*All that we can hope from these inspirations, which are the fruits of unconscious work, is to obtain points of departure for such calculations. As for the calculations themselves, they must be made in the second period of conscious work which follows the inspiration, and in which the results of the inspiration are verified and the consequences deduced.***Henri Poincaré**

From the Steering Bird team, online advisers in business direction, finance and strategy, we continue with this series of articles on **investment projects**.

We have talked about the financial model for projects and the project evaluation. In the latter, we indicated that quantitative and qualitative evaluation techniques existed. This time we will deal with the **quantitative analysis**.

## Quantitative analysis

*We make investment decisions based on our evaluation of the most profitable combination of probabilities.***Warren Buffett**

In the previous article we pointed out that it is the analysis of the financial data of your project through numerical methods: mathematics and statistics. Quantitative analysis, according to Investopedia, “*is a technique that uses mathematical and statistical modeling, measurement, and research to understand behavior. Quantitative analysts represent a given reality in terms of a numerical value*“.

There are several methods of **quantitative analysis** of projects. We will talk about the most used:

### Net Present Value (NPV)

*A successful business maximizes the present value of future earnings. The first requirement, therefore, of business success is sustainable profits. One-time winnings, in business as in casinos, are disappointing. We expect more from our investments than that.***Stephen Young**

The **Net Present Value (NPV)** is the quantitative method that consists of expressing at present value, all the income and expenses of a project or investment. That is, to represent in the value of money of the initial period, all the values of the flows of the financial model of the project.

The formula used for this is:

Where,

- Ft : are the money flows in each period
- t : is each period of time
- n : is the total number of time periods
*i*: is the discount rate or rate of return required of the investment

The **NPV** is used to evaluate if an investment is feasible, in the same way, it is used to compare several investment alternatives. The NPV is evaluated according to the following, always considering the **discount rate** used:

- NPV> 0: The investment will pay off. Financially feasible project.
- NPV = 0: The investment will give neither profit nor loss. Indifferent project. It depends on the case evaluated, it may or may not be feasible.
- NPV <0: The investment will give losses. Project rejected.

Using the **NPV** has some advantages, as it is easy to calculate and you can do it quickly in any spreadsheet. Even Excel comes with a default formula for **NPV**. But it also has disadvantages, as it relies too much on the work done to determine the discount rate.

Finally, we must point out that the **NPV** by itself is insufficient and should not be used as the only method to evaluate a project.

### Internal Rate of Return (IRR)

*Profitability is the sovereign criterion of the enterprise.***Peter Drucker**

The **Internal Rate of Return (IRR)** is the rate of return of an investment, being able to indicate if the project shows losses or gains. It is closely associated with the NPV, and it is also defined as the discount rate with which the NPV of the project is equal to zero. Its formula is the following:

The **IRR** is calculated by iteration, that is, by repetition until reaching the result of NPV = 0. However, some spreadsheets such as Excel have a formula to calculate it. Once the **IRR** has been determined, it must be compared with the expected rate of return (i):

- IRR>
*i*: The return on the investment is higher than the expected rate of return. - IRR =
*i*: Indifference - IRR <
*i*: The return is lower than the opportunity cost, not reaching the minimum return required for the investment.

The use of the **IRR** have some advantages, mainly in simple projects, without reinvestments and without sign variations in the final flows of the financial model:

- It is a simple indicator of the profitability of the project
- Can be easily determined on any financial / scientific spreadsheet or calculator

However, there are some disadvantages, which are more evident in projects with highly variable flows, with reinvestments or with very marked seasonality, which cause fluctuations in the final flows of the financial model:

- It assumes that all positive net cash flows are reinvested at the same rate that negative net cash flows are financed: the
**IRR**itself. - Results may be correct from the mathematical point of view, but inconsistent from the economic-financial point of view, such as the appearance of multiple roots in the solution of the
**IRR****equation**, both positive and negative.

We must point out that the **IRR** by itself is insufficient and should not be used as the only method to evaluate a project. Furthermore, obtaining more than one solution to the **IRR** (multiple roots) makes its usefulness less valid for the correct evaluation of the project.

### Benefit / Cost Ratio

*No enterprise can exist for itself alone.***Calvin Coolidge**

The **benefit / cost ratio** is the ratio between the updated benefits and costs. It helps to determine if a project is feasible, indicating the profitability for each monetary unit invested. It is calculated with the following formula:

However, the calculation is very simple, since it consists of determining the present value of the benefits, determining the present value of the costs and calculating the ratio between them:

- If it is greater than 1, the project is feasible.
- If it is equal to 1, the project is indifferent
- If it is less than 1, the project is not feasible

The **B/C ratio** gives a quick impression of the feasibility of the project. However, like NPV, the great drawback of the B/C ratio is that its entire validity rests on a good determination of the **project’s rate of return**.

We must also indicate that the **B/C ratio** by itself is insufficient. Therefore, it should not be used as the sole method of evaluating a project.

### Payback Period

*Most investors want to do today what they should have done yesterday.***Lawrence Summers**

The **payback period** measures the time it takes the project to recover the initial investment with the future cash flows of the same project.

The sum of future cash flows is considered until they equal the initial investment. Of course, this term must be less than the final term of the project. If you compare investment alternatives, the one that recovers the investment sooner will be better.

In principle, it does not consider the time value of money, but this could be solved by adding a calculation within the financial model.

The **payback period** is simple and gives a very general idea of the project, but like the previous methods, it is insufficient.

### Sensitivity Analysis

*We sail within a vast sphere, ever drifting in uncertainty, driven from end to end.***Blais Pascal**

**Sensitivity analysis** is also known as** what-if analysis**. It is a method that determines how dependent variables are affected based on changes in other variables. As Investopedia states: *“A sensitivity analysis determines how different values of an independent variable affect a particular dependent variable under a given set of assumptions”.*

Sensitivity analysis incorporates **uncertainty** into the financial model, within some predefined limits. In this analysis, one or more variables can be **sensitized**, to see how they affect the general uncertainty of the model. That is, it works as a way to **forecast** the outcome of a decision, according to a **range of variables**. With this set of variables, you can determine how changes in a variable affect the result.

The best known sensitivity analysis method is the Monte Carlo method, or **multiple probability simulation**, which introduces random variables to the financial model of the project.

The **sensitivity analysis** has several benefits, since it involves an in-depth study of the project variables: it provides mathematical-statistical support to the estimates made and allows better decisions to be made, since it incorporates **uncertainty** and **risk** into the model. On the other hand, it also has disadvantages, since its construction is based on **historical assumptions**, which reduces its accuracy in the face of unknown events.

## Synthesis

*Intelligence is not discernment and judgment or critical evaluation.***Jiddu Krishnamurti**

So far, we have presented you with several methods of **quantitative analysis** of projects. They are not all that can be used, as there are many more, including variations to those that we have indicated.

The point is that none of them can be used individually, since none is conclusive. You will need to analyze them together and, even then, you will only get numerical values that you will have to interpret and analyze.

The **combinations of favorable results** in some methods, such as NPV, and unfavorable results in others, such as IRR, are multiple and will lead you, in some cases, to review the data with which you have made the estimates and forecasts of your **financial model** of project.

Moreover, if all the variables of the **quantitative analysis** indicate that your project is favorable, it will not be enough either, since you will have to analyze it from the subjective point of view. The latter is done with a **qualitative analysis**, which we will deal with on another occasion.

We are Steering Bird, online advisers in business direction, management and finance. We specialize in **business analysis**, **control** and analysis of investment **projects**, **results** **analysis**, processes of **budget** and **forecast**, etc.

Contact us if you need help. We invite you to learn about our services and read our articles.