3C Empresa. Investigación y pensamiento crítico. ISSN: 2254-3376 Ed. 43 Vol. 9 N.º 3 Agosto - Noviembre
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INTEGRAL FORMULA FOR THE DETERMINATION OF PRICE
VARIATIONS IN PUBLIC CONTRACTS OF ROAD WORKS
Eddie Enzo Aronés Barbarán
National University Federico Villarreal, (Perú).
E-mail: fkaseng@unfv.edu.pe ORCID: https://orcid.org/0000-0003-1157-5603
Freddy Lizardo Kaseng Solis
National University Federico Villarreal, (Perú).
E-mail: fkaseng@unfv.edu.pe ORCID: https://orcid.org/0000-0002-2878-9053
Ciro Rodriguez Rodriguez
National University Mayor de San Marcos, (Perú).
E-mail: crodriguezro@unmsm.edu.pe ORCID: https://orcid.org/0000-0003-2112-1349
Recepción:
20/04/2020
Aceptación:
16/06/2020
Publicación:
24/08/2020
Citación sugerida:
Aronés, E.E., Kaseng, F.L., y Rodriguez, C. (2020). Integral formula for the determination of price variations
in public contracts of road works. 3C Empresa. Investigación y pensamiento crítico, 9(3), 97-107. https://doi.
org/10.17993/3cemp.2020.090343.97-107
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ABSTRACT
The objective of the research is to generate a new formula to determine the variation in prices in a public
works contract that allows the nancial balance of the counterparts. The methodology for calculating
and adjusting the price variation in public works contracts is given as a function of the K factor, which
is a number that comes from the calculation of polynomial formulas whose theoretical basis lies in the
price indices, which are established in a legal framework of mandatory use of the polynomial formula
to determine the K factor, with eight monomials in the budget and the quantity of supplies that exceeds
one hundred. It is considered a subjective margin since its elaboration depends on the discretion of the
one who elaborates on the polynomial formula. The investigation questions the procedure established
by the state regulations for the calculation of the polynomial formula and shows the margin of error that
exists between the value obtained by the method set for regulations and that obtained using the entries
of the work budget. The result shows the positive variation in inputs, and the prices have increased, with
adjustments paid in the contracts with the benet of contractors.
KEYWORDS
Readjustment of prices, Polynomial formula, Variations, Index numbers, Price index, Contracts.
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1. INTRODUCTION
To regulate the procedure for calculating adjustments, in 1979, DS No. 11-79-VC (Vice-Ministry of
Construction, 1979) was published, where it is established that it will be calculated based on the K factor
resulting from an expression Mathematics that considers the incidence of materials, this expression is
called polynomial formula. K is a number that comes from the calculation of polynomial formulas,
whose theoretical basis lies in the price indices (Muñoz, 2004).
The particularity of this polynomial formula is that it considers only a maximum of eight inputs, the
most representative in terms of costs, regardless of the complexity of the work or budget. It is necessary
to mention that the simplest work has more than one hundred inputs. That is, to date, adjustments are
paid with a polynomial formula that only considers a reduced fraction of all the inputs of a public works
budget, so classication is important (Soto, 2020).
The current methodology of the polynomial formula for calculating the K factor, which restricts only
eight monomials regardless of the complexity of a road work, calls into question the representation of
the variation in the prices of the budget estimated by K.
This situation would be leading to an overestimation or underestimation of the budget adjustment
(Sanchez, 2020), thus aecting the economic balance between the parties. In the present research work,
the analysis of a sample of two polynomial formulas of road works contracts is performed (Huapaya,
2020), calculating the K factor using all the inputs contained in the technical le. The dierences between
the K factors established by each method have been made and the margin of error that exists between
both methods has been determined (Levy, 2020).
2. MATERIAL AND METHODS
The type of research type is applied, prospective, comparative, and correlational since two variables
were related. The factor K obtained by the established polynomial formula and the factor K obtained
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from a polynomial formula considering all the inputs. It is predictive of using inferential statistics to
corroborate the calculations. The design applied for the development of this thesis is oriented to the
study and analysis of the variables that are the subject of our research.
The research design evaluates multiple variables reected in the unied indices have been manipulated,
which have allowed determining the K factors both by the current polynomial formula and by using all
the inputs, proposed in the research.
The source of the data corresponds to the road works contracts of the last ve years. The budget, the
list of inputs, the execution schedule, and its polynomial formula have been used as the base material for
these contracts.
The technical les of road works carried out by the Special Project of Decentralized Transport - PVD of
the Ministry of Transport have been considered, to which the probabilistic sampling was applied to the
technical les with the same possibility of being chosen. The level of condence that has been assumed
is 95%.
The techniques used for the research will be:
• Documentary review: this technique was used to obtain information through the rules, books,
theses, manuals, regulations, directives, and other information.
• Documentary analysis: the technical les of the works contracted by the Ministry of Transport
and Communications were analyzed.
• For the management of data such as budgets, unit price analysis, input relationship, preliminary
grouping, etc., Excel spreadsheets were used.
Dierent statistical techniques and tools were used, such as:
• Verication of data normality.
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• Correlation analysis.
• Regression analysis.
• Data visualization.
• Monte Carlo simulation to measure approximate risk.
The MS Oce and SPSS programs were used to process and analyze the data.
The research was carried out in the city of Lima with data from public road works, and the methodology
process, to determine the K factor, index numbers, and price indices, is showed in Figure 1.
3
• Documentary analysis: the technical files of the works contracted by the
Ministry of Transport and Communications were analyzed.
• For the management of data such as budgets, unit price analysis, input
relationship, preliminary grouping, etc., Excel spreadsheets were used.
Different statistical techniques and tools were used, such as:
• Verification of data normality.
• Correlation analysis.
• Regression analysis.
• Data visualization.
• Monte Carlo simulation to measure approximate risk.
The MS Office and SPSS programs were used to process and analyze the data.
The research was carried out in the city of Lima with data from public road works, and
the methodology process, to determine the K factor, index numbers, and price indices, is
showed in Figure 1.
Figure 1. Methodology for determining K factor differences.
3. Results
The analysis of two polynomial formulas of two public road works contracts that to date
have been concluded and settled has been carried out.
The general information of the two works (Case 1 and Case 2) are:
Case 1:
K = 0.085 (Mr / Mo) + 0.054 (FAMr / FAMo) + 0.112 (ACr / ACo) + 0.118 (PMAr
/ PMAo) + 0.101 (Mr / Mo) + 0.270 (DLr / DLo) + 0.260 (Ir / Io)
The calculated values of K in the execution period are shown in Table 1:
Determination of K values for a
period of one year using the
existing polynomial formula
from the technical files of the
sample
Determination of K values for a
period of one year using the
polynomial formula usimg all
the inputs from the technical
files of the sample
Determination of the difference
for each value of K
Using the statistical tools,
analize the individual results
and the results of the entire
sample
Verification of the null
hypothesis
Make conclusions
Figure 1. Methodology for determining K factor differences.
3. RESULTS
The analysis of two polynomial formulas of two public road works contracts that to date have been
concluded and settled has been carried out.
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The general information of the two works (Case 1 and Case 2) are:
Case 1:
K = 0.085 (Mr / Mo) + 0.054 (FAMr / FAMo) + 0.112 (ACr / ACo) + 0.118 (PMAr / PMAo) + 0.101
(Mr / Mo) + 0.270 (DLr / DLo) + 0.260 (Ir / Io)
The calculated values of K in the execution period are shown in Table 1:
Table 1. K values of Case 1 obtained with the current formula.
oct-16 nov-16 dic-16 ene-17 feb-17 mar-17 abr-17 may-17 jun-17 jun-17
1,01 1,016 1,016 1,014 1,01 1,016 1,013 1,016 1,014 1,013
Case 2:
Its polynomial formula is:
K = 0.066 AMr / AMo + 0.138 ACr / ACo + 0.117 Mr / Mo + 0.082 Jr / Jo + 0.285 Dr / Do + 0.121
Ar / Ao + 0.191 GGUr / GGUo
The calculated values of K in the execution period are shown in Table 2:
Table 2. K values for Case 2 obtained by the current polynomial formula.
may-13 jun-13 jul-13 ago-13 sep-13 oct-13 nov-13 dic-13 ene-14 feb-14
0,995 1,012 1,026 1,031 1,029 1,026 1,03 1,028 1,033 1,035
Correlational analysis in the pretest
The correlational analysis of K in gure x. a) shows the graphic of the correlation
y = -4E-05x4 + 0.0008x3 - 0.0061x2 + 0.018x + 0.9978, and R² = 0.5102
The correlational analysis of K in gure x. b) shows the graphic of the correlation
y = 0.015ln(x) + 1.0018 and R² = 0.8303
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In Table 3, the consolidated values of both cases are shown:
Table 3. K values calculated with the current polynomial formula.
Nª Vinic Case 1 Vinic Case 2
1 1,010000000 0,99500000
2 1,016000000 1,01200000
3 1,016000000 1,02600000
4 1,014000000 1,03100000
5 1,010000000 1,02900000
6 1,016000000 1,02600000
7 1,013000000 1,03000000
8 1,016000000 1,02800000
9 1,014000000 1,03300000
10 1,013000000 1,03500000
Source: own elaboration.
Correlational analysis of the experimental group in the pre-test
The results of the correlational analysis are shown in Figures 2 with the comparison of the K values with
the methods used in cases 1 and 2 and the respective distribution of dierences in K values.
Correlational analysis in the pre-test of the K Vinic values case 1 and case 2.
5
Correlational analysis of the experimental group in the pre-test
The results of the correlational analysis are shown in Figures 2 with the comparison of
the K values with the methods used in cases 1 and 2 and the respective distribution of
differences in K values.
Correlational analysis in the pre-test of the K Vinic values case 1 and case 2.
(a) (b)
Figure 2. Correlational analysis of K values a) Vinic case1 and b) Vinic case 2.
Correlational analysis of the experimental group in the post-test
The results of the correlational analysis post-test are shown in Figure 3 with the
comparison of the K values. Figure 4 shows correlation with the methods used in for
cases 1 and 2.
(a)
(b)
(a) (b)
Figure 2. Correlational analysis of K values a) Vinic case1 and b) Vinic case 2.
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Correlational analysis of the experimental group in the post-test
The results of the correlational analysis post-test are shown in Figure 3 with the comparison of the K
values. Figure 4 shows correlation with the methods used in for cases 1 and 2.
5
Correlational analysis of the experimental group in the pre-test
The results of the correlational analysis are shown in Figures 2 with the comparison of
the K values with the methods used in cases 1 and 2 and the respective distribution of
differences in K values.
Correlational analysis in the pre-test of the K Vinic values case 1 and case 2.
(a) (b)
Figure 2. Correlational analysis of K values a) Vinic case1 and b) Vinic case 2.
Correlational analysis of the experimental group in the post-test
The results of the correlational analysis post-test are shown in Figure 3 with the
comparison of the K values. Figure 4 shows correlation with the methods used in for
cases 1 and 2.
(a)
(b)
(a) (b)
Figure 3. Comparison between K values using the two methods, a) case 1 and b) case 2.
Figure 4. Distribution of differences in K values in cases 1 and 2.
4. DISCUSSION
With the information has been veried that, in all cases, there is a dierence of K more signicant than
0.1%, It has been established as a maximum allowed value of 0.1% since, with current regulations,
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K values are rounded to the thousandth, with which any variation above 0.1% will produce dierent
readjustments.
In road works contracts, there are monthly valuations that on average exceed one million soles, which
means that variations above the 0.1% threshold implied that the readjustments that have been paid were
dierent from those corresponding
According to the graphs that have been shown, where you can see, the dierences are negative, which
means that the readjustments that have been paid have been more than they were due to the contractors.
5. CONCLUSION
The K values obtained, using all the inputs, with a reliability of 95%, are less than those resulting from
the current polynomial formula, the dierence in these values reaches a maximum of -0.043, which
means a dierence, with regarding the oor value of 0.001, of 4,300% dierence, that in terms of
money, in a monthly valuation with a minimum positive dierence, however, if the contracting of works
is considered, annually for more than 10 billion, the approximate value of S /. 430’000,000.00 where
the mean of the dierence for case 2 corresponds to 0.039.
Likewise, the polynomial formula established by current regulations does not reect the correct variation
in input prices and to determine the K value, all the inputs that intervene in the road works budget must
be used, so the polynomial formula should be stated as:
Where:
n = The total amount of inputs from the works budget
A = The incidence of i resulting from the value of the input between the total value of the budget minus taxes
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Iri = The unied index of i one month after recovery
Ioi = The unied index of i per month of the reference value
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