunity.
Modified Internal Rate of Return
The discount rate that sets the NPV of modified cash flows of a project equal to zero. Cash flows are modified so there is only one negative cash flow (and one sign change) to ensure that only one IRR exists.
Mutually Exclusive Projects
Projects that compete with one another; by accepting one, and exclude the others.
NPV Profile
A grah of a projects NPV over a range of discount rates.
Payback Investment
Only Projects that pay back their initial investment within the payback period are undertaken.
Payback Period
The amount of time until the cash flows from a project offset the initial investment. The time it takes to pay back the initial investment.
Profitability Index
Measures the NPV per unit of resource consumed.
REFERENCES
Berk, Jonathan, Et Al. “Investment Decision Rules.” Fundamentals of Corporate Finance. Boston, MA: Prentice Hall, 2008. 204-233.
Print.