If you were evaluating two mutually exclusive projects for a firm with a zero cost of capital

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Mutually Exclusive Projects is the term which is used generally in the capital budgeting process where the companies choose a single project on the basis of certain parameters out of the set of the projects where acceptance of one project will lead to rejection of the other projects.

These projects are such that acceptance of project A will lead to rejection of project B. The projects, in this case, happen to compete with each other directly.

Methods used by Companies to Evaluate Mutually Exclusive Projects

There are various methods adopted by companies to evaluate mutually exclusive projects, and they serve as the criterion on which the acceptance or rejection decision shall be made.

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Source: Mutually Exclusive Projects (wallstreetmojo.com)

#1 – NPV (Net Present Value)

NPV refers to the present valuePresent Value (PV) is the today's value of money you expect to get from future income. It is computed as the sum of future investment returns discounted at a certain rate of return expectation.read more of the future cash flows arising out of the project, which then deducts the initial outlay or investment.

The decision criteria stand as follows:

• Accept if NPV > 0
• Reject if NPV < 0

#2 – IRR (Internal Rate of Return)

It is nothing but the discount rate that would make all of the present values of cash flows equal to the initial outlay. IRRInternal rate of return (IRR) is the discount rate that sets the net present value of all future cash flow from a project to zero. It compares and selects the best project, wherein a project with an IRR over and above the minimum acceptable return (hurdle rate) is selected.read more is the discount rate at which the NPV of the project equals zero. Companies often have a hurdle rateThe hurdle rate in capital budgeting is the minimum acceptable rate of return (MARR) on any project or investment required by the manager or investor. It is also known as the company’s required rate of return or target rate.read more or a required rate of returnRequired Rate of Return (RRR), also known as Hurdle Rate, is the minimum capital amount or return that an investor expects to receive from an investment. It is determined by, Required Rate of Return = (Expected Dividend Payment/Existing Stock Price) + Dividend Growth Rateread more that serves as the benchmark.

The decision criteria therefore are :

• Accept if IRR > r (Required rate of return/hurdle rate).
• Reject if IRR < r (Required rate of return/hurdle rate).

#3 – Payback Period

The payback PeriodThe payback period refers to the time that a project or investment takes to compensate for its total initial cost. In other words, it is the duration an investment or project requires to attain the break-even point.read more method takes into consideration the tenure or rather the number of years required to recover the initial investment based on the cash flows of the project.

#4 – Discounted Payback Period

One drawback of the payback periodPayback period is a very simple method for calculating the required period; it does not involve much complexity and aids in analyzing the project's reliability. Its disadvantages include the fact that it completely ignores the time value of money, fails to depict a detailed picture, and ignores other factors as well.read more is that the cash flows do not consider the impact of the time value of money. Hence discounted payback periodThe discounted payback period is when the investment cash flow paybacks the initial investment, based on the time value of money. It determines the expected return from a proposed capital investment opportunity. It adds discounting to the primary payback period determination, significantly enhancing the result accuracy.read more, therefore, considers the cash flows by discounting them to their present values and then calculating the payback.

#5 – Profitability Index (PI)

Profitability IndexThe profitability index shows the relationship between the company projects future cash flows and initial investment by calculating the ratio and analyzing the project viability. One plus dividing the present value of cash flows by initial investment is estimated. It is also known as the profit investment ratio as it analyses the project's profit.read more refers to the present values of the future cash flows arising out of the project, which is then divided by the initial investment.

The investment criteria are :

• Invest if PI > 1
• Reject if PI < 1

Examples

Example #1

Consider the following cash flows of project A and project B.

Solution:

Calculation of NPV for Project A will be –

Calculation of NPVThe NPV (Net Present Value) of an investment is calculated as the difference between the present cash inflow and cash outflow. It is an Excel function and a financial formula that takes rate value for inflow and outflow as input.read more for Project B will be –

The NPV and IRR calculation using an excelThe internal rate of return, or IRR, calculates the profit generated by a financial investment. IRR is a built-in function in Excel that calculates the IRR using a range of values as an input and an estimate value as the second input.read more workbook is demonstrated asunder. Assuming a discount rate of 13%(future cash flows are discounted at 13% to arrive at their present value), using the NPV function, we are able to arrive at the required NPV after deducting the initial outlay. (Year zero in this case).

Calculation of IRR for Project A will be –

Similarly, IRR can now also be arrived at using the IRR function in excel, as demonstrated below.

Calculation of IRR for Project B will be –

NPV is positive in the case of both projects, and IRR is greater than the discount rate of 13%.

Since the projects are mutually exclusive, we can’t choose all the projects simultaneously. However, since both the NPV and IRR are greater in the case of project A, we would choose project A since these are mutually exclusive projects.

So have you come across scenarios wherein the NPV and IRR conflict against each other while evaluating such projects?

Yes, certainly, there are situations where we counter conflict between NPV and IRR while evaluating such projects.

Example #2

Consider the following cash flows of 2 projects.

Solution:

The NPV and IRR assuming a discount rate of 10%, are displayed below as follows.

Calculation of NPV for Project A will be –

Calculation of NPV for Project B will be –

Calculation of IRR for Project A will be –

Calculation of IRR for Project B will be –

If you happen to notice, NPV of project B is greater than A, whereas the IRR of project A is greater than project B.

Please refer given excel template above for the detailed calculation of mutually exclusiveMutually exclusive refers to those statistical events which cannot take place at the same time. Thus, these events are entirely independent of one another, i.e., one event's outcome has no impact on the other event's result.read more project examples.

Does One Method Have an Advantage Over the Other?

• In instances where the initial cash flows are higher, it is noticed that the IRR shows a higher number, in contrast to the project where the project has cash flows coming in later. Hence IRR will tend to skew towards a higher range when there are higher cash flows initially.
• Usually, the discount rates change over the life of the company. An unrealistic assumption that IRR makes is that all cash flows in the future are invested at the IRR rate.
• There may also be instances wherein there are multiple IRRs or no IRR for a project.

Does NPV Seem Like a Better Option then IRR?

Well yes. An important assumption that NPV makes is that all future cash flows are reinvested at the most realistic discount rate-opportunity cost of funds. NPV, too, has its disadvantages as it does not consider the scale of a project.

Nevertheless, when faced with a conflict between IRR and NPV in the case of mutually exclusive projects, it is suggested to go ahead with the NPV method as this happens to show the amount of real wealth gain for the company.

Advantages and Disadvantages

Advantages

• The company will be able to optimally select the best project/investment that gives in the best returns.
• The company will be able to commit their capital only to the optimal project considering the limited resources.

Disadvantages

• Though both projects generate positive NPVs, companies will have to select the winner and leave out the rest.

Are There any Changes Off Late in Mutually Exclusive Projects?

Conclusion

Well, I think to gauge on the feasibility or viability of the investments, these methods serve as a great decision-making tool for corporates, as when they invest in positive NPV generating mutually exclusive projects, they tend to add to the wealth of the shareholders, which no doubt gets reflected in the increasing share prices.

Recommended Articles

This has been a guide to What are Mutually Exclusive Projects and its definition. Here we discuss the examples of mutually exclusive projects and the best methods for evaluation. You can learn more about financial modeling from the following articles –

• Top Examples of IRR
• Net Present Value | Advantages
• Profile of NPV
• PV vs NPV