The Financial Evaluation of Projects is the process by which, once the initial investment, future benefits and costs during the operation stage have been defined, it allows determining the profitability of a project. Rather than showing the accounting result of an operation in which there may be a profit or a loss, its main purpose is to determine the advisability of undertaking an investment project or not.
Within the scope of the Financial Evaluation of Projects, it is permanently discussed whether the projections of income and expenses should be made at current prices or at constant prices; that is, the inflationary effect should be considered in the projections of income and expenses, or it should be ignored
This article presents a practical case of Financial Evaluation of Projects in which it is intended to demonstrate that only in projects not subject to tax payment it is indifferent to make projections at current prices than at constant prices, when obtaining the same Net Present Value (VPN) and the same Internal Rate of Return (IRR)
Key words: Financial evaluation, current prices, constant prices, inflation, relative prices.
Introduction.
Most people think that the financial evaluation of an investment project consists only in calculating the Net Present Value (NPV) or the Internal Rate of Return (IRR) known the forecasts of the Net Cash Flows. In truth, this is the easiest part and corresponds to a mechanical operation whose execution is carried out nowadays with the financial calculator or the computer. The part that deserves more attention is that of the projections of income and expenses, which, when related, result in Net Cash Flows, which are the values that, when compared with the initial investment, allow the profitability of the project to be measured.
It is permanently discussed whether these projections should be made at current prices or at constant prices. The projections at current prices consider the effect of inflation on prices. It is as if things were worth more every day, and this is so in a nominal way, that is, each day the same thing will be bought with a greater amount of money, but it is possible that it is not really increasing in value. Constant price projections abstract from the inflationary effect on prices, resulting in price invariance.
In fact, when a project study is carried out, the data on prices, expenses, etc., correspond to time zero, that is, before the project starts, so that if we want to inflate them, we must proceed as follows way: if the income of the first year of operation of the project was $ 10,000,000 and the estimated annual inflation rate is 10%, the value of the income of the following year will be $ 11,000,000 and for the following year it will be of $ 12,100,000. To make the projections at constant prices, the inflationary effect is not taken into account, that is, all income and expenses remain constant over time, which is equivalent to expressing them in zero year pesos.
The explanation in the previous paragraph is true in an economy with pure inflation, that is, in an economy in which prices and expenses increase in the same proportion (general inflation rate). However, this is not so in reality; prices and expenses vary at differential or specific rates, which conflicts between the projections at current prices and at constant prices.
CURRENT PRICES
Also called nominal or absolute prices, they are the prices of the products affected by inflation and are those given by the market. These are the prices that we observe, for example, in supermarkets every day. Yes a year ago we bought product A for $ 1,000 and today we bought it for $ 1,200, these are the current prices of the same product; the price of product A increased by 20% due to inflation.
REAL OR CONSTANT PRICES
The real or constant price of a product is its price expressed in purchasing power units of year zero. The real or constant price ignores the inflationary effect on the price of a good or service. In an inflationary economy you do have $ 1,000 at the beginning of the year, with that money you can buy a quantity of goods, identifying the purchasing power of $ 1,000. After a year, if inflation is 10%, to maintain purchasing power, you must have $ 1,100. Both the $ 1,000 from year zero and the $ 1,100 at the end of the year give the consumer the same purchasing power. The real or constant price of $ 1,200 would be $ 1,000 that we would obtain by removing the inflationary effect from $ 1,200. In consecuense,the inflationary factor (1 + i) ^ n constitutes the factor that allows us to compare the purchasing power of sums of money that are located at different times. If we multiply an amount of money by the factor (1 + i) ^ n we will find an equivalent amount in purchasing power within n periods. Likewise, a future quantity expressed in current terms can be expressed in terms of current purchasing power by dividing it by the factor (1 + i) ^ n, which is known as Deflation. Thus, for example, if we want to express the price of product A in real or constant terms, we deflate it as follows:A future quantity expressed in current terms can be expressed in terms of current purchasing power by dividing it by the factor (1 + i) ^ n, which is known as deflation. Thus, for example, if we want to express the price of product A in real or constant terms, we deflate it as follows:A future quantity expressed in current terms can be expressed in terms of current purchasing power by dividing it by the factor (1 + i) ^ n, which is known as deflation. Thus, for example, if we want to express the price of product A in real or constant terms, we deflate it as follows:
P = = = $ 1,000
This means that with the $ 1,200 at the end of the year, the same amount of goods and services is purchased as was purchased at the beginning of the year with $ 1,000.
RELATIVE PRICES
They express the price relationship of a pair of products (or group of products). The relative price of a product is its price expressed in terms of the quantity of other products that need to be sacrificed to acquire a unit of the product in question.
If the price of a product A is $ 100 and the price of a product B is $ 50, the relative price A / B is equal to 2, which means that to acquire product A it is necessary to sacrifice two quantities of the product B.
Relative prices may remain unchanged or vary depending on whether the price variation (current or constant) occurs in an economy with pure inflation (the prices of all products vary in the same proportion) or that the prices are taken into account. variations in prices, income and expenses at specific rates of increase. If the prices of all products simultaneously increased or decreased in the same proportion, their relative prices would remain unchanged. In the event that these prices vary in a different proportion, the relative prices undergo variations. A general example will help us better understand these concepts.
Suppose that we are in an economy with pure inflation in which the price variation is 50%. The current and constant prices of products A, B and C are shown in the following table:
CURRENT PRICES CONSTANT PRICES
| PRODUCT | YEAR 0 | YEAR 1 | YEAR 2 | YEAR 0 | YEAR 1 | YEAR 2 |
| TO | $ 100 | $ 150 | $ 225 | $ 100 | $ 100 | $ 100 |
| B | $ 40 | $ 60 | $ 90 | $ 40 | $ 40 | $ 40 |
| C | $ 20 | $ 30 | $ 45 | $ 20 | $ 20 | $ 20 |
In this case it is observed that the current prices of the three products increase in the same proportion (50%) and that the real or constant prices are the same prices for year 0.
We can calculate the relative prices for each year by establishing the relationship between the different prices of the three products
| RELATIVE PRICE | YEAR 0 | YEAR 1 | YEAR 2 |
| A / B | 2.5 | 2.5 | 2.5 |
| A / C | 5 | 5 | 5 |
| B / C | two | two | two |
Relative prices calculated based on current prices or based on real prices remain unchanged.
Consider, now, that the variation in prices is not due to general inflation, but rather that the price of each product increases at a specific rate. The price of product A increases at an annual rate of 50%, the price of product B increases at an annual rate of 30%, and the price of product C increases at an annual rate of 20%. Furthermore, consider that the generalized inflation rate is 50% per year.
CURRENT PRICES CONSTANT PRICES
| PRODUCT | YEAR 0 | YEAR 1 | YEAR 2 | YEAR 0 | YEAR 1 | YEAR 2 |
| TO | $ 100 | $ 150 | $ 225 | $ 100 | $ 100 | $ 100 |
| B | $ 40 | $ 52 | $ 67.60 | $ 40 | $ 34.70 | $ 30 |
| C | $ 20 | $ 24 | $ 28.80 | $ 20 | $ 16 | $ 12.80 |
We observe that the current prices of products B and C for years 1 and 2 are different from those projected assuming a generalized inflation rate of 50% (pure inflation) and, furthermore, that the real prices of these products for these same years they do not correspond to year zero prices.
Let's calculate relative prices based on new current prices and real or constant prices.
| RELATIVE PRICE | YEAR 0 | YEAR 1 | YEAR 2 |
| A / B | 2.5 | 2.9 | 3.3 |
| A / C | 5 | 6.25 | 7.80 |
| B / C | two | 2.2 | 2.3 |
It is observed that there is a variation in relative prices when using specific growth rates. The increase in relative prices indicates that products B and C are cheaper compared to product A.
Based on the results obtained from the analysis of current, real or constant prices and relative prices, we can conclude that:
- Actual or constant prices are not always year zero prices. These prices coincide only if price projections are made in an economy with pure inflation. Specific or differential growth rates allow us to project current prices and the general inflation rate to deflate these current prices and express them in terms of purchasing power for year zero., what are known as real or constant prices.
There are many approaches that exist to make the financial projections necessary for calculating Net Cash Flows. The most simplistic maintain that the results of the profitability indicators of the VPN and IRR project are identical when making projections at current prices and constant prices, if the methodologies are consistent in terms of not mixing current prices with constant rates and vice versa, in a scenario with pure inflation. In other words, if the projections are made at current prices, the discount rate must be a current rate, and if the projections are made at constant prices, the discount rate must be constant or real. Other approaches recognize the variation in relative prices in real or constant prices and propose deflating projected current prices at specific rates,with the generalized inflation rate and make the projections in constant terms.
PRACTICAL EXAMPLE
An investor has been analyzing the idea of setting up a manufacturing company dedicated to the manufacture of a model of sports shoes. The investor wants to know the profitability of the project and the convenience of investing in it or not. After the market, technical, organizational and financial studies were carried out, the following results were obtained:
- There is an unsatisfied demand Once the projections of the demand for the product were made, it was possible to obtain a projected demand of 1,200 units per year, which will remain constant during the first 5 years, the initial investment in its entirety will be provided with its own resources:
INITIAL INVESTMENT
| Land $ 10,000,000 |
| Machinery and equipment $ 25,000,000 |
| Working capital $ 8,000,000 |
| Total initial investment $ 43,000,000 |
ADDITIONAL INFORMATION
| Operational expenses $ 3,000,000 |
| Useful life of machinery and equipment 10 years |
| Tax rate 35% |
| Estimated pure inflation 6% |
| Evaluation horizon 5 years |
| Depreciation of fixed assets Straight line |
| Projections in current terms |
| Investor opportunity rate 30% per year |
| Redemption value $ 6,000,000 |
| Variable unit cost $ 20,000 |
| Unit Sale Price $ 40,000 |
To make the financial evaluation of the project, it is necessary to know the following information:
- Initial investment required for the project to go into operation The project evaluation horizon The surrender value of the project The Net Cash Flows Investor opportunity rate
From the previous data we need to know the Net Cash Flows, which constitute the real availability of cash for each evaluation period of the project, and are the values that, when confronted with the initial investment, allow us to determine the Net Present Value (NPV) and the Internal Rate of Return (IRR)
Table 1 and Table 2 show the values from the formulation of the project in reference to the market study, technical study, administrative study and financial study, which were described in the example.
Table 1 (View PDF)
Table 2
Table 3 shows the calculations of the variable unit cost, variable unit sale price, operating expenses and the value of depreciation and amortization for each of the 5 years taken as the project evaluation horizon.
Table 3
Table 4 shows the Project Cash Flow in current terms. Annual sales revenue results from multiplying the unit variable price for each year by the number of units sold each year. Annual production costs result from multiplying the variable unit cost of each year by the number of units sold. We calculate the NPV at a 30% discount rate (investor opportunity rate) and obtain a NPV of $ 4,413,632 (see cell B25). In the same cash flow, if we take as Net Cash Flows the profits before tax (UAI) for each evaluation year (that is, without considering taxes and surrender value: range of cells C17: G17), we obtain a NPV of $ 9,258,766 (see cell B27).
Table 4
Table 5 shows the Project Cash Flow in constant terms. Annual sales revenue results from multiplying the variable unit price of each year (which does not vary because it abstracts from inflation) by the number of units sold each year. Annual production costs result from multiplying the variable unit cost of each year (which does not change because it abstracts from inflation) by the number of units sold. We calculate the NPV at a discount rate of 22.64% that corresponds to the investor's opportunity rate expressed in constant terms, that is, it is the investor's real opportunity rate and we obtain a NPV of $ 3,569,452 (see cell B25), less than the NPV value of $ 4,413,632 obtained by building the project's cash flow in current terms.In the same cash flow in constant terms, we do take as Net Cash Flows the profits before tax (UAI) for each evaluation year (that is, without considering taxes and surrender value: cell range C17: G17), We obtain a NPV of $ 9,258,766 (see cell B27), the same as that obtained when making the evaluation in current terms.
Table 5
However, in these two scenarios (current prices and constant prices) the decision to invest or not in the project is the same, however the value of the NPVs is different. Let's now increase the initial investment to $ 46,600,000 and look at the new results.
If we analyze table 6, a NPV value of $ 813,632 greater than zero is observed in cell B25, which indicates that the project is still attractive to investors. Also observed in cell B27 is a NPV of $ 5,658,766 calculated with Net Cash Flows corresponding to earnings before taxes (UAI).
Table 6
In Table 7, which corresponds to the cash flow of the project in constant terms, with the new value of the initial investment we obtain a NPV of - 30,548 (cell B25) less than zero, so the project is not recommended. However, if we look at cell B27 it can be seen that we obtain a NPV of $ 5,658,766, equal in value to that obtained when evaluating the project in current prices
Table 7
Bibliographic references
- Armani, Mariano. (2007). The limits of traditional accounting. http: www.mdp.edu.ar/rectorado/secretarías/investigaciones/nexos/16/16contabilidad.htm. Reference: 07-02-08 Flores, Pedro (2001). Intellectual capital: Concepts and tools: http: //www.sistemas de knowledge.org/Materiales_de_difusion/archivos_pdf/notas-tecnicas/2001-pdf/csc2001-01.pdf. Reference: 06-30-08 Mantilla, Samuel (2004). Intellectual Capital & Knowledge Accounting. Third edition. Ecoe Editions. BogotáNevado, Domingo & López, Víctor (2000). How to measure the intellectual capital of a company?: http: //www.Docencia.udea.edu.co/ingenierías/ semgestiónconocimiento / documents / Mod10_Captlntl.pdf. Consultation: 06-28-08 Osorio, Maritza. (2006). Intellectual capital in knowledge management. Palomo, Miguel A. (2003). The evaluation of intangible assets.:http: //www.Ingenierías.uanl.mx/20/pdf/201evaluacióndeactivos.pdf. Consultation: 06-23-08Ramirez, Duván Emilio. (2007). Intellectual capital. Some reflections on its importance in organizations.: http://www.ciruelo.ininorte.edu.co/pdf/pensamiento_gestion/23/5_Capital%20intelectual.pdfRodriguez, Franz (2006). Measurement and valuation of intangible assets in the financial statements. Doctoral thesis before the University of Zaragoza, Spain Román, Nélida. (2005). Intellectual capital: Generator of success in companies.: http://www.saber.ula.ve/…/visiongerencial/año3num2/articulo6.pdf&term_termino_3=&Nombrebd=saber. Consultation: 07-10-08.
