A PROJECT SELECTION CASE

Published: 2014-03-27
Last updated: 2022-03-18

The following project selection case puts the rather theoretical introduction given in sub-section 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 sub-section.

We explain the selection procedure step by step, using some basic mathematics, which you can transfer to other, similar situations.

Starting point

Our company is considering to invest into one of three projects, X, Y and Z, with the following key figures:

We can only choose one project, due to limited resources.

Step 1: Calculation of the net present value

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:

Thus, we might choose project Y because it has the highest net present value, NPV = 11.6 Mill. USD.

Step 2: Calculation of the internal rate of return

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

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?

Step 3: Benefit cost ratio, payback period and other aspects

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 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 non-discounted future value FV, only “averaged” by the project duration n (in different ways though, n-th 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.

Annex: Derivation of the formula for IRR

We mentioned above that IRR is the interest rate that corresponds to

NPV = 0

How to calculate IRR, (1)

We also know:

How to calculate IRR, (2)

Therefore, we have

How to calculate IRR, (3)

We convert this equation

How to calculate IRR, (4)

Finally, we obtain

How to calculate IRR, (Result)

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