IntroductionHave you ever wondered what money is? Many people confuse money with value, but we have to understand that money is neither gold nor a piece of paper. [1]Money is nothing more than an item with extreme liquidity due to a social construction (or social pact). A highly liquid asset is one that can be sold quickly without a significant loss of value. Imagine the situation below:- Selling an item worth 100 reais for 50 bills of 2 reais each;- Selling an item worth 100 reais for 50 pencil cases worth 2 reais each;In the end, there is no loss of value in either situation, but why does the second one sound so strange? You will hardly be able to exchange those same pencil cases for another item worth 100 reais (maybe for 20 reais or 30?), so we give preference to the piece of paper, simply because it will be more widely accepted elsewhere. This ease of exchanging the item is what we call liquidity.We should therefore realize that money is not tied to its value; everything in life has value, but rather to the liquidity it has. Thinking more deeply, the truth is that the value of money is not what it says it is: a R\$ 100.00 bill today will not exchange for the same items 1 year from now.“Money continuously changes in value”- Leon, your teacherThink about how many items you could buy with a 100-real bill 10 years ago and how many you can buy now!“One of the basic premises of financial mathematics is that we cannot compare cash flows in different time periods”- Your teacher againFollowing the previous reasoning, R$ 100.00 today will not be worth the same after 1 year for several reasons. Initially, we have to consider the deterioration of purchasing power over time, also called inflation.In practice, this means that to buy the same quantity of goods in the future, we need to have more money than today.InflationThere are two main forces that affect inflation: costs and demand.On the cost side, we can mention price adjustments in so-called basic inputs (such as electricity and fuel). These items put pressure on the costs of all companies, being partly passed on to the final consumer when the product reaches the shelves of stores and supermarkets.And, as stated, there is demand-pull inflation.This demand comes from consumption (both by households and the government) and from business investment. The economy’s productive capacity is determined by the stock of machines, factories, infrastructure, labor force and its qualifications, etc. In the short term, these things are difficult to change. Therefore, when demand grows very rapidly, it becomes greater than supply. And this process ends up pulling prices upward and generating inflation.The persistent and widespread increase in the prices of goods and services is considered normal by the market as long as it remains small, because as the magnitude of inflation increases, major distortions occur in the economy, such as loss of workers’ purchasing power when wages are not adjusted; losses for those who receive fixed income; market uncertainty resulting in less investment, etc.To measure this inflation and be able to understand the value of money over time, we use price indices.Price indicesConsider a product that at time 0 has price p0, and at time t has price pT. The price index can be obtained by:\[ P_{0,t} = \frac{P_t}{P_0}\]The percentage change is given by:\[ j = P_{0,t} - 1 \]ExampleAt the beginning of September of a certain year, the price of a product was R\$ 30.00, and at the beginning of October of the same year it was R\$ 31.00. What is the price index of this product between the two dates? What is the percentage change?\[ \text{price index: }P_{0,t} = \frac{P_t}{P_0} = \frac{31}{30} = 1.0333... \]\[ \text{percentage change: }j = P_{0,t} -1 = 1.0333... -1 = 3.33\%\]Accumulated rateThe problem with inflation, among other post-fixed indices, is the constant change in their rates. To find the inflation rate for a given period, we can use the price index for that period or check the rates of the periods that segment the period we want to study. An example: to find the quarterly rate, we can check the rate of the first, second, and third month within the quarter studied.The following relationship is valid:\[ i_{\text{quarterly rate}} = (1 + i_{\text{first-month rate}})(1 + i_{\text{second-month rate}})(1 + i_{\text{third-month rate}}) - 1 \]ExamplesIn two successive years, a certain product increased by 10% and 12%, respectively. What is the accumulated rate of increase over the period?\[ i_{\text{two-year rate}} = (1 + 0.1)(1 + 0.12) - 1 = 0.232 = 23.2\% \]In January, February, March, and April of a certain year, the price of a product underwent the following increases, respectively: 1.2%, 1.5%, 0.6%, and 0.7%. What is the accumulated rate of increase for the four-month period?\[ i_{\text{four-month rate}} = (1 + 0.012)(1 + 0.015)(1 + 0.006)(1 + 0.007) - 1 = 0.0406 = 4.06\% \]Main aggregate price indices - measures of inflationUsually, an aggregate price index, called a measure of inflation, is constructed based on the monthly evolution of prices of a basic basket, previously defined based on the physical quantities of its components. Thus, for example, a hypothetical basic basket could be a set consisting of 2 kg of rice and 1 kg of beans.The inflation rate for a given month is the percentage change in the average price of the basic basket in that month in relation to the average price of the basic basket in the previous month.Wholesale price index (IPA)The calculation is based on hundreds of products in wholesale transactions. In 1964, when monetary correction was introduced in Brazil, the IPA was chosen as the reference index for correcting the Adjustable National Treasury Bonds (ORTN). [2]Consumer Price Index (CPI) and Cost of Living Index (CLI)These are indexes that aim to measure price variations of consumer products for families with well-defined characteristics. [3]National Construction Cost Index (INCC)It is a single index calculated monthly, covering products and services used in civil construction. It measures the evolution of costs in the construction sector, one of the indicators of the level of economic activity. [4]General Price Index (IGP)The IGP was conceived in the late 1940s as a broad measure of price movements. By broad, it meant an index that encompassed not only different activities but also distinct stages of the production process. Constructed in this way, the IGP could be used as a deflator of the business evolution index, resulting in a monthly indicator of the level of economic activity.General Real Estate Market Index - Commercial (IGMI-C)The IGMI-C is a profitability index for the Brazilian commercial real estate market, whose objective is to portray, as comprehensively as possible, the evolution of price appreciation and returns in the commercial real estate segment throughout Brazil. The index is presented in three versions, whose calculation formulas are presented in the Methodologies topic.National Consumer Price Index (INPC) and Broad Consumer Price Index (IPCA)The INPC/IBGE was initially created with the objective of guiding workers’ salary adjustments. The National Consumer Price System - SNIPC carries out the continuous and systematic production of consumer price indexes, using as collection units commercial and service-providing establishments, public service concessionaires, and households (for surveying rent and condominium fees). The target population of the INPC covers families with monthly incomes between 1 (one) and 5 (five) minimum wages (approximately 50% of Brazilian families), whose head of household is salaried in their main occupation and resides in urban areas of the regions, regardless of the source of income, as well as other residents in the urban areas of the covered metropolitan regions. [5]The IPCA/IBGE was initially established for the purpose of adjusting the financial statements of publicly traded companies. The National Consumer Price System - SNIPC carries out the continuous and systematic production of consumer price indexes, using as collection units commercial and service-providing establishments, public service concessionaires, and households (for surveying rent and condominium fees). The target population of the IPCA covers families with monthly incomes between 1 (one) and 40 (forty) minimum wages, regardless of the source of income, and residents in urban areas of the regions (this is equivalent to approximately 90% of Brazilian families). Indexes with specific objectives are also produced, as is currently the case with the Special Broad National Consumer Price Index - IPCA-E. Since May 2000, IBGE has also made available through the Internet the Broad National Consumer Price Index-15 - IPCA-15. Other indexes were published in the following periods: Consumer Price Index - IPC (March 1986 to February 1991); Fiscal Value Adjustment Index - IRVF (June 1990 to January 1991); Basic Food Basket Index - ICB (August 1990 to January 1991); Minimum Wage Adjustment Index - IRSM (January 1992 to June 1994); Special National Consumer Price Index - INPC-E (November 1992 to June 1994); Consumer Price Index series r - IPC-r (July 1994 to June 1995). [6]ExamplesLet us consider that, in the base month, the average price of a basic food basket is R\$ 500.00 and, in the subsequent months, it is R\$ 510.00, R\$ 520.00, and R\$ 540.00. Obtain the inflation rates for each month.\[ i_{1} = \frac{510}{500} - 1 = 0.02 = 2\% \]\[ i_{2} = \frac{520}{510} - 1 = 1.96\% \]\[ i_{3} = \frac{540}{520} - 1 = 3.85\% \]Exercises1. In January, the average price of a basic food basket was R$ 150.00 and, in February, the average price was R$ 153.00. What is the inflation rate for February?2. In August of a given year, the price of a product increased by 2% and, in September of the same year, it increased by 3%. What is the accumulated increase rate over the two-month period?3. In January, February, and March of a given year, the inflation rates were, respectively, 1.6%, 0.76%, and 0.92%. What is the accumulated inflation rate for the quarter?4. In four consecutive months, the price of a product increased by 2%, 2.6%, 3.1%, and 1.2%. What is the accumulated increase rate over the four-month period?5. Over a two-month period, the accumulated inflation rate was 1.8%; in the first month, the rate was 0.5%. What is the inflation rate in the second month?6. The accumulated inflation rate over five months was 4%. What should the inflation rate be in the sixth month so that the accumulated rate for the semester is 5%?7. If in each of six consecutive months the inflation rate is 0.7%, what is the accumulated rate for the semester?8. If from January to December of a given year (January and December included) the monthly inflation rate is 0.87%, what is the accumulated inflation rate for the year?9. Suppose that, in four consecutive months, the price of a stock has fallen 5% per month. What is the accumulated decrease rate over the four-month period?10. If, in June, the price of a stock rises 20% and, in July of the same year, falls 20%, what will be the accumulated rate over the two-month period?Answer Key1. 2%2. 5.06%3. 3.31%4. 9.19%5. 1.29%6. 0.96%7. 4.27%8. 10.95%9. - 18.5510. −4%References[1] https://financaspessoais.organizze.com.br/o-que-e-e-o-que-nao-e-dinheiro/[2] http://portalibre.fgv.br/main.jsp?lumPageId=402880811D8E34B9011D984D9EE23590[3] https://www.dieese.org.br/analiseicv/icv.html[4] http://portalibre.fgv.br/main.jsp?lumChannelId=402880811D8E34B9011D92B7684C11DF[5] http://www.portalbrasil.net/inpc.htm[6] http://www.portalbrasil.net/ipca.htm[7] http://portalibre.fgv.br/main.jsp?lumChannelId=4028818B33F047B80133F53367111455
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