What is the probability that the payments made in Cash will exceed the collections in a given period? What is the maximum value that this can reach?
These questions constitute some of the questions that we ask ourselves daily in our company and whose answer we intend to approach with our study, by determining the probability of the occurrence of negative Net Flow 1 (financial overdraft) in the Cash account at the Bank in the year 2005 and the estimate of the maximum monthly negative Net Flow to occur in the year 2005.
Real case
We will take an example in a company in the telecommunications sector; the Cash in Bank account, with which the main transactions are carried out, as well as the movements that take place in the different items that comprise it from January 2002 to December 2004.
Below is the actual behavior of the Net Cash Flow in the Bank from January 2002 to December 2004.
As can be seen in the graph, the Net Flow reaches negative values in more than half of the observations made. What probability of occurrence does said event have? What is the maximum negative Net Flow (FN (-)) possible to reach in a month?
To begin answering the questions outlined as guidelines in our research, we will perform a simulation 2 using the sequential Monte Carlo method 3 with the aim of forecasting the behavior of Net Cash Flow in Bank in 2005, fundamentally, with what probability this will reach negative values; using for it, the monthly data that we have of the Entries (collections) and Departures (payments) from January 2002 to December 2004.
Initially we will discuss the common aspects for both Cash In and Cash Out in Bank and then we will separate the study.
In this type of data, to group them the use of ranges was necessary, to facilitate our work, so the probability that a number is in the range (according to the frequency of observations by range) was calculated. Ranges with a distance of 50,000 pesos were selected; the distance was not further reduced, since as will be seen in the Tables of the Distribution of Cash Inflows and Outflows in Bank with assigned probability of occurrence, there are several ranges in which the frequency is 1, and even 0; being a priority of ours that, while being as explanatory as possible, the least number of ranges remain without observations, as this would lead to a probability of occurrence of 0 since they are not generated later.
Sample size: 36 observations, corresponding to the months from January 2002 to December 2004, as shown below:
| MONTHS | TOTAL TICKETS | TOTAL DEPARTURES | NET FLOW |
| Jan-02 | 859,450.43 | 719,257.59 | 140,192.84 |
| Feb-02 | 667,613.52 | 335,803.88 | 331,809.64 |
| Mar-02 | 895,304.63 | 1,003,230.91 | -107,926.28 |
| Apr-02 | 853,965.98 | 698,402.74 | 155,563.24 |
| May-02 | 942,900.42 | 570,396.61 | 372,503.81 |
| Jun-02 | 581,456.05 | 939,753.29 | -358,297.24 |
| Jul-02 | 975,097.46 | 630,379.75 | 344,717.71 |
| Aug-02 | 865,320.04 | 818,077.54 | 47,242.50 |
| Sep-02 | 729,604.80 | 820,446.31 | -90,841.51 |
| Oct-02 | 965,754.02 | 404,057.00 | 561,697.02 |
| Nov-02 | 914,753.99 | 1,020,713.38 | -105,959.39 |
| Dec-02 | 809,182.36 | 805,401.90 | 3,780.46 |
| Jan-03 | 868,361.50 | 375,597.64 | 492,763.86 |
| Feb-03 | 807,036.95 | 1,239,714.62 | -432,677.67 |
| Mar-03 | 1,104,316.72 | 1,233,883.16 | -129,566.44 |
| Apr-03 | 885,887.30 | 946,920.93 | -61,033.63 |
| May-03 | 905,917.32 | 935,959.15 | -30,041.83 |
| Jun-03 | 831,357.46 | 954,158.58 | -122,801.12 |
| Jul-03 | 1,063,491.39 | 766,108.18 | 297,383.21 |
| Aug-03 | 1,030,345.88 | 1,753,592.57 | -723,246.69 |
| Sep-03 | 1,051,765.62 | 811,704.19 | 240,061.43 |
| Oct-03 | 1,095,993.02 | 1,121,984.94 | -25,991.92 |
| Nov-03 | 1,260,032.06 | 950,738.92 | 309,293.14 |
| Dec-03 | 1,265,237.94 | 1,484,963.50 | -219,725.56 |
| Jan-04 | 1,253,132.16 | 584,763.14 | 668,369.02 |
| Feb-04 | 1,119,206.05 | 1,403,191.66 | -283,985.61 |
| Mar-04 | 1,426,958.85 | 776,354.35 | 650,604.50 |
| Apr-04 | 1,040,309.38 | 1,260,285.10 | -219,975.72 |
| May-04 | 1,343,312.75 | 981,554.54 | 361,758.21 |
| Jun-04 | 989,691.74 | 1,373,505.33 | -383,813.59 |
| Jul-04 | 846,891.52 | 964,937.43 | -118,045.91 |
| Aug-04 | 1,203,325.86 | 1,235,504.10 | -32,178.24 |
| Sep-04 | 907,206.72 | 1,160,438.26 | -253,231.54 |
| Oct-04 | 1,053,571.56 | 1,347,142.12 | -293,570.56 |
| Nov-04 | 1,386,013.45 | 1,477,911.69 | -91,898.24 |
| Dec-04 | 1,285,618.99 | 1,202,471.12 | 83,147.87 |
We will define a series of Stages that were carried out in the simulation, up to the scope of the results, that is, until the estimation of the probability with which FN (-) will occur, as previously stated.
Stages of the study:
- Simulation of Bank Cash Entries. Distribution of Bank Cash Entries in ranges. Estimate by intervals of the population mean of ranges. Distribution of ranges of Entries in reported and above. Interval estimate of population mean. of the ranges (reported and higher). Simulation of the Cash Outflows in the Bank. Distribution of the Cash Outflows in the Bank in ranges. Interval estimation of the population mean of the ranges. Distribution of the ranges of the Outflows in reported and Estimates for intervals of the population mean of the ranges (reported and higher). Estimate of the probability of occurrence of FN (-) for the year 2005. Estimate of the maximum FN (-) to occur in each month of the year.Comparison of study results with actual values reported in the first quarter of 2005.
- Cash inflows in bank.
We will now begin to develop Stage 1, corresponding to the Simulation of Bank Cash Entries.
Distribution of Bank Cash Receipts by ranges, with assigned probability of occurrence:
| Not. | TICKET RANGE | QUANTITY | PROBABILITY |
| one | 550,000-600,000 | one | 0.0278 |
| two | 600,001-650,000 | 0 | 0.0000 |
| 3 | 650,001-700,000 | one | 0.0278 |
| 4 | 700,001-750,000 | one | 0.0278 |
| 5 | 750,001-800,000 | 0 | 0.0000 |
| 6 | 800,001-850,000 | 4 | 0.1111 |
| 7 | 850,001-900,000 | 6 | 0.1667 |
| 8 | 900,001-950,000 | 4 | 0.1111 |
| 9 | 950,001-1,000,000 | 3 | 0.0833 |
| 10 | 1,000,001-1,050,000 | two | 0.0556 |
| eleven | 1,050,001-1,100,000 | 4 | 0.1111 |
| 12 | 1,100,001-1150000 | one | 0.0278 |
| 13 | 1,150,001-1200000 | one | 0.0278 |
| 14 | 1,200,001-1,250,000 | one | 0.0278 |
| fifteen | 1,250,001-1,300,000 | 4 | 0.1111 |
| 16 | 1,300,001-1,350,000 | one | 0.0278 |
| 17 | 1,350,001-1,400,000 | one | 0.0278 |
| 18 | 1,400,001-1,450,000 | one | 0.0278 |
| TOTAL | 36 | 1,0000 |
The lower limit of the first range was 550,000 pesos, because the minimum value of Bank Cash Receipts reported in the selected sample is 581,456.05 pesos and the upper limit of the last range was 1,450,000 pesos, since the maximum value reported in the sample is 1,426,958.85 pesos.
Then we proceeded to the Generation of Random Numbers using Microsoft Excel, introducing the numbers of the ranges and the probability corresponding to each one. 1,200 random numbers were generated, that is, 100 observations for the twelve months of the year; so that it was a sufficient number of iterations, in order to obtain the most representative results possible from reality.
Frequencies were calculated for each of the ranges per month, as shown below:
| MONTHS | one | two | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | eleven | 12 | 13 | 14 | fifteen | 16 | 17 | 18 |
| January | 4 | 0 | two | two | 0 | eleven | 9 | 8 | 8 | 6 | 10 | 0 | 9 | 5 | 17 | two | one | one |
| February | 4 | 0 | 3 | one | 0 | 13 | 17 | 13 | 5 | 4 | 13 | 0 | 4 | two | 6 | two | 3 | 3 |
| March | two | 0 | two | one | 0 | 9 | 17 | 10 | 8 | 7 | 14 | 0 | 5 | two | eleven | 8 | one | 0 |
| April | one | 0 | 5 | 4 | 0 | 12 | fifteen | 5 | 10 | 7 | 6 | 0 | 4 | 3 | 12 | 7 | 4 | two |
| May | 3 | 0 | 4 | 5 | 0 | eleven | 19 | 16 | 10 | two | 8 | 0 | 3 | one | 9 | two | 4 | two |
| June | 4 | 0 | one | one | 0 | 13 | 13 | 10 | 6 | 5 | twenty-one | 0 | 3 | 3 | 13 | 0 | 0 | 3 |
| July | 3 | 0 | one | 5 | 0 | 10 | 16 | fifteen | 4 | two | 9 | 0 | 4 | 3 | 14 | 5 | two | 6 |
| August | 5 | 0 | two | 3 | 0 | 14 | 14 | eleven | 7 | 6 | 13 | 0 | two | 0 | 14 | one | 3 | two |
| September | two | 0 | 3 | 5 | 0 | 7 | fifteen | 9 | 6 | 8 | 10 | 0 | 5 | 3 | 12 | one | 6 | 4 |
| October | 3 | 0 | 3 | two | 0 | fifteen | 19 | twenty | 7 | two | 12 | 0 | one | two | 6 | 3 | one | two |
| November | 7 | 0 | one | 4 | 0 | 10 | 17 | 16 | 5 | 4 | eleven | 0 | one | one | 9 | 4 | 4 | 3 |
| December | 0 | 0 | 4 | one | 0 | 13 | 7 | 10 | 14 | 8 | eleven | 0 | 3 | 7 | 13 | 3 | one | 3 |
As shown below, the population mean was estimated to estimate the behavior of the Entries, with the following data:
- Sample mean of the ranges observed, in one hundred observations per month:
Where:
: Range.
: Frequency of each range in the month.
: Sample size (total number of observations).
- Standard deviation (s): Through Microsoft Excel functions Lower limit: Upper limit:
Where:
: Value of the student distribution for a sample size and reliability.
Data:
observations per month.
The results of the calculations appear below.
The formulas for the interval estimation of the parameter µ (population mean of the ranges) mentioned above were used, since the population variance was unknown.
Statistical analysis of the simulation of the behavior of bank cash inflows and selection of the range per month:
|
MONTHS |
HALF | STANDARD DEVIATION | LOWER LIMIT | UPPER LIMIT | SELECTION |
| January | 9.62 | 4.00 | 8.8352 ≈ 9 | 10.4048 ≈ 10 | 9.10 |
| February | 8.53 | 3.96 | 7.7531 ≈ 8 | 9,3069 ≈ 9 | 8.9 |
| March | 9.64 | 3.70 | 8.9146 ≈ 9 | 10.3654 ≈ 10 | 9.10 |
| April | 9.65 | 4.27 | 8.8131 ≈ 9 | 10.4869 ≈ 10 | 9.10 |
| May | 8.84 | 4.03 | 8.0501 ≈ 8 | 9.6299 ≈ 10 | 8,9,10 |
| June | 9.25 | 3.76 | 8.5125 ≈ 9 | 9.9875 ≈ 10 | 9.10 |
| July | 9.99 | 4.44 | 9.1206 ≈ 9 | 10.8594 ≈ 11 | 9,10,11 |
| August | 6.88 | 4.11 | 6.0744 ≈ 6 | 7.6856 ≈ 8 | 6.7.8 |
| September | 9.71 | 4.24 | 8.8791 ≈ 9 | 10.5409 ≈ 11 | 9,10,11 |
| October | 8.50 | 3.62 | 7.7905 ≈ 8 | 9,2095 ≈ 9 | 8.9 |
| November | 8.87 | 4.37 | 8.0141 ≈ 8 | 9.7259 ≈ 10 | 8,9,10 |
| December | 10.01 | 3.74 | 9.2775 ≈ 9 | 10.7425 ≈ 11 | 9,10,11 |
How was the selection made?
The limits were first approximated, both lower and higher than integer values, and then those values that were between the limits were selected, including the same limit values. For example:
In the month of July, and then the values that are selected are ranges 9, 10 and 11.
So far everything seemed to be going satisfactorily; However, it occurred to us that in this method we were left out, at least in this case study, of the possibility that a higher rank than those registered would appear next year, as generally occurs; because when detailing the behavior of these accounts a tendency to increase was perceived. How to take this aspect into account? He jumped as a question before our eyes. Consecutively we will detail the contribution made to answer said concern.
Now we will work with only two values, assigning the value of 0 to the ranges that we have previously studied, that is, to those reported so far and 1 to those that could occur above the upper limit of the last reported range.
How was the probability of occurrence of these events calculated?
In a simple way; As the work was carried out for years, it was analyzed how many ranges appeared in 2003 above the upper limit of the last range reported in 2002 and similarly in 2004 with respect to 2003. Let's see:
The highest value reached in 2002 is 975,097.46 pesos, which indicates that the last reported range is equivalent to 950,001-1,000,000. In 2003, above 1,000,000 pesos (upper limit of the last reported range) there are seven values (1,104,316.72; 1,063,491.39; 1,030,345.88; 1,051,765.62; 1,095. 993.02; 1,260,032.06 and 1,265,237.94); therefore, in that year an annual increase probability was reached, above the upper limit of the last range reported in 2002 of 7/12, which is equivalent to 0.58333. As can be seen in the seven values written here that exceeded the upper limit of the last range reported in 2002, the highest was 1,265,237.94 pesos, so the last range reported until 2003 will correspond to 250,001-1,300,000.
In 2004, above 1,300,000 pesos, there are three values (1,426,958.85; 1,343,312.75 and 1,386,013.45); therefore, in that year an annual increase probability was presented, above the upper limit of the last range reported in 2003 of 3/12, which is equivalent to 0.25.
The probability of annual increase above the upper limit of the last range reported in 2004, that is, the one necessary for our study, was calculated as the average of the two probabilities of increase reported so far, obtaining a probability of annual increase, above the upper limit of the last range reported in 2004 of 0.41667.
The probability that the ranges will behave as recorded so far would be 1 - 0.41667, which is equivalent to 0.58335.
Distribution of the ranges of Bank Cash Entries, according to whether they are reported or higher than those reported:
| Not. | RANGES | PROBABILITY |
| 0 | reported | 0.58335 |
| one | superiors | 0.41665 |
| TOTAL | 1,00000 |
Then we proceeded to the Generation of Random Numbers using Microsoft Excel, in the same way as it was done for the previous definition studied, of the ranges of the Inputs.
We worked on this analysis with a new definition of range, as we could see previously. Now it corresponds to ranges, the previous or already reported and the upper ones, which as we saw implies that they are above the upper limit of the last reported range.
The frequencies of each range per month were calculated:
| MONTHS | 0 | one |
| January | 61 | 39 |
| February | 63 | 37 |
| March | 59 | 41 |
| April | 58 | 42 |
| May | 60 | 40 |
| June | 52 | 48 |
| July | 55 | Four. Five |
| August | 56 | 44 |
| September | 53 | 47 |
| October | 56 | 44 |
| November | 60 | 40 |
| December | 61 | 39 |
Then we proceeded to estimate the population mean again, based on the proportion of annual increase:
- Proportion of annual increase, that is, the rank is 1, in the 100 observations per month:
Where:
: Frequency that the range is 1.
: Sample size (total number of observations).
In this case, in which the values are 0 and 1, the proportion of 1 coincides with the sample mean, since the other values are 0.
- Standard deviation: Lower limit: Upper limit:
Where:
: Value of the normal distribution for a sample size and reliability.
Data:
Statistical analysis of the simulation of the behavior of cash inflows and selection of the range per month:
|
MONTHS |
PROPORTION | STANDARD DEVIATION | LOWER LIMIT | UPPER LIMIT | SELECTION |
| January | 0.39 | 0.4877 | 0.2944 ≈ 0 | 0.4856 ≈ 0 | 0 |
| February | 0.37 | 0.4828 | 0.2754 ≈ 0 | 0.4646 ≈ 0 | 0 |
| March | 0.41 | 0.4918 | 0.3136 ≈ 0 | 0.5064 ≈ 1 | 0 |
| April | 0.42 | 0.4936 | 0.3233 ≈ 0 | 0.5167 ≈ 1 | 0 |
| May | 0.40 | 0.4899 | 0.3040 ≈ 0 | 0.4960 ≈ 0 | 0 |
| June | 0.48 | 0.4996 | 0.3821 ≈ 0 | 0.5779 ≈ 1 | 0.1 |
| July | 0.45 | 0.4975 | 0.3525 ≈ 0 | 0.5475 ≈ 1 | 0.1 |
| August | 0.44 | 0.4964 | 0.3427 ≈ 0 | 0.5373 ≈ 1 | 0 |
| September | 0.47 | 0.4991 | 0.3722 ≈ 0 | 0.5678 ≈ 1 | 0.1 |
| October | 0.44 | 0.4964 | 0.3427 ≈ 0 | 0.5373 ≈ 1 | 0 |
| November | 0.40 | 0.4899 | 0.3040 ≈ 0 | 0.4960 ≈ 0 | 0 |
| December | 0.39 | 0.4877 | 0.2944 ≈ 0 | 0.4856 ≈ 0 | 0 |
How was the selection made?
First, the limits were approached, both lower and higher than integer values, then, as it is obvious, the value 0 is present in all months, in addition to the fact that the sample mean never reaches 0.50 in order to be rounded to 1 Therefore, 1 was selected in those months in which the upper limit equaled or exceeded the value of 0.50 and the sample mean was greater than 0.45. Therefore, in the months of June, July and September, it is most likely that a value above the upper limit of the last range reported until 2004 was reported.
Where 0 appears, the behavior would be as shown in the Table in which the range per month was selected for the first definition of ranges; where 0 or 1 appears, the behavior would be as we show in said Table and in turn figures higher than the upper limit reported in the last range up to 2004 may occur, which we will designate as "> 1,450,000".
- Cash Outflows in Bank.
In the simulation of Cash Outflows, corresponding to the development of Stage 2, the same procedures were carried out as in Stage 1; highlighting as a significant difference the Cash Inflows in Bank, that no month reported probability of a value above the last range reached until 2004.
- Estimate of the probability of occurrence of FN (-) of Cash in Bank for the year 2005.
We proceeded to estimate the probability of occurrence of FN (-), a process corresponding to the third defined stage. Below is the range equivalent to the selection made for both Cash In and Cash Out in Bank, according to the numbers assigned to each range.
Equivalent ranges to simulate the behavior of Cash Inflows and Outflows in Bank for the year 2005:
| MONTHS | TICKETS | DEPARTURES |
| EQUIVALENT RANGE (S) | EQUIVALENT RANGE (S) | |
| January | 950,000-1,000,000 or 1,000,001-1,050,000 | 950,000-1,000,000 or 1,000,001-1,050,000 or 1,050,001-1,100,000 |
| February | 900,000-950,000 or 950,001-1,000,000 | 950,000-1,000,000 or 1,000,001-1,050,000 or 1,050,001-1,100,000 |
| March | 950,000-1,000,000 or
1,000,001-1,050,000 |
850,000-900,000 or 900,001-950,000 or 950,001-1,000,000 or 1,000,001-1,050,000 |
| April | 950.001-1,000,000 or
1,000,001-1,050,000 |
900,001-950,000 or 950,001-1,000,000 or 1,000,001-1,050,000 |
| May | 900,000-950,000 or 950,001-1,000,000 or 1,000,001-1,050,000 | 900,000-950,000 or 950,001-1,000,000 or 1,000,001-1,050,000 or
1,050,001-1,100,000 |
| June | 950,000-1,000,000 or
1,000,001-1,050,000 or> 1,450,000 |
900,000-950,000 or 950,001-1,000,000 or 1,000,001-1,050,000 or
1,050,001-1,100,000 |
| July | 950,000-1,000,000 or
1,000,001-1,050,000 or 1,050,001-1,100,000 or> 1,450,000 |
850,000-900,000 or 900,001-950,000 or 950,001-1,000,000 or 1,000,001-1,050,000 |
| August | 800,000-850,000 or 850,001-900,000 or 900,001-950,000 | 900,000-950,000 or 950,001-1,000,000 or 1,000,001-1,050,000 |
| September | 950,000-1,000,000 or
1,000,001-1,050,000 or 1,050,001-1,100,000 or> 1,450,000 |
900,000-950,000 or 950,001-1,000,000 or 1,000,001-1,050,000 |
| October | 900,000-950,000 or 950,001-1,000,000 | 850,000-900,000 or 900,001-950,000 or 950,001-1,000,000 or 1,000,001-1,050,000 |
| November | 900,000-950,000 or 950,001-1,000,000 or 1,000,001-1,050,000 | 800,000-850,000 or 850,001-900,000 or 900,001-950,000 or 950,001-1,000,000 |
| December | 950,000-1,000,000 or
1,000,001-1,050,000 or 1,050,001-1,100,000 |
850,000-900,000 or 900,001-950,000 or 950,001-1,000,000 |
How was the probability of FN (-) estimated?
For this, the same probability of occurrence was assigned to each possible combination in each month. Let's see:
January:
- E: 950,000-1,000,000
S: 950,000-1,000,000
- E: 950,000-1,000,000
S: 1,000,001-1,050,000
- E: 950,000-1,000,000
S: 1,050,001-1,100,000
- E: 1,000,001-1,050,000
S: 950,000-1,000,000
- E: 1,000,001-1,050,000
S: 1,000,001-1,050,000
- E: 1,000,001-1,050,000
S: 1,050,001-1,100,000
As observed, there are six possible combinations in January, so each one has a 16.67% (100/6) probability of occurrence.
Now what rules were followed to estimate the probability of FN (-) of Cash in Bank:
- If the range of Inputs is greater than that of Outputs (E> S) there is a 0% probability of FN (-). If the range of Inputs is less than that of Outputs (E <S) there is a 100% probability of FN (-), which in this case will correspond to the probability of occurrence of said combination.If the range of Inputs is equal to that of Outputs (E = S) there is a 50% probability of FN (-), which in this case will correspond to half the probability of occurrence of said combination. In the months of June, July and August when values can be increased above the upper limit reported up to 2004, events have the same probability of occurrence, that they increase above the upper limit reported until 2004, that is, "> 1,450,000" and that they continue with the previous behavior.
So, we continue with the analysis for January:
- E = S ……………………… 8.33% probability of FN (-) E <S ……………………… 16.67% probability of FN (-) E <S ……… ……………… 16.67% probability of FN (-) E> S ……………………… 0% probability of FN (-) E = S ……………………… 8, 33% probability of FN (-) E <S ……………………… 16.67% probability of FN (-)
If we add the probabilities of FN (-) obtained by combination, we have that in January there is a total 66.67% probability of FN (-); proceeding like this, successively with the other months.
Probability of occurrence of FN (-) for the year 2005:
|
MONTHS |
ESTIMATED CHANCE OF FN (-) |
| January | 66.67% |
| February | 91.68% |
| March | 25% |
| April | 33.34% |
| May | 62.50% |
| June | 25% |
| July | 8.33% |
| August | 94.44% |
| September | 11.11% |
| October | fifty% |
| November | 16.67% |
| December | 5.56% |
As it can be observed, in every month there is some probability of FN (-), reaching in January, February, May and August, a value above 50%, even in February and August above 90%; something really alarming for the entity.
- Calculation of the maximum FN (-) of Cash in Bank that can occur in each month.
The maximum FN (-) of Cash in Bank that can occur in each month was calculated according to the estimated behavior in the simulation of the Inflows and Outflows of Cash in Bank. Said calculation was made by subtracting the upper limit of the highest estimated range for Bank Cash Outflows with the lower limit of the lowest estimated range for Bank Cash Outflows. Below we illustrate how this was done in January.
January:
Maximum FN (-) = 1,100,000 - 950,000
Maximum FN (-) = 150,000
As we can see in the Table of the ranges equivalent to the simulation, in the month of January, 1,100,000, is the upper limit of the last range (or higher range) estimated for Cash Outflows in Bank in that month, which is 1,050,001-1,100,000; and 950,000 is the lower limit of the lowest range (or first range) estimated for Bank Cash Entries in that month, which is 950,000-1,000,000; therefore, the maximum FN (-) estimated for January is 150,000 pesos.
Estimated maximum FN (-) of Cash in Bank for the year 2005, according to the results of the Simulation of Cash Inflows and Outflows in Bank:
|
MONTHS |
MAXIMUM FN (-) ESTIMATED |
| January | 150,000 |
| February | 200,000 |
| March | 100,000 |
| April | 100,000 |
| May | 200,000 |
| June | 150,000 |
| July | 100,000 |
| August | 250,000 |
| September | 100,000 |
| October | 150,000 |
| November | 100,000 |
| December | 50,000 |
As it can be observed, the maximum estimated FN (-) reaches its highest value in the month of August, a result that should not surprise us since it is precisely in that month in which the greatest probability of FN (-) exists, with a 94, 44%.
- Comparison of the Simulation of Cash Inflows and Outflows in Bank for 2005 and what happened in the first quarter of 2005.
Below is a comparison of the results of the simulation of Cash Inflows and Outflows in Bank with what happened in the first quarter of 2005.
Inflows, Outflows and Net Cash Flow in Bank in the first quarter of 2005:
| MONTHS | TICKETS | DEPARTURES | NET FLOW |
| January | 1,032,460.61 | 999,680.12 | 32,780.49 |
| February | 959,238.48 | 1,128,463.3 | -169,224.82 |
| March | 1,034,718.29 | 1,027,067.78 | 7,650.51 |
As can be seen, in January, combination 4 occurred, shown in the estimate, in which, of course, being E> S, there was no probability of FN (-) and therefore the Net Flow is positive (FN (+)), finding said result in the 33.33% probability of FN (+) that existed.
In February, the value of Bank Cash Entries is among the ranges presented, however, the value of Outlets exceeds the upper limit of the last estimated range for that month, which falls within the margin of error it contains All estimates, despite this, said month was the second with the highest probability of FN (-) and this was its final result; In addition, the reported FN (-) was lower than the maximum FN (-) estimated that could be reported that month.
In the month of March, both Cash inflows and Cash Outflows in the Bank are in the aforementioned ranges, corresponding in the order followed in the January example to combination 8, where there was half the probability of FN (-), by be in the same rank; In this case, the real behavior was that the Entries exceeded the Exits by 7,650.51 pesos, with FN (+) of Cash in Bank, a result equivalent to the 75% probability of FN (+) that existed in that month.
When making this comparison, we have verified the validity of the study carried out, since all the other values with those obtained in the simulation coincide, except in the Cash Outflows in the Bank for February.
conclusion
With these results, the entity has at its disposal a useful tool to prevent the future behavior of the Cash in Bank account, given what has historically happened, in its hands is the power of decision at the right time and the efficiency of its management.
Bibliography
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1 Net Flow: Inflows minus Cash Outflows in Bank.
2 Simulation: It can be briefly defined as a technique that tries to imitate the behavior of different phenomena in an artificial reality; It is applicable to a large number of situations, although as it does not have an optimization criterion, in no case does it guarantee obtaining an optimal solution, but rather a good solution. Simulation is an experimental technique in which logical-mathematical models are used. The information obtained from the simulations helps the administration to explore the new policies. You can also examine current policies under other future economic conditions. Repetition is common in simulation. The reason is that the results of a simulation experiment are subject to probabilities if the model includes random variables.
3 Sequential Monte Carlo Method: The Monte Carlo Method consists of simulating a considerable number of situations, generated randomly, where the values of the reliability indices correspond to the values of the moments of the probability distributions. One of its versions is the Sequential Monte Carlo Method, which implies that the current state depends on the previous states (system with memory).
Author data
- Name and Surname: Martha Ileana Suau Peraza Title: Lic. Economics: Business Sciences Place of origin: Havana City, Cuba Age: 24 years Havana City, CubaJune 2005
