Summary
The work that is carried out consists of the creation of a procedure that allows to demonstrate that from two mathematical models, linear and modular, respectively, sales can be anticipated and distributed for periods of time not exceeding one year, making the investigation strong in the determination of the estimators for both models.
All the scientific basis is based on the historical valuation of the sales of the last three years, based on the consideration that these are the ones that most closely resemble the period under planning, thus avoiding the possible large differences that imply or motivate the actions of a world with an economy in constant motion.
Development
For any company, whether of production, sale or service that is carrying out an economic anticipation process or evaluating the economic result of a concluded period of time, it is of the utmost importance to know exactly the amount of sales that must be achieved or that should have been achieved under the fulfillment of certain conditions that are foreseen or that should have existed, since they constitute the primary link or starting point of said process of planning or evaluation of results. From the definition of this indicator, the behavior of the rest of the indicators that determine the economic management of the company begins to be assessed.
It can also be pointed out that sales constitute a form of link between the market and the company, since they must identify the maximum presence of the latter in said market according to their possibilities, and can also indicate whether the presence in it is correct or no.
It is important to note that for the planning of the pro forma statements, knowing the maximum possible sale is very important, since anticipating amounts of sales with a defect would imply the lack of use of all available capacity, as well as a share in the market below the real possibilities, which may imply that the void that is created in it is filled by another company and therefore in the immediate future that part of the market that was not satisfied will be lost.
Undoubtedly, the absence of use of all the available capacity in the time object of analysis directly affects the company's income and its profits, but also generates an opportunity cost that depresses the results, since the capacities that are not used constitute immobilized money that has no participation in the generation of income and profits.
It should also be noted that it is not healthy for the company to anticipate sales amounts above the real possibilities, since among other difficulties, false expectations can be created in the market, resulting in a bad image by not being able to meet the commitments assumed and lose credibility in it, which may imply at the same time the abandonment of customers from the sales services that until now was guaranteed.
It is also important to know the market demand, their degree of satisfaction from all the bidders who participate in the competition, since conceiving a sales amount above the demand would lead to the execution of a set of actions that would motivate the expenditure of resources that could have been used for other purposes that will increase the value of the company and its profits, as well as waste of time.
In this regard, Gillman O. states that… 1 The main input in the development of pro forma statements is the sales forecast… In turn, Weston, J. Fred. Fundamentals of Financial Management _7. Ed. (SL), (SN), (SA). Express that…
The starting point for determining cash requirements is the sales forecast… 2
The authors consider that in a process of planning or analysis of the economic management of a company, for any given period of time, it lacks security by default for decision-making, if it is not part of the sales level for which it is due. work or should have worked.
There are numerous techniques for the anticipated calculation of the amount of sales to be achieved, among others we can mention regression, moving averages, exponential ordering, etc. In the present work, the author proposes a technique that starts from the statistical evaluation of the sales behavior in the last three years, creates a balance between the differential of the sales growth rates of those three years and the growth differential of sale that is intended to be achieved in the year object of planning in relation to the last past year, as well as the consideration or addition to said balance of the conditions of the period of time that it is anticipated that did not exist in the three preceding years and from a derivation process to arrive at a linear mathematical model of fit and another modular;with the objective of making estimates and sales distributions respectively over intermediate periods of less than one year.
First of all, it is essential to conclude in this part the why of the importance of knowing the amount of sales.
As can be seen, from the determination of the sales the conception of the rest of the activities of the entity that guarantee its achievement is developed, for this reason a correct anticipation of the same is needed, otherwise the planning of the economic management of the entity and all the decision-making that it generates would be incorrect.
Also note the double link between the market and sales, one of them indicates the information that the market provides to the company about its level of satisfaction and the other the company's market share based on sales.
The proposed technique consists of the following steps:
1. Determination of the equilibrium sale.
2. Determination of the conditions that are expected to exist in the planned year and that did not exist in the last three years.
3. Determination of sales for the period.
4. The best option for the distribution of sales in the period under evaluation.
Determination of the equilibrium sale.
It is the sale that must exist for the period of time being planned, according to the growth rate of sales in the last three years and its determination starts from the balance to be achieved between the differential of the growth rates of sales in the last three years and the growth differential to be achieved in the year being planned.
Where:
ia = sales growth rate in the last past year. Example Year 2005.
iaa = sales growth rate for the year preceding the last past year. Example year 2004 which in turn depends on the year 2003.
ia´: growth rate of the last expired period considering the conditions for the new period.
V = equilibrium sales.
Va = sales in the last past year. Example Year 2005
Vaa = sales that preceded the last past year. Example Year 2004
Vab = sales that preceded the penultimate year past due. Example 2003
Vca = update of the sales of the previous period according to the period under planning
C = Conditions assumed in the planning period
The last three years that have elapsed are assumed to be the closest to the year anticipated and therefore the ones that can best characterize the current behavior of the company, as long as the company does not have certain cyclical behaviors that limit this conception. Keep in mind that when referring to the time period year, apart from indicating for example years 2003, 2004, 2005, etc. You can also indicate month, two-month period, quarter or other period less than one year.
In the opinion of the authors, the larger the estimation period, the less efficient the anticipation model will be, since the precision of the elements and details necessary for planning is more difficult, given how changing the characteristics that define can become. the internal and external conditions of the company. For this reason, models are recommended for periods of no more than one year.
Solving for V in L 1 gives the so-called equilibrium sales, as shown below:
Assess that the sales achieved with this derivation are in balance with the behavior of those held in the last three years, reliably assume their particularities. This appraisal at first sight may indicate that the difficulties of the previous years are dragged along (it also drags the positive), however this is solved later when the conditions of the planning period are included, since they are aimed at solving said difficulties; as well as those that did not exist in those three years and that are anticipated to exist. It is implicit the consideration of the positive that is dragged, as what is expected of the new conditions that are assumed.Therefore, the union of equilibrium sales and conditions provide a tool that continuously improves the efficiency of design and sales achievement.
Next, an analysis will be carried out on the differential of the sales growth rate (valid for L1 and L2), which will show that the equilibrium sale depends on the behavior of sales in the last three years.
Where:
Va = Sales amount of the last year due, example: 2005.
Vaa = Sales amount for the year prior to the last year due, example: 2004.
Vab = Sales amount for the year prior to the one preceding the last year due, example: 2003.
As can be seen, the sales growth rate (ia) for the year 2005 (if we assume the previous example), depends on the sales of the years 2004 and 2005 and the sales growth rate (iaa) for the year 2004 depends on the sales of the years 2003 and 2004, being shown that the valuation of the equilibrium sales was based on three years, considering that for the interest of the technique that is developed, they are the last ones that have elapsed.
Note that L2 can be derived in a simpler formula, for this purpose we will assume that the differential of the sales growth rate is id, that is:
Therefore, it can be stated that equilibrium sales can be calculated from the following formula:
However, due to a problem of comfort and convenience for when the linear mathematical adjustment model is to be defined and considering that the order of the factors does not alter the product, we will modify the formation structure of (L2a), leaving it as follows:
Determination of the conditions that are expected for the year being planned and that did not exist in the last three years.
Once the equilibrium sales are known, it is necessary to consider the new conditions that the period under analysis holds and that in the previous one existed or did not exist.
But what are the conditions for the interests pursued. They are all those that directly or indirectly intervene in updating the equilibrium sales and specify the definition of the sales for the period. They can be internal and external, where the internal ones are defined within the company and the external ones are defined outside of it.
The definition and assessment of the conditions depend on the experience and knowledge of both the internal and external environment of the entity, the greater the knowledge and experience the better anticipation and therefore better planning will bring. A general classification of the conditions that affect sales can be made in order to guide the work of their defection, for example:
- Market behavior Level of exploitation of capacities Work organization Scientific technical progress Development policies Others.
Each specialist will have his vision in this regard and will make his classification according to the knowledge and experience he has. As is logical, other more specific ones can be made from the general classification to be able to know everything that the planning period holds. This not only depends on the attributes indicated above for the person doing the work, but also on their sagacity. For example:
Market behavior
- Demand within the national territory.
- Within the territory where the company is located. Outside the territory where the company is located.
- Demand outside the national territory.
- Geographic area Countries.
The previous classification can be made more specific, it all depends on the knowledge, experience and sagacity of the analyst or analysts as already expressed above. But note that there is no doubt that a reasoning of this type would motivate a series of information that would adjust the already known equilibrium sale and would allow us to know the anticipated amount of sales for the period, with a high degree of precision and scientific rigor.
The conditions have to be translated into a monetary expression, that is, their original calculation has to be in monetary terms and not in percent, since it would always imply a margin of error, therefore, as a consequence, said margin of error would be assumed by the rest of the indicators that make up the pro forma statements.
This margin of error is generally to the right of the point of a value expressed with decimals. Consider for this purpose that expressions in percent are generally expressed with two decimal places, which gives reason to practice approximations, these being the margin of error referred to by the author. In small amounts of values, some specialists may understand that it is negligible, however in this work meditation is called on this through the following allusion: If the debit and the credit have a difference of one cent, the general balance of the entity is deficient. If this allusion is assumed, then the criterion is valid that the conditions are expressed in monetary values and not as a percentage. For example,If the sales of the previous year were 3 and those expected this year are 4 due to the commissioning of the optical fiber, it indicates a growth of 1. However, if we were to express the growth as a percentage, it would be as follows:
If this result is assumed with two decimals, it would always imply a variation that would grow as a function of the size or amount represented by the value 4, that is, it could be, 40, 400, 4000, 4000000, etc. Being shown that the absolute value with its respective causes that motivate it is preferable and not the value expressed as a percentage.
However, the work does consider the use of the percentage due to force majeure, since the situation may arise that companies, due to ignorance or ease, lightly raise the amount of sale to be achieved in the planning period by means of hundreds of growth in relation to the previous period or that the amount of sale to be achieved in a year is fully known and its opening is not known for months and the specialist is forced to make a proration of that total figure for months from a percentage structure, for this reason the present work provides a solution to this problem by creating the conditions to work with percentage structures.
The foregoing indicates that the classifications we make will have to be quantified monetarily and their algebraic sum would be the amount of the conditions to be considered in the calculation of sales for the period. An algebraic sum is proposed because there can be positive and negative values, and the final result can also be positive or negative.
Determination of sales for the period (Vp)
Once the conditions are known, the anticipated amount of sales for the period can then be determined, using the conditions in the calculation of a new improved growth rate to find an estimator for the year being planned, this is achieved from the addition of the conditions obtained to the sales of the previous period in the L3 model which divided by the result of the L4 model allows to obtain an improved estimator, which will be used in the calculation of the period sales, all of which conditions the growth rate and to the estimator so that they respond to the sales of the period to be anticipated, which is detailed below:
First we start from the assumed condition,
This condition is taken to the L3 model, which allows calculating the growth rate of the last expired period, on which the modification proposed in the assumed condition is made, that is, to Va or actual sales of the previous period, the own conditions are added that They are anticipated to the planning period, with L3 being modified as follows and assuming the name L3a:
However, to make the expression of the L3a model easier, the following can be considered:
So leaving the expression of L3a as detailed below:
If everything previously discussed is fulfilled, then the following equalities or proportions can be considered:
The first two proportions allow us to obtain the estimator we are looking for for our interests, so the following will be assumed from their approaches:
Note that the new estimator obtained to determine the sales for the period has a quotation mark that makes it different from the point of view of its visual identification to the estimator of the sales according to history:
Then, if what is expressed in the proportions 1 and 2 is known as valid, then
Note how the previously considered is fulfilled, that is, how the new conditions that are foreseen in the new anticipated period are considered, which can be not only of addition but can also be of subtraction.
However, the previous expression can be derived into a simpler one if we consider that the sign by or of multiplying is not necessary to identify it in the model, so the notation of said model would be as follows:
Where:
ai: sales growth rate of the last expired period
ia´: growth rate of the last expired period considering conditions for the new period.
id´: estimator of the sales of the period.
VP: sales for the period.
As can be seen, we are in the presence of a linear fit model that starts from the point of origin of the coordinate axis system as detailed below:
The image reflected in Figure 1 is based on the criterion that at a certain level of Va (independent variable X) a certain amount of Vp (dependent variable Y) is needed. Note that if the conditions that give rise to the line OA defined by the model
1Microsoft Excel. Statistical functions. Linear estimation.
It must be borne in mind that the valuation or calculation of the sales of the period (VP) not only depends on the behavior of the history, but is also nuanced with the new conditions imposed by the new period under analysis, which are incorporated by adding of its value with the value of the sales of the last expired period at the time of calculating the new growth rate for the year under planning. This is very important since continuously the development of the entity over time is adjusting to the new conditions that assume each new period of work.
Others allow very important evaluations such as being able to define that a company may be in favorable conditions in relation to the previous period but not with history, that is, sales can grow in relation to the previous year, but not in relation to the last three years expired, historical period that the author assumes for the present investigation and that at the beginning of this work explained the reasons why this historical period.
However, this model only responds to one of the requirements pursued, since it only indicates the total sales for a given period of time and does not detail its best distribution over time. In the authors' discretion, it is considered that the sale included in the L6a model is the maximum possible, based on the potential of available resources, since it is based on the assumption that there are no immobilized resources. If this is true, then it can be stated that after the first half of the period for which the sale was conceived, half of it must also have been executed, because if the opposite happens, there would be immobilized resources that do not generate sale and that represent an investment that does not generate money.
The L6a model does not allow this analysis to be viewed, since it is not defined from an independent variable expressed in time (t), however we can improve this if we incorporate time in the image analysis of the L6a model:
Observe that the total sales obtained through the L6a model for the independent variable Va is the same for the period of time t, that is, for both Va and t there is a sales level Vp = id'Va, that all what is below the OA line is sale. However, there is something that is not clear, if it is assumed in the analysis 1/2 t that represents 1/2 Vac, it divides the figure into two parts k and H which should be equal, however at first glance it can be seen that K is less than H (K <H), that is, in the first part of the period under analysis there is less sale than in the second, given that Va is cumulative, this means that said model only determines the best sale but not its distribution, For this reason, it is necessary to look for said distribution and that it be the optimal one.
Assuming Vp = id´Va at point 1/2 Va for 1/2 t, the area K is obtained, so for the other half of Va at t there must be an area H equal to the area K, which can be achieve if the following image is assumed:
The previous procedure produces the OBVa image that can be determined by three functions if we value it in three parts, these parts defined by OB, BVa and OBVa respectively. The first is represented by a linear function with increasing monotony of the type
It is important to assess the information provided by the image of the function obtained from the independent variable Va with the addition of the time factor (T), which does not alter the judgment made regarding the amount of sale to be obtained, since that said amount unobjectionably responds to a specific time, month, two-month period, quarter, etc.
denominated by T, however, in a similar way it is necessary to add another valuation factor that will finally make up the result of the analysis that is carried out, this factor is the resources (R) that are needed to achieve said sale amount in the time T, see figure 4.
Starting from the assumption that the company works efficiently and that it makes all its resources available to its economic management, then in order to achieve a sale equal to VP in time T, an amount of resources equal to R is needed and that half of it is completed. of the expected working time 1/2 T, 1/2 VP of sales must have been achieved. But note that to achieve VP and a 1/2 VP in T and 1/2 T respectively, amounts of resources equivalent to R and 1/2 R are needed for each of these time periods.
If the above is assumed as valid, the company has to work to achieve at all times that at the end of time T area K is equal to area H:
conclusion
K = H
If what is stated in the previous conclusion is not achieved, two situations may occur that would affect the results of the company, since the efficiency and effectiveness of its economic management would be affected. Efficiency due to not knowing how to use the entity's time and resources correctly and effectiveness is represented in the failure to achieve profits and the increase of the owners' capital. This can be explained as follows:
Yes
K <H
Then from 0 to 1/2 T there will be immobilized resources, which do not generate sales and therefore do not generate income, which implies an opportunity cost for having an investment of money in resources that does not contribute anything to the profitability of the company, being able measure this cost by the economic profitability that the entity would have had in the event that said investment of resources had been used and therefore had contributed a certain amount of sale with its respective participation in the company's profit. If this situation exists, where K <H it is concluded that costs increase, profitability decreases and therefore the value of the company and the capital of the owners. Yes K> H
The same would happen as under the condition of K <H, having the same conclusion, costs increase, profitability decreases and therefore the value of the company and the capital of the owners.
Without a doubt, we are in the presence of a single condition that provides the best results (K = H), if this condition is not met in a planning process, then losses are anticipated for a certain period of time. Sales must be worked under this condition and in its real execution process it is necessary to ensure that this is fulfilled through a comprehensive process of scientific administration that entails, among other actions, planning, execution, control, regulation and settlement.
It could be thought that the sales plan can be achieved mostly or totally at the beginning or end of time, then the question remains, what would be being done during the time that it is not sold if the reason for being is to sell. It could be said that preparing the conditions for the sale, then there would be two management criteria, one for preparation and the other for sale. Assuming that this is the case, this does not change anything, because if there is no coincidence, the preparation and the sale do not need the same amount of resources, suppose personnel, that is, salary expense. Therefore it is clear that unquestionably the best option is where K = H, that is, the distribution that allows obtaining the model
In order to apply the previous conclusion, it is necessary to carry out a financial interpretation of the assumed modular function model, using for this purpose figure 4 that we reproduce below
During the first part of this work, we worked on achieving the best estimator or slope for the Y = mx type model that would determine the best sale option, which, when interpreted from a financial point of view, is VP = idVca. In this second part of the work, which consists of determining the best distribution of the VPs, the estimator or calculated slope (id) does not respond to the requirements and demands of the modular function model, since id only expresses the slope of the sides of this function as shown below:
However, the estimator that defines the amplitude of the modular function is needed, as well as determining the values of the independent terms, for this case of b and c, but from the financial point of view, for which the adaptation will be helped with the information that provides figure 4 and that they are already known values.
Determination of the independent term c
In this type of function it is shown that the independent term c is constituted by its maximum value, for the case that we occupy 1 / 2VP.
Determination of the independent term b
The assessment will be made at the point (1 / 2Va; 1 / 2VP)
Determination of the estimator or amplitude of the function (m)
The assessment will be made at the point (1 / 4Va; 1 / 4VP)
Reflect the figure of the point (1 / 4Va; 1 / 4VP)
Financial value of the slope or estimator for the modular function
Substituting in equation 1 am by its financial value to know the financial value of b.
Financial value of b
Financial interpretation of the model of the modular function being evaluated.
As can be seen, the objective set out in this investigation has been reached in a theoretical way, which is nothing more than knowing the best sale for a given period of time and its best distribution within said period, as well as its implementation through a set of tables on Excel in a concatenated way one with others forming a valuation system that has allowed to verify the authenticity of the hypothesis raised for the defined scientific problem.
This procedure not only allows to get to know the best sale and its distribution over time, but also constitutes a financial analysis of the company based on the valuation of sales during the last three years past due and a fourth year that It constitutes the year object of planning, which as a whole represents an important tool for the achievement of the objectives set by the company from a group of assessments and information that it provides and that allows decision-making at the appropriate time to control and regulate the economic activity of the entity.
It should be noted that the application of this procedure does not constitute any difficulty for its application and development for ETEC. SA. Since it is conformed in the form of a program, where there is a database entry that automatically generates the results that you want to obtain.
Notes:
1- Gillman O. Fundamentals of financial management. (SL), (SN), (SA). P. 139-140
2- Weston, J. Fred Fundamentals of Financial Management _7. Ed. (SL), (SN), (SA).
Bibliography:
1- Bolten Stevan E. «Financial Administration». Mexico 1995. p. 44-48, 64-67, 76-88, 109-114, 487-591, 617.
2- Brealey, R. Myers S. «Foundation of business financing». Mc Publishing. Graw-Hill. Ed. 4 Madrid, 1993. p. 4-10, 190-195, 377-388, 763-783, 853-860, 881-983.
3- Gillman O. Fundamentals of financial management. (SL), (SN), (SA). P. 139-140
4- Weston, J. Fred Fundamentals of Financial Management _7. Ed. (SL), (SN), (SA).
5- Domínguez Machuca, JA «The investment and financing subsystem of the company». Pyramid Madrid, 1986. p. 35-62, 90-110.
