Indicadores Financieros y Económicos

Sensitivity Analysis and Finances

Juan Gaytán Cortés
Universidad de Guadalajara, México

Sensitivity Analysis and Finances

Mercados y Negocios, núm. 51, pp. 131-142, 2024

Universidad de Guadalajara

The financial projections used in decision-making are associated with a degree of uncertainty regarding the correct choice of the hypotheses used or the certainty of the value of the variables, which is why it is necessary to place ourselves in several scenarios, in which the hypotheses and the value of the variables over which we have less control and which in turn have the greatest impact on the results must be varied. expected results. The above process is known as Sensitivity Analysis.

Purpose of sensitivity analysis: it consists of improving the quality of the information used so that the decision maker has additional tools that allow them to achieve better results and generate greater competitive advantages.

Sensitivity Analysis, also called Post-Optimization Analysis, also consists of determining how sensitive the optimal solution is to the change of some of the data or parameters, keeping the rest fixed (John & Faulín, 2023).

Intangible and intangible financial modeling, sensitivity analysis consists of analyzing how the different economic values of a set of independent variables affect a specific dependent variable, as well as knowing how it will respond, among the different economic scenarios.

In finance, sensitivity analysis is used to model the performance outcome of changes in interest rates, and asset prices, as well as changes in demand, in the formation of investment portfolios and the mix of their assets. Also, changes in systemic or market risk, unsystematic risk, as well as the change in the variables associated with different investment strategies.

Sensitivity analysis is the procedure by which it is possible to determine how much the objective function (IRR or NPV) is affected or how sensitive it is to changes in certain variables of the investment, considering that the others do not change. (Baca, 2022; Morales & Morales, 2009).

Forms of study of sensitivity: according to research conducted by John and Faulín (2023).

The first is to solve the entire problem again every time some of the original data has been modified. This method can take a long time to determine all the variants when we are faced with a large set of possible changes.

The second way is that once a problem has been solved, we proceed to analyze how the optimal result obtained would be affected by the variation within a "tolerable" range, of the value of one of the variables, keeping the value of the remaining variables fixed.

If the effects of varying more than one parameter (or a parameter beyond the “tolerance range”) are studied, the problem must be reprogrammed.

Methods to study sensitivity: to obtain a measure of the variability in the results according to the research of Tejeda and others (2015) and Pérez and others (2012), the following methods can be mentioned:

Informal method: the analyst assesses the stability of the variables.

Decision tree: Future decision points and possible uncertain events are displayed; in which case each alternative is presented as a branch of the tree.

Monte Carlo model: links sensitivities and probability distributions of input variables. An uncertainty analysis allows you to quantitatively assess the variability of the model components for a specific situation and deduce an uncertainty distribution for each state or output variable of the model (Monod et al., 2006). Generally, this analysis is carried out using Monte Carlo simulation (Saltelli et al., 2008).

Dupont Method: measures the company's profitability about sales, and total asset turnover, which indicates how efficiently assets have been used to generate sales.

Software and sensitivity: there are different software’s on the market, among them we can mention the following: @RISK, Managerial Analyzer Delfos Pro, Oracle Crystal Ball, EasyPlanEx, RealiaSoft RENO, MultiPlanEx, these softwares perform financial analysis, investment projection, as well as the financial sensitivity analysis.

Economic and financial indicators are useful tools that benefit organizations by facilitating timely and appropriate decision-making in relation to their corporate and financial strategies.

Next, the evolution of some economic and financial indicators of the Mexican environment is described and shown to facilitate decision-making related to personal and business strategies in an integral manner.

1. NATIONAL CONSUMER PRICE INDEX (INPC)

Born in 1995 and reflecting changes in consumer prices, it measures the general increase in prices in the country. It is calculated fortnightly by the Bank of Mexico and INEGI (2021). INPC is published in the Official Gazette of the Federation on the 10th and 25th of each month. The reference period is the second half of December 2010.

Table 1
Accumulated inflation in the year (Base: 2nd. Fortnight of December 2010 = 100 with data provided by Banco de México)
Periodo20102011201220132014201520162017201820192020202120222023
Enero1.480.770.980.790.90-0.090.381.700.530.090.480.860.590.76
Febrero2.151.421.471.461.150.090.822.290.910.060.901.501.431.24
Marzo2.521.841.551.991.430.510.972.921.240.440.852.342.431.51
Abril1.980.720.691.811.240.250.653.040.900.50-0.172.672.981.47
Mayo0.60-0.70-0.650.950.91-0.260.202.920.730.210.222.883.171.27
Junio0.49-0.41-0.411.121.09-0.090.313.181.120.270.763.434.04 1.37
Julio0.56-0.040.321.141.420.060.573.571.660.651.434.044.811.86
Agosto0.910.300.921.311.730.270.864.082.260.631.824.245.54 2.42
Septiembre1.270.731.121.612.180.271.474.412.690.892.064.886.192.88
Octubre2.352.332.122.772.741.162.095.063.221.442.685.766.793.27
Noviembre3.894.873.864.573.571.712.896.154.102.262.766.977.413.93
Diciembre4.195.813.975.214.082.133.366.774.832.833.157.357.824.66
Source: Own elaboration (INEGI, 2024). Route: Indicadores económicos de coyuntura > Índices de precios > Índice nacional de precios al consumidor. Base segunda quincena de julio de 2018=100 > Mensual > Índice > Índice general

Inflation in Mexico (2010-2023 accumulated at the end of the year)
Graph 1
Inflation in Mexico (2010-2023 accumulated at the end of the year)
Source: Own elaboration (INEGI, 2024). Route: Indicadores económicos de coyuntura > Índices de precios > Índice nacional de precios al consumidor. Base segunda quincena de julio de 2018=100 > Mensual > Índice > Índice general

Inflation in Mexico (accumulated  January-August 2023)
Graph 2
Inflation in Mexico (accumulated January-August 2023)
Source: Own elaboration (INEGI, 2024). Route: Indicadores económicos de coyuntura > Índices de precios > Índice nacional de precios al consumidor. Base segunda quincena de julio de 2018=100 > Mensual > Índice > Índice general

2. THE PRICE AND QUOTATION INDEX OF THE MEXICAN STOCK EXCHANGE (IPC)

Represents the change in the values traded on the Mexican Stock Exchange concerning the previous day to determine the percentage of rising or falling of the most representative shares of the companies listed therein.

Table 2
The Price and Quotation Index of the Mexican Stock Exchange (Base: October 1978, 0.78=100)
2011201220132014201520162017201820192020202120222023
36,98237,42245,27840,87940,95143,63147,00150,45643,98844,86242,98651,33154,564
37,02037,81644,12138,78344,19043,71546,85747,43842,82441,32444,59353,40152,758
37,44139,52144,07740,46243,72545,88148,54246,12543,28134,55447,24656,53753,904
36,96339,46142,26340,71244,58245,78549,26148,35444,59736,47048,01051,41855,121
35,83337,87241,58841,36344,70445,45948,78844,66342,74936,12250,88651,75352.736
36,55840,19940,62342,73745,05445,96649,85747,66343,16137,71650,29047,52453.526
35,99940,70440,83843,81844,75346,66151,01249,69840,86337,02050,86848,14454.819
35,72139,42239,49245,62843,72247,54151,21049,54842,62336,84153,30544,91953.021
33,50340,86740,18544,98642,63347,24650,34649,50443,01137,45951,38644,62750,875
36,16041,62041,03945,02844,54348,00948,62643,94343,33736,98851,31049,92249,062
36,82941,83442,49944,19043,41945,28647,09241,73342,82041,77949,69951,68554,060
37,07743,70642,72743,14642,99845,64349,35441,64043,54144,06753,27248,46457,386
Source: Own elaboration (BANXICO, 2024). https://www.banxico.org.mx/SieInternet/consultarDirectorioInternetAction.do?sector=7&accion=consultarCuadro&idCuadro=CF57&locale=es

The Price and Quotation Index of the Mexican Stock Exchange, 2011 - 2023 (Score at the end of each year)
Graph 3
The Price and Quotation Index of the Mexican Stock Exchange, 2011 - 2023 (Score at the end of each year)
Source: Own elaboration (BANXICO, 2024). https://www.banxico.org.mx/SieInternet/consultarDirectorioInternetAction.do?sector=7&accion=consultarCuadro&idCuadro=CF57&locale=es

The Price and Quotation Index of the Mexican Stock Exchange, January-December 2023 (Score at the end of each month)
Graph 4
The Price and Quotation Index of the Mexican Stock Exchange, January-December 2023 (Score at the end of each month)
Source: Own elaboration (BANXICO, 2024). https://www.banxico.org.mx/SieInternet/consultarDirectorioInternetAction.do?sector=7&accion=consultarCuadro&idCuadro=CF57&locale=es

3. EXCHANGE RATE

It is the value of the Mexican peso concerning the dollar calculated with the daily average of the five most important banks in the country, which reflects the spot price (cash), negotiated between banks. It is highly related to Inflation, the interest rate, and the Mexican Stock Exchange.

Table 3
Exchange rate (National currency per US dollar, parity at the end of each period)
Period2011201220132014201520162017201820192020202120222023
January12.0212.9512.7113.3714.6918.4521.0218.6219.0418.9120.2220.7418.79
February12.1712.8712.8713.3014.9218.1719.8318.6519.2619.7820.9420.6518.40
March11.9712.8012.3613.0815.1517.4018.8118.3319.3823.4820.4419.9918.11
April11.5913.2012.1613.1415.2219.4019.1118.8619.0123.9320.1820.5718.07
May11.6313.9112.6312.8715.3618.4518.5119.7519.6422.1819.9219.6917.56
June11.8413.6613.1913.0315.5718.9117.9020.0619.2123.0919.9120.1317.07
July11.6513.2812.7313.0616.2118.8617.6918.5519.9922.2019.8520.3416.73
August12.4113.2713.2513.0816.8918.5817.8819.0720.0721.8920.0620.0916.84
September13.4212.9213.0113.4517.0119.5018.1318.9019.6822.1420.5620.0917.62
October13.2013.0912.8913.4216.4518.8419.1519.8019.1621.2520.5319.8218.08
November14.0313.0413.0913.7216.5520.5518.5820.4119.6120.1421.4519.4017.14
December13.9913.0113.0814.7217.2120.7319.7919.6818.8719.9120.4719.4716.89
Source: Own elaboration (BANXICO, 2024). https://www.banxico.org.mx/SieInternet/consultarDirectorioInternetAction.do?sector=6&accion=consultarCuadro&idCuadro=CF102&locale=es NOTE: Exchange rate FIX by The Banco de México, used for settling obligations denominated in foreign currency. Quote at the end

Source: Own elaboration (BANXICO, 2024).

Exchange rate (National currency per US dollar, 2011-2023, FIX parity at the end of each year)
Graph 5
Exchange rate (National currency per US dollar, 2011-2023, FIX parity at the end of each year)
Source: Own elaboration (BANXICO, 2024). https://www.banxico.org.mx/SieInternet/consultarDirectorioInternetAction.do?sector=6&accion=consultarCuadro&idCuadro=CF102&locale=es

Exchange rate (National currency per US dollar, January-December 2023, FIX parity at the end of each month)
Graph 6
Exchange rate (National currency per US dollar, January-December 2023, FIX parity at the end of each month)
Source: Own elaboration (BANXICO, 2024). https://www.banxico.org.mx/SieInternet/consultarDirectorioInternetAction.do?sector=6&accion=co nsultarCuadro&idCuadro=CF102&locale=es

4. EQUILIBRIUM INTERBANK INTEREST RATE (TIIE)

On March 23, 1995, the Bank of Mexico, to establish an interbank interest rate that better reflects market conditions, released the Interbank Equilibrium Interest Rate through the Official Gazette of the Federation.

Table 4
Equilibrium interbank interest rate (28-day quote)
Periodo20102011201220132014201520162017201820192020202120222023
Enero4.914.864.794.843.783.293.566.157.668.597.504.475.7210.78
Febrero4.924.844.784.803.793.294.056.617.838.547.294.366.0211.10
Marzo4.924.844.774.353.813.304.076.687.858.516.744.286.3311.34
Abril4.944.854.754.333.803.304.076.897.858.506.254.286.7311.53
Mayo4.944.854.764.303.793.304.107.157.868.515.744.297.0111.54
Junio4.944.854.774.313.313.304.117.368.108.495.284.327.42 11.50
Julio4.924.824.784.323.313.314.597.388.118.475.194.528.04 11.50
Agosto4.904.814.794.303.303.334.607.388.108.264.764.658.50 11.50
Septiembre4.904.784.814.033.293.334.677.388.128.044.554.758.8911.50
Octubre4.874.794.833.783.283.305.117.388.157.974.514.989.5611.50
Noviembre4.874.804.853.803.313.325.577.398.347.784.485.1310.0011.50
Diciembre4.894.794.853.793.313.556.117.628.607.554.495.7210.5311.50
Source: Own elaboration (BANXICO, 2024). https://www.banxico.org.mx/SieInternet/consultarDirectorioInternetAction.do?sector=18&accion=c onsultarCuadro&idCuadro=CF101&locale=es

Equilibrium interbank interest rate, 2010- 2023 (at the end of each year)
Graph 7
Equilibrium interbank interest rate, 2010- 2023 (at the end of each year)
Source: Own elaboration (BANXICO, 2024). https://www.banxico.org.mx/SieInternet/consultarDirectorioInternetAction.do?sector=18&accion=c onsultarCuadro&idCuadro=CF101&locale=es

Equilibrium interbank interest rate, January-December 2023 (28-day quote)
Graph 8
Equilibrium interbank interest rate, January-December 2023 (28-day quote)
Source: Own elaboration (BANXICO, 2024). https://www.banxico.org.mx/SieInternet/consultarDirectorioInternetAction.do?sector=18&accion=c onsultarCuadro&idCuadro=CF101&locale=es

5. CETES RATE OF RETURN

Table 5
CETES rate of return (28-day)
Period20102011201220132014201520162017201820192020202120222023
January4.494.144.274.153.142.673.085.837.257.957.044.225.5010.80
February4.494.044.324.193.162.813.366.067.407.936.914.025.9411.04
March4.454.274.243.983.173.043.806.327.478.026.594.086.5211.34
April4.444.284.293.823.232.973.746.507.467.785.844.066.6811.27
May4.524.314.393.723.282.983.816.567.518.075.384.076.9011.25
June4.594.374.343.783.022.963.816.827.648.184.854.037.5611.02
July4.604.144.153.852.832.994.216.997.738.154.634.358.0511.09
August4.524.054.133.842.773.044.246.947.737.874.504.498.3511.07
Sep.4.434.234.173.642.833.104.286.997.697.614.254.699.2511.05
Oct.4.034.364.213.392.903.024.697.037.697.624.224.939.0011.26
Nov.3.974.354.233.392.853.025.157.027.837.464.285.059.7011.78
Dec.4.304.344.053.292.813.145.617.178.027.254.245.4910.1011.26
Source: Own elaboration (BANXICO, 2024). https://www.banxico.org.mx/SieInternet/consultarDirectorioInternetAction.do?sector=22&accion=c onsultarCuadro&idCuadro=CF107&locale=es

CETES rate of return 2010- 2023 (at the end of each year)
Graph 9
CETES rate of return 2010- 2023 (at the end of each year)
Source: Own elaboration (BANXICO, 2024). https://www.banxico.org.mx/SieInternet/consultarDirectorioInternetAction.do?sector=22&accion=c onsultarCuadro&idCuadro=CF107&locale=es

CETES rate of return, January-December 2024 (at the end of each month)
Graph 10
CETES rate of return, January-December 2024 (at the end of each month)
Source: Own elaboration (BANXICO, 2024). https://www.banxico.org.mx/SieInternet/consultarDirectorioInternetAction.do?sector=22&accion=c onsultarCuadro&idCuadro=CF107&locale=es

6. INVESTMENT UNITS (UDIS)

The UDI is a unit of account of constant real value to denominate credit titles. It does not apply to checks, commercial contracts, or other acts of commerce.

Table 6
Investment units (value concerning pesos)
Period20102011201220132014201520162017201820192020202120222023
January4.374.564.734.895.105.295.415.625.976.256.446.647.127.69
February4.414.574.754.925.135.295.435.696.006.256.466.707.187.74
March4.444.594.754.945.155.305.445.716.026.266.496.757.247.77
April4.464.594.754.975.155.325.455.756.036.286.436.797.317.78
May4.434.584.714.965.135.295.425.756.016.276.426.817.337,78
June4.414.554.744.955.135.285.425.756.016.266.446.837.367.77
July4.424.574.774.955.145.285.425.766.046.276.496.877.437.79
August4.434.584.784.955.165.295.445.796.076.296.526.907.477.83
September4.444.594.804.975.185.315.455.826.116.296.556.927.537.87
October4.474.614.834.995.205.335.495.846.136.316.576.977.577.90
November4.504.644.855.025.235.365.535.896.176.356.607.047.627.94
December4.534.694.875.065.275.385.565.936.236.396.617.117.657.98
Source: Own elaboration (BANXICO, 2024). https://www.banxico.org.mx/SieInternet/consultarDirectorioInternetAction.do?accion=consultarCua dro&idCuadro=CP150&locale=es

Investment units 2010-2023 (At the end of the year)
Graph 11
Investment units 2010-2023 (At the end of the year)
Source: Own elaboration (BANXICO, 2024). https://www.banxico.org.mx/SieInternet/consultarDirectorioInternetAction.do?accion=consultarCua dro&idCuadro=CP150&locale=es

Investment units, January-December 2023
Graph 12
Investment units, January-December 2023
Source: Own elaboration (BANXICO, 2024). https://www.banxico.org.mx/SieInternet/consultarDirectorioInternetAction.do?accion=consultarCua dro&idCuadro=CP150&locale=es

In these uncertain times, it is very important to apply the best mathematical models to carry out the appropriate analyzes that offer us the necessary information to make business decisions related, among others, to investment, opportunity costs, market share, sales forecasts, plans business, business valuation or risk assessment.

REFERENCES

Baca, G. (2022). Project evaluation. México: McGraw Hill.

BANXICO. (2024). Sistema de Información Económica. México, Banco de México. Link: http://www.inegi.org.mx/sistemas/bie/

INEGI. (2024). Banco de Información Económica. Mexico: Instituto Nacional de Geografía y Estadística. Link: http://www.inegi.org.mx/sistemas/bie/

John, A. A, & Faulín, J. (2023). Sensitivity Analysis with Excel and Lindo. UOC, e-Math Project: Funded by the Secretary of State for Education and Universities (MECD).

Monod, H.; Naud, C. & Makowski, D. (2006). Uncertainty and sensitivity analysis for crop models, pp 55-96. In Working with dynamic crop models. Evaluation, analysis, parameterization, and applications. Wallach, D.; Makowski, D.; Jones, J.W. (eds). Elsevier. Amsterdam.

Morales, A., & Morales, J. (2009). Investment projects. Evaluation and formulation. McGraw Hill: Mexico.

Pérez, S., Cruz, D. & Quiroz, L. (2012). Sensitivity analysis of financial indicators in the evaluation of investments. In MSMEs. VI Meeting of Research in Economic and Administrative Sciences.

Tejeda, R., Trueba, A., López, N., & Rodríguez, R. (2015). Development of an information system for the analysis of financial sensitivity for Mexican Micro, Small and Medium Enterprises. In Micro, small and medium-sized enterprises in the economic, cultural and technological development of Mexico.

Saltelli, A.; Ratto, M.; Andrew, T.; Campolongo, F.; Cariboni, J.; Gatelli, D.; Saisana, M. & Tarantola, S. (2008). Global sensitivity analysis. The first. John Wiley and Sons. New Jersey, USA. 292 p. doi: 10.1002/9780470725184.oth1

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