Economic analysis of projects can be divided into two categories:
1) Mutually Exclusive
2) NonMutually 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.
NonMutually 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 41: 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) 


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) 


0  1  2  3  4  5 
C: Cost, I:Income, L:Salvage
ROR analysis for project A:
$0\text{}=40,000+40,000\left(P/{A}_{i,5}\right)+40,000\left(\text{}P/{F}_{i,5}\right)$
With trial and error or using the IRR function in Excel, we can calculate $i\text{}=\text{}RO{R}_{A}=\text{}100\%\text{}\text{}15\%$. So project A is satisfactory.
ROR analysis for project B:
$0\text{}=400,000+200,000\left(P/{A}_{i,5}\right)+400,000\left(P/{F}_{i,5}\right)$
With trial and error or using the IRR function in Excel, we can calculate $i\text{}=\text{}RO{R}_{B}=\text{}50\%\text{}\text{}15\%$ . 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 $\left(400,00040,000=360,000\text{}dollars\right)$ 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 $Project\text{}A\text{}+\text{}Project\left(BA\right)$
Please note that the investing in Project B (requires $400,000) is equivalent to investing $\$40,000\left(Project\text{}A\right)+\$360,000\left(Project\text{}BA\right)$
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 (BA)
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  
BA 


0  1  2  3  4  5 
$0\text{}=360,000+160,000\left(P/{A}_{i,5}\right)+\text{}360,000\left(P/{F}_{i,5}\right)$
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 BA (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).
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:
$$\begin{array}{l}NP{V}_{A}=40,000*\left(P/{A}_{15\%,5}\right)+40,000*\left(P/{F}_{15\%,5}\right)40,000=\$113,973.27\\ NP{V}_{B}=200,000*\left(P/{A}_{15\%,5}\right)+400,000*\left(P/{F}_{15\%,5}\right)400,000=\$469,301.71\end{array}$$
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:
$NP{V}_{BA}=160,000*\left(P/{A}_{15\%,5}\right)+360,000*\left(P/{F}_{15\%,5}\right)360,000=\$355,328.44$ Note that incremental NPV is exactly equal to the difference between NPV_{A} and NPV_{B}:
$NP{V}_{B}\u2013\text{}NP{V}_{A}=\text{}NP{V}_{BA}=\$355,328.44$
The incremental $NPV\left(NP{V}_{B}\u2013\text{}NP{V}_{A}\text{or}NP{V}_{BA}\right)$ 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 (BA)
The NPV for the first decision is:
1) NPV_{A} + 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) $\begin{array}{l}NP{V}_{A}+\text{}NPV\left(\text{ofinvestingremainderoftheavailablemoneysomewhereelsewith15\%rateofreturn}\right)=\\ NP{V}_{A}+\text{}0\text{}=\text{}NP{V}_{A}\text{}=\text{}\$113,973.27\end{array}$
The NPV for the second decision is:
2) $NP{V}_{B}=NP{V}_{A}+NP{V}_{BA}=\$113,973.27+\$355,328.44=\$469,301.71$
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 36 in Lesson 3.
Please watch the following video (3:37): Mutually exclusive alternatives
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:
$$\begin{array}{l}PV{R}_{A}=NP{V}_{A}/\left(Present\text{}value\text{}of\text{}cost\right)=113,973.27/40,000=2.85\\ PV{R}_{B}=NP{V}_{A}/\left(Present\text{}value\text{}of\text{}cost\right)=469,301.71/400,000=1.17\end{array}$$
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.
$$PV{R}_{BA}=NP{V}_{BA}/\left(Present\text{}value\text{}of\text{}investment\right)=355,328.44/360,000=99\%$$
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.