Mutually exclusive projects compete for resources and management can therefore only pick one or a few out of a group of profitable projects. Usually, the project(s) with the highest NPV is (are) the most suitable. However, projects that need to be replaced and/or that have unequal lives complicate the analysis. In finance, this is often called a replacement chain.
Ways of Comparing Mutually Exclusive Projects in a Replacement Chain
We can determine the NPV of the replacement chain as follows:
For both projects, the least common multiple of 2 and 3 is 6.
Project A: Two replacements.
Project B: Three replacements.
The above means that means investing in Project A is equivalent to receiving $76.18 at times 0 and 3 while investing in Project B is equivalent to receiving $68.60 at times 0, 2 and 4.
The equivalent annual annuity (EAA) is a series of payments over the life of the project that is equal to the NPV.
EAA can be calculated in two steps:
Determine the NPV of the investment.
Calculate the annuity payment that has a value equal to the NPV.
Project A
\(\text{NPV}= $76.18\)
\(\text{N} = 3\)
\(\text{i} =10\%\)
\(\text{PMT} =$30.63\)
Project B
\(\text{NPV}=$68.60\)
\(\text{N} = 2\)
\(\text{i}=10\%\)
\(\text{PMT} =$39.53\)
We will select Project B since it has a higher equivalent annual annuity (EAA) of $39.53.
Capital Rationing
Capital rationing is an approach that investors or companies adopt to limit the number of projects that they choose to invest in at a time. With several profitable investments, capital rationing helps in selecting the project with highest profitability. This is applicable when the company has a fixed capital budget.
Suppose Company X has a fixed capital budget of $1,200 and the opportunity to invest in 3 projects. The exhibit below details the 3 projects.
With a fixed capital budget of $1,200, the analyst will choose Project A and Project B to get an NPV of $290 and will remain with $200 of the capital budget. If the analyst chooses to invest in Project C, he will reduce his NPV to $230. When a company has a fixed capital budget, the PI is handy since it shows the profitability of each investment per dollar amount invested. However, the IRR is not as reliable as NPV and PI in selecting projects under capital rationing because high IRR investments may have low NPVs.
Capital rationing has a tendency of misallocating resources and violating the market efficiency hypothesis if resources are not invested in areas that generate the highest returns. Corporations that use capital rationing either use hard capital rationing (managers have a fixed capital budget that they cannot change) or soft capital rationing (managers have more freedom to go beyond the budget if the investment is profitable).
Question
Cran Ltd. has come across two projects it would like to consider investing in. The two projects are mutually exclusive. The companies required rate of return is 10%.
Now that we have calculated the NPV, we will go ahead and calculate the EAA for each project.
$$\text{EAA for Project Alpha}=\frac{13,268.50}{\frac{1}{0.1}\bigg[1-\frac{1}{(1+0.1)^{6}}\bigg]}=$3,046.50$$
$$\text{EAA for Project Delta}=\frac{11,428.50}{\frac{1}{0.1}\bigg[1-\frac{1}{(1+0.1)^{4}}\bigg]}=$3,605.36.50$$
We will select Project Delta since it has a higher equivalent annual annuity of $3,605.36.
A is incorrect. While Project Alpha has a higher NPV than Project Delta, its equivalent annual annuity is lower than that of Project Delta. This means that Project Alpha has lower constant annual cashflows over its lifespan.
C is incorrect. Because we can only choose one project since the question clearly states that the two projects are mutually exclusive.
Reading 19: Capital Budgeting
LOS 19 (c) Evaluate capital projects and determine the optimal capital project in situations of;
Mutually exclusive projects with unequal live using either the least common multiple approach or the equivalent annual annuity approach and
I have finished my FRM1 thanks to AnalystPrep. And now using AnalystPrep for my FRM2 preparation. Professor Forjan is brilliant. He gives such good explanations and analogies. And more than anything makes learning fun. A big thank you to Analystprep and Professor Forjan. 5 stars all the way!
michael walshe
2021-03-18
Professor James' videos are excellent for understanding the underlying theories behind financial engineering / financial analysis. The AnalystPrep videos were better than any of the others that I searched through on YouTube for providing a clear explanation of some concepts, such as Portfolio theory, CAPM, and Arbitrage Pricing theory. Watching these cleared up many of the unclarities I had in my head. Highly recommended.
Nyka Smith
2021-02-18
Every concept is very well explained by Nilay Arun. kudos to you man!
Badr Moubile
2021-02-13
Very helpfull!
Agustin Olcese
2021-01-27
Excellent explantions, very clear!
Jaak Jay
2021-01-14
Awesome content, kudos to Prof.James Frojan
sindhushree reddy
2021-01-07
Crisp and short ppt of Frm chapters and great explanation with examples.