What is the sufficient level of cash that I must have in my company? Between what limits should it oscillate? These questions constitute some of the questions that we ask ourselves daily in our organization and whose answer we intend to approach in our article, by estimating the limits of the sufficient level of Cash in the Bank and analyzing them within the real behavior of the first quarter from 2005.
- Brief relate.
Since the mid-20th century, inventory-like models have been built to help the financial manager determine the optimal cash balances for the business. Among these models are: the Baumol (1952) model that applies the economic quantity order (EOQ) model, used in inventory management, to the problem of cash management; considering that cash is an article, represented in money. The Beranek (1963) model addresses the problem of determining the optimal choice between cash balance and marketable securities, relative to available funds. Finally, the Miller Orr (1966) model, perfecting Baumol's model, considering that it is applicable to only one type of companies,that have the behavior of continuous and uniform money outflow, being more applicable to people than to companies.
In this article we will work with an adequate cash balance according to the treasurer's judgment, instead of defining it as an optimal cost-minimizing balance; as in the aforementioned models, based on marginalist criteria, which are increasingly out of use and do not respond to the reality of companies' treasury management.
sufficient-level-of-treasury-by-a-probabilistic-modelIn an article published in the Actualidad Financiera magazine in November 1999, entitled: “Day-to-day treasury management. A probabilistic model based on a sufficient level of treasury ”; reference is made to a new method of calculating the appropriate level of treasury; Let's first look at some references to that article.
This model is based on the Miller Orr model, previously mentioned.
Z is defined "as the adequate or sufficient level of treasury that the treasurer should maintain, which will be determined from the available information and his own experience."
This level, Z, is proposed in the article, consists of a lower limit and an upper limit, where “the lower level must be sufficient to avoid any possibility of overdraft. In other words, (…) the treasurer starts from a balance T t at the beginning of each day and after making the corresponding investments or divestments in short-term financial assets, he manages to equalize the treasury with the desired level, Z t. "
The article refers mainly to the fact that they are in "a continuous environment, where the treasury fluctuates throughout the day (hours, minutes, seconds)"; where after the treasurer (in this case with an active treasury management), achieves the desired level of treasury Z, this equality is broken throughout the day as a result of the various collections and payments that occur for various reasons.
“However, in a low-key environment; (as in the one found in this study), where the minimum time unit is a single day, the cash balance throughout each day does not matter, so we can take the equality T t = Z for the entire day. "
"This adequate level of treasury Z t must be lower than a maximum level H, and in turn sufficiently high to avoid incurring a deficit during day t as a result of checks and other instruments that are presented for payment on the value date of that day. That is to say:
Where:
: Average charge per collection instrument.
: Average payment per payment instrument.
: Mathematical expectation of the number of payment instruments presented on day t.
: Mathematical expectation of the number of collection instruments presented on day t.
Being the average amount of each charge and the average amount of each payment, it follows that:
is the net cash flow with a negative sign that the treasurer foresees for day t, so it is clear that the appropriate balance Z t must be greater than or equal to said net cash flow with a negative sign:
where it symbolizes the adequate or sufficient net cash flow with a negative sign, that is, as the difference between payments and collections.
To estimate the lower limit of the sufficient level of cash, it will be necessary to know the variables involved:,,,. The amount of and of can be known by the treasurer from databases and statistics based on experience, so there is no additional complication.
When the treasurer makes cash forecasts, he does not make estimates about the expected balance on the accounting date, but rather estimates about the balances on the value date. This means that it is from the date of receipt of the check (accounting date) that the treasurer can reliably estimate the date on which the check will be credited by the bank on the value date. "
These clarifications of the last paragraph were fulfilled in this study, since we worked with the balances of accounts registered in the accounting in 2004, whose registration takes place when a check is cashed or a check is paid to the bank, after the respective transits: commercial, mail, etc.
- Application of the model.
We will work with the movements of the items that make up the Cash In and Out of Bank of a telecommunications company.
As mentioned above, we worked with the movements of the items that make up the Cash Inflows and Outflows in the Bank for the year 2004, therefore all the pertinent calculations were carried out to find the values of each of the variables of the formula of the sufficient level of treasury (,,,), according to the 2004 data. When using this method, the company is recommended that the more data used to carry out the analysis, the closer to reality the result will be, so it is suggested include more years in the study.
The variables were calculated for each of the items that make up the Cash inflows and outflows in the Bank and then they were grouped according to whether they are collections or payments to calculate the Net Cash Flow with a negative sign.
Unlike what is mentioned in the article, where we work with the daily treasury level, we work with the monthly treasury level, therefore t corresponded to month t and not to day t.
2.1 Collections (Items that make up the Cash Receipts in the Bank).
The items that make up the collections are: Sales of Merchandise and Services and Other Income. Below we will detail how the Sales of Goods and Services were proceeded. We will start in each case from the number of collection items presented in each month according to the classifications given and the cancellations (check cancellations or errors in them, registering with the opposite sign to the item), as well as the average per item. They are presented as an average, since it would be very cumbersome to put in this work all the sheets of the movements of these items in 2004; however, these averages will not negatively influence our result.
- Sales of Goods and Services:
They were classified by territories in the West, Center, East and Headquarters, and in the Cancellations already mentioned. This form of grouping was sought as there were numerous movements in this game.
The Table shows the calculation of the Expected Value (EV) or mathematical expectation of the number of collection instruments presented per month, expressed as:
Where:
: Number of collection instruments that are presented in a month.
: Probability of the number of collection instruments presented in a month.
For:
Where:
: Number of months in which the same is presented.
: Number of months studied.
Expected Values of the Number of Collection Instruments in the item Sales of Goods and Services per month:
| WEST | CENTER | EAST | MATRIX HOUSE | CANCELLATIONS | |||||
| # | PROB | # | PROB | # | PROB | # | PROB | # | PROB |
| one | 0.4167 | two | 0.0833 | two | 0.0833 | 5 | 0.0833 | 3 | 0.3333 |
| two | 0.1667 | 3 | 0.0833 | 6 | 0.0833 | 6 | 0.1667 | 4 | 0.0833 |
| 3 | 0.1667 | 4 | 0.0833 | 8 | 0.1667 | 7 | 0.1667 | 5 | 0.2500 |
| 5 | 0.0833 | 5 | 0.1667 | 9 | 0.1667 | 8 | 0.1667 | 6 | 0.0833 |
| 6 | 0.1667 | 6 | 0.1667 | 10 | 0.3333 | 9 | 0.0833 | 7 | 0.2500 |
| 7 | 0.0833 | 13 | 0.1667 | eleven | 0.1667 | ||||
| 8 | 0.1667 | 12 | 0.0833 | ||||||
| 9 | 0.0833 | 14 | 0.0833 | ||||||
| 14 | 0.0833 | ||||||||
| GO | 2.67 | 6.42 | 9.00 | 8.67 | 4.83 | ||||
| VE approx | 3 | 6 | 9 | 9 | 5 |
Average according to the classifications given of the receipts of the item Sales of Merchandise and Services.
| SALES OF GOODS AND SERVICES | ||
| West | 3,296.10 | |
| Center | 5,501.01 | |
| East | 7,566.18 | |
| Matrix house | 130,032.58 | |
| Cancellations | 17,715.51 |
The total receipts for Sales of Merchandise and Services according to the classifications given is calculated as:
Where:
: Months.
: Average charge per month.
: Total number of collection instruments in the study time (in this case in 2004).
Finally, the estimated value of collections per month from Sales of Merchandise and Services is calculated, as follows:
If there are several classifications, as in the case of Merchandise and Services Sales, all the estimated charges per month for each classification are added and in the case of cancellations, the estimated cancellations per month are subtracted.
The total charges for Merchandise and Service Sales were calculated as we saw in the review of the article, by multiplying the mathematical expectation of each classification by the average charges corresponding to it (as already explained, cancellations in this case they are subtracted); Therefore, the estimated value of collections per month resulting from the Sales of Merchandise and Services in total was 1,192,705.65 pesos.
- Other income:
From now on the results of all the games will be posted; the calculations were made with the same procedure as for Sales of Merchandise and Services.
Expected Values of the Number of Collection Instruments in the item Other Income per month.
| # | PROB |
| 0 | 0.5000 |
| one | 0.4167 |
| two | 0.0833 |
| GO | 0.58 |
| VE approx | one |
It is not necessary to put another table for the average of Other Income, since there are not several classifications or cancellations, the value of the average collections corresponding to Other Income being 1,878.55 pesos and the mathematical expectation of the number of collections of 1, estimated a monthly collection for Other Income of 1,878.55 pesos.
2.2 Payments (Items that make up the Cash Outflows in the Bank).
The items that make up the payments are: Energy Carriers; Raw Materials and Materials; Maintenance; Cost of Merchandise for Sale; Investments; Diets and travel; Commissions and Banking Expenses; Contribution of Utilities; Debts; Previous Years Expenses and Other Expenses.
- Energy Carriers:
Expected Values of the Number of Payment Instruments in the Energy Carriers item per month.
| # | PROB |
| two | 0.5833 |
| 3 | 0.3333 |
| 4 | 0.0833 |
| GO | 2.50 |
| VE approx | two |
The EV is rounded to 2 payment instruments, since between 2 and 3, 2 has a higher probability of occurrence. A monthly payment for Energy Carriers was estimated at 4,186.80 pesos.
- Raw Materials and Materials:
In every month there is a payment instrument, so the EV would be 12/12, that is, 1. The average monthly payments of Raw Materials and Materials would be 16,054.33 pesos and that exactly would be equivalent to the estimated value of the payments Monthly Raw Materials and Materials.
- Maintenance:
Expected Values of the Number of Payment Instruments in the Maintenance per month item.
| CANCELLATIONS | |||
| # | PROB | # | PROB |
| one | 0.8333 | 0 | 0.9167 |
| two | 0.0833 | one | 0.0833 |
| 4 | 0.0833 | ||
| GO | 1.33 | 0.08 | |
| VE approx | one | 0 |
It is observed in the table that the EV of Cancellations was 0, therefore we do not calculate the average. Regarding the average maintenance payment per month, this was 6,108.68 pesos, which in turn corresponded to the estimated monthly maintenance payment, since the EV was 1.
- Cost of Merchandise for Sale:
Expected Values of the Number of Payment Instruments in the item Cost of Merchandise for Sale per month.
| CANCELLATIONS | |||
| # | PROB | # | PROB |
| one | 0.9167 | 0 | 0.9167 |
| 3 | 0.0833 | one | 0.0833 |
| GO | 1.17 | 0.08 | |
| VE approx | one | 0 |
The same happens in this item, with the estimated monthly payment of the Cost of the Merchandise for Sale of 335,450.07 pesos.
- Investments:
Expected Values of the Number of Payment Instruments in the Investments per month item.
| CANCELLATIONS | |||
| # | PROB | # | PROB |
| one | 0.8333 | 0 | 0.8333 |
| two | 0.1667 | one | 0.0833 |
| two | 0.0833 | ||
| GO | 1.17 | 0.25 | |
| VE approx | one | 0 |
The average monthly payment for Investments was 18,560.45 pesos, which in turn corresponds to the estimated monthly payment for Investments, since the EV was 1.
- Diets and travel:
Expected Values of the Number of Payment Instruments in the Diets and Trips per month item.
| CANCELLATIONS | |||
| # | PROB | # | PROB |
| 0 | 0.5000 | 0 | 0.7500 |
| one | 0.5000 | one | 0.1667 |
| 3 | 0.0833 | ||
| GO | 0.50 | 0.42 | |
| VE approx | one | 0 |
It is rounded to 1, to consider the payment; being the average payment of Diets and Travel per month of 6,089.03 pesos, which in turn is equivalent to the estimated monthly payment.
- Commissions and Banking Expenses:
Expected Values of the Number of Payment Instruments in the Banking Commissions and Expenses per month.
| CANCELLATIONS | |||
| # | PROB | # | PROB |
| 8 | 0.0833 | 0 | 0.8333 |
| 9 | 0.2500 | one | 0.1667 |
| eleven | 0.0833 | ||
| 12 | 0.1667 | ||
| 13 | 0.0833 | ||
| 14 | 0.2500 | ||
| twenty | 0.0833 | ||
| GO | 12.08 | 0.17 | |
| VE approx | 12 | 0 |
The average payment per month of Commissions and Banking Expenses was 2,380.58 pesos and the estimated monthly payment of the item would be 28,566.96 pesos.
- Contribution of Utilities:
Expected Values of the Number of Payment Instruments in the Profit Contribution item per month.
| # | PROB |
| 0 | 0.0833 |
| one | 0.0833 |
| two | 0.5833 |
| 3 | 0.2500 |
| GO | 1.99 |
| VE approx | two |
The average payment per month of the Profit Contribution was 226,995.35 pesos and the estimated monthly payment of the Profit item would be 453,990.70 pesos.
- Debts:
In every month there is a payment instrument, so the EV would be 12/12, that is, 1. The average monthly payments of Debts would be 51,182.73 pesos and that would be exactly the value of the estimated monthly payment of Debts.
- Previous Years Expenses:
Expected Values of the Number of Payment Instruments in the item Previous Years Expenses per month.
| CANCELLATIONS | |||
| # | PROB | # | PROB |
| 0 | 0.0833 | 0 | 0.7500 |
| one | 0.7500 | one | 0.0833 |
| two | 0.0833 | 3 | 0.0833 |
| 3 | 0.0833 | 5 | 0.0833 |
| GO | 1.17 | 0.75 | |
| VE approx | one | one |
This time it was necessary to find the average of cancellations since the EV of the number of payment instruments per month was 1. The average of payments per month of the previous year was 10,900.46 pesos and that of Cancellations of 1,212.33 pesos; As each EV is 1, the estimated monthly payment corresponding to Previous Years Expenses would be the subtraction of the two figures mentioned above, this result being 9,688.13 pesos.
- Other expenses:
Expected Values of the Number of Payment Instruments in the item Other Expenses per month.
| CANCELLATIONS | |||
| # | PROB | # | PROB |
| 6 | 0.0833 | 0 | 0.9167 |
| 7 | 0.1667 | two | 0.0833 |
| 8 | 0.3333 | ||
| 9 | 0.0833 | ||
| 10 | 0.0833 | ||
| eleven | 0.2500 | ||
| GO | 8.67 | 0.17 | |
| VE approx | 9 | 0 |
As for the average payment per month of Other Expenses, it turned out to be 20,688.35 pesos and the estimated monthly payment of the item was 186,195.15 pesos.
With this we conclude the pertinent calculations to find the total estimated collections and payments. To determine the FNC (-) t, we would only need to subtract the estimated total charges and payments from each other, as we will see below:
Total Collections: 1,194,584.20 pesos
Total Payments: 1,116,073.03 pesos
So the resulting FNC (-) t is - 78,511.17 pesos.
This positive balance is then defined as the lower limit of the range of the sufficient level of treasury, which the company must maintain monthly, after the collections and payments of the period, to avoid that a FN (-) of treasury causes a deficit banking. Defining bank deficit as a negative balance in the Bank Cash account. Therefore, we consider this to be the lower limit of the initial balance of the Cash in Bank account at the beginning of the period.
Therefore, the sufficient level of cash (Z) for month t would be equivalent to a value that would fluctuate between the minimum limit and the maximum limit:
78,511.17 <Z <H
“The treasurer may choose a different value of Z based on his attitude to risk. The risk averse treasurer will opt for elevated Z levels that are close to the maximum level; (…) While the most risky treasurer will choose to maintain lower levels of treasury, so that Z will be closer to the minimum level. "
“The treasurer should work with a cash balance that he thinks is adequate or sufficient, for which he can be based on how much information he has available and on his own experience. Although we have considered that said sufficient cash balance is the same for the period analyzed, nothing prevents the treasurer from varying it depending on the circumstances that occur daily. "
Lower limit of the sufficient level of cash as the Initial Bank Cash Balance in the first quarter of 2005.
Next, we will proceed to analyze if it were to start in January 2005, with an initial balance of Cash in Bank equivalent to the defined lower limit of the sufficient level of treasury, that is, 78,511.17; the existence of negative balances in the month, that is, of bank deficit, would have been avoided, after adding to the initial balances of each month, the corresponding Net Flows (Inputs - Cash Outflows in the Bank).
It is valid to mention that the lower limit of the interval (78,511.17) is found, we would say, penalized by Cancellations, which are subtracted when they reach an EV> 0, in the items of Sales of Goods and Services and Expenses Previous Years, because if these did not exist, the lower limit would be 168,301.05 pesos, a value closer to reality. We say penalized, since Cancellations constitute inefficiencies in the work of the company that can be influenced.
Due to this, we will show the behavior that the company would have in two scenarios: Scenario A: including Cancellations at the lower limit of the sufficient level of cash (Pessimistic Scenario) and Scenario B: not including Cancellations at the lower limit of the sufficient level of Treasury (Optimistic Scenario).
- Scenario A:
Calculated opening balance, Net Flow and Ending Balance for the first quarter of 2005 including Cancellations.
| MONTHS | NET FLOW | INITIAL BALANCE | FINAL BALANCE |
| January | 32,780.49 | 78,511.17 | 111,291.66 |
| February | -169,224.82 | 111,291.66 | -57,933.16 |
| March | 7,650.51 | -57,933.16 | -50,282.65 |
As can be seen in the table, based on an initial balance estimated in January of 78,511.17 pesos, it was not possible to cover the FN (-) presented in February; As can be seen in the column of the final balance of each month, both in February and in March the balances were negative.
- Scenario B:
Calculated beginning balance, Net Flow and Ending Balance for the first quarter of 2005 without Cancellations.
| MONTHS | NET FLOW | INITIAL BALANCE | FINAL BALANCE |
| January | 32,780.49 | 168,301.05 | 201,081.54 |
| February | -169,224.82 | 201,081.54 | 31,856.72 |
| March | 7,650.51 | 31,856.72 | 39,507.23 |
As can be seen in the table, starting from an initial balance estimated in January of 168,301.05 pesos, it is possible to cover the FN (-) presented in February, avoiding the bank deficit.
- Upper limit of the sufficient level of treasury.
According to Miller Orr's model, “the lower limit of the treasury is usually set at zero, while the upper limit is defined (…) as H = 3Z; that is, three times the optimal cash balance. "
Applying the Miller Orr Model to calculate the upper limit we have:
- Scenario A:
H = 3 * 78,511.17
H = 235,533.51
78,511.17 <Z <235,533.51
With this upper limit of the interval, the negative value of the month of February of -169,224.82 pesos is covered.
- Scenario B:
H = 3 * 168,301.05
H = 504.903.15
168,301.05 <Z <504,903.15
It is evident that the upper limit covers the negative balance for February, since it was already covered with the lower limit of the interval.
It is valid to point out that the initial balance of Cash in Bank for January 2005 of the company under study was 1,182,390.96 pesos; which represents a difference with the upper limit of the interval in Scenario A of 946,857.45 and with Scenario B of 677,487.81 pesos.
The selection of H will be a reflection of the specific behavior of each company in its sector and of each entrepreneur regarding risk, without forgetting that said decision must be carried out under the premise of avoiding bank deficits and the possession of unnecessarily immobilized money.
3.2.2.4 Performance of the treasurer.
"The treasurer does not act (investing or disinvesting) except in those cases in which the accumulated treasury exceeds the upper or lower limits, and his intervention is not necessary when the treasury fluctuates between said limits."
In this study, the same suggestion is made, that is, try to make the Cash balance in the Bank oscillate between the defined limits; With the purpose that it does not reach a value lower than the lower limit of the interval, since the probability of a bank deficit would increase and that it does not exceed the upper limit, to avoid keeping money immobilized unnecessarily. In the event that it happens, the entity must take measures to avoid the consequences raised above.
Next we will graph the behavior of Cash in Bank under both scenarios.
- Scenario A:
Behavior of Cash in Bank in the first quarter of 2005 taking 78,511.17 as the initial balance in January.
The previous graph shows what we mentioned about the selection criterion for Z; the closer Z gets to the lower limit; the more risk the company will be running.
Let's analyze: We started January within the estimated limits, but with the FN (-) that occurred in February, the Cash balance in the Bank became -57,933.16, below the lower limit; catastrophic cash balance for the entity, leading to a bank deficit. In March, despite the fact that there was FN (+); the bank deficit is maintained, so it is not advisable to take the value of Z so close to the lower limit.
We will see what happens if we take Z as the upper limit.
Behavior of Cash in the Bank in the first quarter of 2005 taking 235,533.51 as the initial balance in January.
In this case: As there was FN (+) in January and we were at the upper limit of the sufficient cash level, we went 32,780.49 pesos over the upper limit. However, with the FN (-) that occurred in February, we are within the estimated Cash in Bank limits and we remain within the same in March. Situation, somewhat better than the previous one. However, when we went above the upper limit, we kept money immobilized for a month, which could have been used in the investment (for example, in a fixed-term deposit).
- Scenario B:
Behavior of Cash in Bank in the first quarter of 2005 taking 168,301.05 as the initial balance in January.
Let's see: We started January within the estimated limits, but with the FN (-) that occurred in the month of February, the cash balance in the Bank became 31,856.72, below the lower limit, although it does not imply a deficit banking. In March, this value amounts to 7,650.51 pesos, but it still falls outside the defined lower limit.
Behavior of Cash in Bank in the first quarter of 2005 taking 504,903.15 as the initial balance in January.
The same behavior as Scenario A, which when working with higher figures for Cash in the Bank, let us observe: As in January there was FN (+) and we were at the upper limit of the sufficient level of treasury, we went 32,780.49 pesos above the upper limit. However, with the FN (-) that occurred in February, we are within the estimated Cash in Bank limits and we remain within the same in March.
Our mission in this research has been to limit the results to entrepreneurs and help them in the use of ingenious methods for day-to-day cash management. It remains for the entity to define the value of Z that it considers would be best for its management, the possible paths to take are reflected in this work and a low risk decision within an average behavior between scenario A and B would be the most successful.
conclusion
With these results, the entity has at its disposal a useful tool to avoid the bank deficit and idle money in the Bank Cash account, in its hands is the decision-making power at the right time and the efficiency of its management.
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