How to Evaluate the Profitability of an Investment - Pt. 3

So far we have analyzed the possibility of evaluating an investment project through the simple Payback Period technique and, after a brief example on the financial value of time, through the NPV method.

Let's now look at the last method: the calculation of the Internal Rate of Return .

This method is quite simple to interpret from an evaluative perspective, as it encloses in a single value the judgment on the quality of an investment in terms of profitability.

Some analogies in terms of logical assumptions between NPV and IRR have already been mentioned: well, the IRR is that rate of return that makes the NPV equal to zero .

In practice, to calculate the NPV we saw that:

1. the incoming cash flows during the life of the project are quantified;
2. their value is brought back to the present time (updating);
3. the NPV is calculated as the sum of all flows, including the outgoing flow relating to the initial investment.

Instead, to calculate the IRR, point 1 remains fixed, while points 2 and 3 are inverted, in the following order:

1. the cash flows are quantified during the life of the project;
2. it is established that the NPV, that is the sum of all flows, including the outgoing one relating to the initial investment, is equal to zero;
3. the rate (equal to the IRR) that makes the sum in the previous point equal to 0 is calculated.

So, to recap:

In the VAN:

• the rate is the independent variable (i.e. it is known)
• NPV is the dependent variable

In the TIR:

• the NPV is the independent variable (i.e. it is known, and equal to zero)
• the rate is the dependent variable

Returning to our example, we will have

Looking at the results, contrary to the NPV method, this time the use of the IRR suggests that the entrepreneur should opt for solution A, i.e. to repair the system.

But how is it possible that these two methods, NPV and IRR, both more sophisticated than the Payback Period and both based on the same logic (although seen from different angles), can lead to opposite results?

The explanation lies in the different distribution of flows within the two series, and always starts from the same assumption: time is money !

The first series of flows, the one related to hypothesis A, as can be easily seen, presents decreasing values, this means that the two highest values ​​(50,000) are also the closest in time (years 1 and 2), so their current value will have a notable impact on profitability; vice versa, the flows with the lowest value are also the most distant, consequently their weight in the calculation of profitability will be marginal.

Instead, the second series of flows, the one relating to hypothesis B, is strongly penalised by having the smallest value (30,000) as the most recent flow (year 1), while the highest value (100,000) is in year 2, with the rest of the flows diluted in equal parts (70,000) in the three periods furthest away in time.

Assuming for a moment that the values ​​of the second series of flows (hypothesis B, purchase of new plant) are also decreasing (therefore with the largest flows closer in time to the current period), we note how the new values ​​of the NPV and IRR thus calculated lead this time to homogeneous evaluations, both converging coherently with each other in the choice for solution B, as shown in the following table in which, compared to the previous ones, only the distribution of the flows relating to this solution changes (highlighted in red).

In particular, the table shows how, with this new redistribution of flows in hypothesis B (purchase), using the Payback Period method, solution A (repair) continues to be preferable.

On the contrary, if the more advanced NPV and IRR methods are used, this time both agree in preferring solution B, as it is considered capable of creating more value for the company.

The conclusion that can be drawn from these examples - deliberately exaggerated - is that each of the three methods described has its own reason for being and that, therefore, in order to make an informed investment decision it is appropriate to evaluate the entire project from multiple angles, using the various methods available and critically analyzing the results thus obtained.