Published: 20140327
Last updated: 20220318
The following project selection case puts the rather theoretical introduction given in subsection Project Selection into the context of a realistic situation. It is based on a question that reached us for our Q & A section. A quick scan encouraged us to create this subsection.
We explain the selection procedure step by step, using some basic mathematics, which you can transfer to other, similar situations.
Our company is considering to invest into one of three projects, X, Y and Z, with the following key figures:
Project X  Project Y  Project Z  
As cash outflow for each project, we have only the initial investment at the beginning of each project  10.000  10.000  10.000 
Project revenue, or Future Value of the project, FV  11.770  28.750  17.939 
Project Duration, in number of accounting periods (in this case, in years), n  1.0  3.0  1.2 
Interest Rate, r, in % per year  0.1 = 10%  0.1 = 10%  0.1 = 10% 
We can only choose one project, due to limited resources.
The present values refer to the beginning of the project, the point in time of the investment. Cash outflow is 10 Mill. USD for each project, paid at the beginning of the project. Therefore, the present value of cash outflow, PVout is 10 Mill. USD for each project.
In order to calculate the respective present value of cash inflow, PVin, of each project, we use the formula
In this formula we use the future value or revenue of each project in order to calculate PVin.
For the calculation of the respective net present value (NPV) of each project, we then use
Here are the results for our project selection case:
Project X  Project Y  Project Z  
Present Value of cash outflow, PVout  10.000  10.000  10.000 
Future Value, FV  11.770  28.750  17.939 
Present Value of cash inflow, PVin  10.700  21.600  16.000 
Net Present Value, NPV  0.700  11.600  6.000 
Thus, we might choose project Y because it has the highest net present value, NPV = 11.6 Mill. USD.
The internal rate of return (IRR) of a project is a theoretical interest rate which we calculate based on the assumption, NPV = 0.
This means PVin – Pvout = 0, or consequently PVin = PVout.
With the formula for PVin above, but now with the IRR instead of the real interest rate r, we obtain
(For the mathematics behind this formula, please refer to the annex below.)
Inserting all the figures of our project selection case, we get
Project X  Project Y  Project Z  
FV  11.770  28.750  17.939 
PVout  10.000  10.000  10.000 
n  1.0  3.0  1.2 
Internal rate of return, IRR  17.7%  42.2%  62.7% 
With these results, we should choose project Z – and we are in a dilemma: Shall we make our decision based on the highest net present value, NPV, or the highest internal rate of return, IRR?
For the calculation of the respective benefit cost ratio (BCR) and the payback period (PP) of each project, we use
and
In our project selection case, we get these results
Project X  Project Y  Project Z  
Total cash outflow, PVout  10.000  10.000  10.000 
Total cash inflow, FV  11.770  28.750  17.939 
Present Value, PVin  10.700  21.600  16.000 
n  1.0  3.0  1.2 
Average per period cash inflow  11.770  9.583  14.949 
Benefit Cost Ratio, BCR  1.07  2.16  1.60 
Payback Period, PP  0.850  1.043  0.669 
Project Y has the greatest benefit cost ratio, the project with the shortest payback period is project Z, which leads us to the same dilemma as with the comparison of net present value and internal rate of return. This should not surprise us: NPV and BCR both relate to PVin and PVout, where PVin is the total cash inflow discounted by the interest rate r over the project duration n. In contrast, IRR and PP are based on the nondiscounted future value FV, only “averaged” by the project duration n (in different ways though, nth root and simple average).
In order to come to a conclusion in our project selection case, we have to analyze other aspects as well:
Without further information about the project results and processes and corresponding project risk values, our recommendation in this project selection case is to select the project with the highest expected value creation, that is project Y with NPV = 11.6 Mill. USD or BCR = 2.16, predicting the highest benefit for our company or shareholders.
We mentioned above that IRR is the interest rate that corresponds to
NPV = 0
We also know:
Therefore, we have
We convert this equation
Finally, we obtain
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