PrintEconomic analysis of projects can be divided into two categories:
1) Mutually Exclusive
2) Non-Mutually Exclusive
Mutually Exclusive type analysis is where the investor faces different investment alternatives, but only one project can be chosen for investment. Selecting one project excludes other projects from investment.
Non-Mutually Exclusive assessments are where the investor faces different alternatives, but more than one project can be selected regarding capital or budget constraint.
Rate of Return Analysis for Mutually Exclusive Alternatives
Example 4-1: Assume an investor has two alternatives, project A and project B, and other opportunities exist to invest at 15% ROR. The total money that investor has is 400,000 dollars.
Project A: Includes investment of 40,000 dollars at present time which yields an income of 40,000 dollars for 5 years and the salvage value at the end of the fifth year is 40,000 dollars.
| C=$40,000 | I=$40,000 | I=$40,000 | I=$40,000 | I=$40,000 | I=$40,000 | L=$40,000 | |
| A) |
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| 0 | 1 | 2 | 3 | 4 | 5 | ||
Project B: Includes investment of 400,000 dollars at the present time which yields the income of 200,000 dollars for 5 years and the salvage value at the end of the fifth year is 400,000 dollars.
| C=$400,000 | I=$200,000 | I=$200,000 | I=$200,000 | I=$200,000 | I=$200,000 | L=$400,000 | |
| B) |
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| 0 | 1 | 2 | 3 | 4 | 5 | ||
C: Cost, I:Income, L:Salvage
ROR analysis for project A:
With trial and error or using the IRR function in Excel, we can calculate . So project A is satisfactory.
ROR analysis for project B:
With trial and error or using the IRR function in Excel, we can calculate . So project B is also satisfactory.
Many people think because project A has a higher ROR, project A has to be selected over project B. But remember, we assumed 400,000 dollars is available for the investment, and the investor can only choose one of the projects. Project A takes just 10 percent of the money and gives 100% ROR, while project B takes the entire 400,000 dollars and gives 50% ROR. If the investor chooses project A and spends 40,000 dollars on this project, the rest of the money can only be invested with a 15% ROR. So, we need one more step that is called incremental analysis to be able to compare two projects and determine which project is better. The incremental analysis helps up to find a common base to compare two projects. To do so, incremental analysis breaks project B into two projects: one is similar to project A and the other is an incremental project.
Project B is equivalent to
Please note that the investing in Project B (requires $400,000) is equivalent to investing
Choosing project A with 100% ROR + investing the rest of money with 15%
Or
Choosing project B, which is equivalent to an investment in project A with 100% ROR+ investment in the incremental project (B-A)
The incremental analysis has to be done for the bigger project minus the smaller one as:
| C=$360,000 | I=$160,000 | I=$160,000 | I=$160,000 | I=$160,000 | I=$160,000 | L=$360,000 | ||
| B-A |
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| 0 | 1 | 2 | 3 | 4 | 5 | |||
This investment gives 44.4 % return.
So, incremental analysis shows that investment in project B is equivalent to investing in A (which gives 100% ROR) plus investing in project B-A (which gives 44%).
Thus, the second alternative, project B, is more desirable.
1) the rate of return on total individual project investment must be greater than or equal to the minimum rate of return, i*.
2) the ROR on incremental investment compared to the last satisfactory level of investment must be greater than or equal to the minimum ROR, i*.
The largest level of investment that satisfies both criteria is the economic choice.
Therefore, in mutually exclusive projects, a smaller ROR on a bigger investment often is economically better than a big ROR on a smaller investment. Therefore, it is often preferable to invest a large amount of money at a moderate rate of return rather than a small amount at a large return with the remainder having to be invested elsewhere at a specified minimum rate of return.
Please watch the following video (11:56): Mutually exclusive projects (Rate of return analysis).
PRESENTER: In this video, I'm going to explain how we can evaluate mutually exclusive projects. If you are given more than one investment project to evaluate, then you're facing two types of investments. It is either a non-mutually exclusive or mutually exclusive kind of problem. In a non-mutually exclusive assessment, you can choose more than one project. In this case, you will rank the project based on the parameter that you learn, such as the MPV rate of return and so on, and choose the projects from the best to worse.
But here, in this lesson, we are going to work on mutually exclusive evaluations. In this case, in mutually exclusive assessments, we have a budget constraint, so we can only choose one project. So we need to evaluate all projects and select the best project that is economically satisfactory.
Let's work on an example. Assume an investor has two alternatives, project A and project B, and other opportunities exist to invest at a 15% rate of return. And this 15% rate of return means we can make at least 15% on the $400,000 if we invest somewhere else. The $400,000 that isn't required for investment in project A or project B.
So it means each of these two projects, project A and project B are economically satisfactory only if each of them gives a return of higher than 15%. If they don't, they are not economically satisfactory, and we can invest in the other project with the 15% rate of return. So our minimum rate of return or minimum discount rate is 15%. This is the rate that we have to compare our individual assessment with.
So let's calculate the rate of return for these projects. So in order to evaluate and find-- in order to evaluate and find the best project, first, we have to evaluate each project individually. Then we compare the projects that are economically satisfactory and choose the best one. So let's calculate the rate of return for project A and project B.
First, we write the equation for the rate of return-- the present value of cost equals the present value of income plus salvage. And we calculate rate of return for project A as 53%, which is higher than 15% minimum rate of return. So it tells us that project A is economically satisfactory.
Now let's calculate the rate of return for project B. We write the equation. So we can see the rate of return for project B is 50%, which is higher than 15% of the minimum rate of return. So project B is also economically satisfactory. So because project A has a higher rate of return with the same amount of investment, we can conclude that project A has to be selected for the investment.
Now let's work on a slightly different example. Let's assume that the investor has $400,000 available for the investment. The investor has two alternatives, project A and project B, and other opportunities exist to invest at 15% rate of return. As you can see here, project A requires $40,000, but we have $400,000 money available for the investment. Again, first, we have to evaluate the projects individually, and then we compare the projects that are economically satisfactory and choose the best one.
So for project A, we write the equation to calculate the rate of return. And we calculate rate of return as 100%, which is higher than the 15% of minimum rate of return, so project A is economically satisfactory. Then we calculate the rate of return for project B. We write the equation, and we calculate the rate of return, which is 50%. 50% is higher than the minimum rate of return of 15%, so project B is also economically satisfactory.
So the results show that project A has a higher rate of return than project B. Let's see if project A is the best project for the investment or not. Using the rate of return for mutually exclusive projects can be confusing, and it doesn't necessarily give us the best economic choice. Remember, we had $400,000 available to investment, but project A is using only $40,000 of that $400,000. Project A is giving us a 100% return on $40,000, but project B is giving us a 50% return on the total $400,000.
This means if you invest in project A, then you will have an extra $360,000 that you can only invest in the other project with 15% return because project A requires only $40,000, but we have $400,000 available for the investment. So the rest of the money, that $360,000, can't be put in any other project other than the project that gives the minimum rate of return of 15%.
So there are two alternatives for the investment of $400,000. The first one is investing the $40,000 in project A with the rate of return of 100%, plus investing the rest of $360,000 with the rate of return of 15%. Or the second alternative is investing the entire $400,000 in project B with the rate of return of 50%. So we need to find a base to compare these two projects together.
In this case, we need incremental analysis, which breaks the project B into two projects. One is similar to project A and the other is an incremental project or B minus A. So project B is equivalent to project A-plus project B minus A because project A requires much less investment, and the rest of the money can only be invested in the minimum rate of return of 15%.
In order to evaluate the project B minus A, we need to deduct the project A cash inflow from the project B cash flow. So here, each year, each column, cash flow equals the project B minus project A. We write the rate of return equation for incremental cash flow-- the present value of cost equals the present value of income plus the present value of salvage. The present value of cost equals $360,000, which is the difference between project A and project B investment, and the $160,000, which is the difference between annual income for project A and Project B, and the $360,000 in year five, which is the difference between salvage values.
And we can use the Excel IRR function to calculate the rate of return. So incremental cash flow has the rate of return of 44.4%, and it is economically satisfactory. It means project B that has a rate of return of 50% is equivalent to project A with a 100% rate of return plus an incremental project with 44%.
So we have two alternatives. The first one is investing $40,000 at the rate of return of 100% plus investing $360,000 at the minimum rate of return of 15% or investing the entire $400,000 in project B, which is equivalent for investing in a project, similar to project A, with $40,000 of investment and the rate of return of 100% plus investing in the incremental project, which needs $360,000.
And the rate of return would be 44.4%. And we can conclude that project B is more desirable investment although project B has a lower rate of return. But because it uses the entire $400,000, it is a better project to invest.
When using the rate of return analysis for the evaluation of mutually exclusive projects, we need to keep two things in our mind. First, the rate of return for each individual project has to be higher than the minimum rate of return. And also, the rate of return on the incremental investment has to also be higher than the minimum rate of return.
And the largest level of investment that satisfies both criteria is the economic choice, So it is often more desirable to invest a large amount of money at a moderate rate of return rather than investing a small amount of money at a large rate of return because we need to invest the rest of the money at a minimum rate of return.
Net Present Value (NPV) Analysis of Mutually Exclusive Alternatives “A” and “B”
Considering a discount rate of 15% (minimum rate of return), the NPV for project A and B can be calculated as:
Since the NPV for project A and B is positive at the 15% discount rate (minimum rate of return on investment), then we can conclude that both projects are economically satisfactory. But NPV for project B is higher than A, which means B is a better choice to invest.
Incremental NPV Analysis
We can also calculate the incremental NPV as:
Note that incremental NPV is exactly equal to the difference between NPVA and NPVB:
The incremental at a 15% discount rate is positive, which means the incremental investment is economically satisfactory.
Remember the two decision alternatives that the investor faces:
1) Choosing project A + investing the rest of money with 15%
2) Choosing project B, which is equivalent to an investment in project A + investment in the incremental project (B-A)
The NPV for the first decision is:
1) NPVA + NPV (of investing the remainder of the available money somewhere else with a 15% rate of return)
If an investment return of 15%, then the NPV at a discount rate of 15% for that investment cash flow equals zero. So:
1)
The NPV for the second decision is:
2)
Therefore, it can be concluded that investment in project B is a better decision.
In summary, for net present value analysis of mutually exclusive choices, two requirements need to be tested: 1) the net value on total individual project investment must be positive, and 2) the incremental net value obtained in comparing the total investment net value to the net value of the last smaller satisfactory investment level must be positive. The largest level of investment that satisfies both criteria is the economic choice. Or simply, the project with the largest positive net present value is the best choice.
Note: You can use Microsoft Excel and the NPV function in order to calculate Net Present Value as explained in Example 3-6 in Lesson 3.
Please watch the following video (3:37): Mutually exclusive alternatives
PRESENTER: Another method to evaluate the mutually exclusive projects is the NPV analysis. So let's work on the same example using the NPV analysis.
Assume an investor has two alternatives, Project A and Project B, and the total money that the investor or has is $400,000, and the minimum rate of return is going to be 15%
First, we have to evaluate each project individually, and then we compared to projects that are economically satisfactory and choose the best one. So first, we have to calculate the NPV for Project A. We used the minimum rate of return of 15% as a discount rate for calculating the NPV. And because the NPV of Project A at a discount rate of 15% is positive, so we can conclude that Project A is economically satisfactory.
And then we calculate the NPV for Project B. NPV of Project B at a minimum rate of return of 15% is also positive, so Project B is also economically satisfactory.
So Project A and Project B, both have positive NPVs, so both of them are economically satisfactory. And because Project B has a higher NPV, we can conclude that Project B is a better project to invest in. This is a very good thing about NPV, that if a project has a higher NPV, we can directly conclude that that project is a better choice to invest.
We can also calculate the NPV for the incremental cash flow, which we can see here, it is positive, and we can conclude Project B is better than Project A.
But there is a good property for NPV operator is NPV of the incremental analysis, NPV of B minus A equals NPV of Project B minus NPV of Project A. So that's the reason that if we calculate the NPV of Project B higher than Project A, we can conclude that Project B is a better project to invest, because the difference shows us the increment, directly shows us the NPV of the incremental cash flow.
So again, we have two alternatives here, choosing Project A and investing the rest of the money at the 15% minimum rate of return, or choosing Project B, which is equivalent to investing in Project A plus investing in the incremental Project B minus A.
And because incremental NPV at a 15% discount rate is positive, it means that incremental investment is economically satisfactory, which means that a second alternative, or Project B, is a more desirable scenario.
Ratio Analysis of Mutually Exclusive Projects A and B
Present value ratio (PVR) also can be applied to analyze two mutually exclusive projects, A and B:
Positive PVR for project A and B indicates that both projects are economically satisfactory. But higher PVR for project A doesn’t necessarily mean project A is better than B for investment and PVR needs to be calculated for an incremental project as well.
Accepting the incremental investment indicated accepting project B over A, even though the total investment ratio on B is less than A. Just as with ROR analysis, the mutually exclusive alternative with bigger ROR, PVR is not necessarily a better mutually exclusive investment. Incremental analysis along with total individual project investment analysis is the key to a correct analysis of mutually exclusive choices.