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# FINANCIAL MANAGEMENT - Part 4 1578

## 3.3 The Underlying Assumptions for Simple Linear Regression

While using this method in financial forecasting, the following assumptions should be taken into consideration.

• Assumption that the underlying relationship is linear
• The assumption of independence
• The assumption that the errors are normally distributed
• The assumption that for any given value of x, the expected value of e is zero for instance E(ε) =0
• The variance of ε is constant for all values of x, i.e. the variance ε= s 2

However, the assumption only hold if the sample of the population of y values for agiven x is normal with a mean μy/x = α + βx .

### 3.3.1 Advantages of Linear Regression

The linear regression analysis tool is a very important tool to managers, this is because, it provide the managers with prior information as relates to what is happening in the external and internal environment of the organization. It has been observed that most mangers will prefer the regression analysis technique because of its ability to provide superior reliable information. Regression analysis ensures that the results produced are very accurate. This enables the manager to make objective measures concerning the relationship between the independent and the dependent variables instead of relying on personal judgments,. The use of linear regression analysis provides accurate information which the manager can rely on especially during decision making process. This is because, the results obtained from simple linear regression can empirically be tested for accuracy and reliability with the other parties and still finds the same results.

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The results obtained from the linear regression can be tested using specific tools and packages that are available in the computer. Most of the computers used within the company have specific packages and softwares that can be used to provide a few statistics. For instance, R-square and the student T-value statistics. This two statistical test help the managers to  determine the accuracy of the predictions and hence the level of reliability of the result got using the regression analysis is ascertained.

The use of the multiple regression analysis enables the managers to test for several independent variables which may explain different things about the  dependent variables. Despite the method being complex, the manager can still test all the factors which he may think that can have an effect on a given dependent variable. By using several variables, the accuracy of the model is greatly improved.

The use of regression analysis in the organization provides the needed input for the activity based-cost and the management techniques. The techniques enable the manager to understand what activities or transactions cause the acquisition and use of resources. It enables the managers to establish objective in decision making processes.

### 3.3.2 Disadvantages of the Linear Regression Analysis

One of the disadvantages of linear regression analysis is that it only considers linear relationships between dependent and the independent variables. It is important to note that at times, this may not be correct because of certain factors. For instance, when we consider the relationship between age and income, we realize that it is curved. This is because, income does tend to rise in the early parts of adulthood, then flatten out in later adulthood and later decline after an individual retires.

Another disadvantage of the linear regression model is that it only looks at the relationship between the mean of the dependent variable and the independent variable. Because the mean itself is not a complete description of relationships among variables, this means that simple regression may not be very accurate unless if you apply quintile regression.

Linear regression is very sensitive to outliers. The outliers refer to the data which are very surprising, it is crucial to note that outliers can either be univariat or multivariate variable. For instance, if we consider age and income we find that univariat variables will be things like a person who is 120 years old or one who made \$12 million last year. On the other hand a multivariate variable would be things like an 18 year old that made \$200000. In this case, we realize that neither income nor age is very extreme, but very few 18 year old people make that much.

Another disadvantage of linear regression is that it assumes that the data are independent. This would imply that the score of one subject of a person could have nothing to do with those of another. This is not very sensible.

## 3.4 Simulation Method (Monte Carlo Simulation)

This is an advanced forecasting technique which can be used to understand the impact of risk and uncertainties in a financial, project management and cost. The Monte Carlo simulation can tell you based on the ranges the likely estimates of the resulting income.

How Monte Carlo model works

A random value is selected for each of the task based on the range of estimates. The result of the model is calculated and recorded and the process is repeated several times for instance hundreds or thousands of times in each time using different randomly selected values.

At the time when the simulation is complete, a large number of results is obtained and then used to describe the likelihood of reaching various results. This is an advance technique that can prove to be very useful in forecasting financial statements. It can be used to determine whether the statements will reflect profit or losses.

The moving average technique

This is another technique which is used in financial forecasting. The technique is based on the historical trend of any given business organization. However, the method is not convenient in forecasting the financial statements because of myriad of uncertainties that is involved in extending such a series of historical trend.

Sales of a successful new product Sales of a product nearing the end of the life The above method can be used to forecast sales of a given business organization for a period of one week a day or during the week this will give the company or the business organization an hourly seasonal pattern superimposed on daily seasonal pattern. Any deviation or fluctuation that may be realized is described as cyclical factors

## 3.5 Computerized Forecasting Technique

At times the managers may find the linear regression model to be a very complicated tool for forecasting in the organization especially in occasions where the data to be used in financial forecasting is too large. The use of computers as a method of forecasting in the business organization have proved to be vital to the managers because it carry out forecasting at a much shorter time compared to the linear regression which involves tedious calculations which at time may not be very accurate because of arithmetic errors. The role of the manager here will be simple, only to feed the data into the computer and within a shorter period of time, the computer program will produce a linear model for forecasting purposes. ## 3.6 Percentage of Sales Method

This is another technique that may be applied in financial forecasting, in this method, the items in the balance sheet which are related to sales are expressed as a percentage of sales by following the steps mentioned below.

Step 1.  The first thing to do is to identify the items in the balance sheet which are directly related to sales. For instance current assets-increase in sales due to increased stock of raw materials, work in progress and the finished goods. Increased credit sales will increase debtors while more cash will be required to buy more raw materials in cash.

Current liabilities.

It is estimated that increased sales may lead to increased purchase of the raw materials

Retained earnings; the retained earnings may increase as the sales increases only if the firm is operating at a profit

Step 2; in step two the above mentioned is expressed as a percentage of sales then determine the relationship between the item and the current sales. Determine the increase in the total assets as a result of the increase in sales.

Determine total increase in the spontaneous sources of finance and the increase in the retained earnings.

Retained earnings=net profit-dividend paid

Net profit margin=net profit

Sales

Meaning that the net profit=net profit margin× sales.

The next step for the manager therefore is to get the financing which is needed. And then prepare the proforma financial statements; proforma financial statements are the projected statements at the end of the forecasting period.

N/B.  information could be given which necessitates the determination of forecast sales, this will be determined using the following formula:

Sn =So(1+ g)n

Where:    Sn = sales n years from now

So=current sales

g=growth rate

n= forecasting period

Assumptions of percentage of sales method.

• The fundamental assumption is that there's no inflation in the economy .i.e. the increase in sales is caused by an increase production and not increase in selling price.
• The firm is operating at full capacity. hence, the increase in production will require an increase in fixed assets
• The capital remains constant during the forecasting period i.e. no issue of ordinary or preference shares and debentures
• That the relationship between the balance
• sheet items and sales remains the same during the forecasting period.
• The net profit margin will be achieved and shall remain constant during the forecasting period

Advantages of the percentage of sales method

The percentage of sales forecasting is important because it is easy to compute because computation is based on the already existing data. On the other hand, one of the disadvantages of this method is that internal resources are allocated differently either in growth or decline. This might affect the planned budget hence may not be a good way for analyzing future expenditure.

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## 3.7 The Additive Component Model

The model is one in which variation of the value of the variable overtime can be described by adding the relevant components. The model uses the following formulae

Actual value=trend +seasonal variation + error

A=T+S+E

Procedure for using this model

Step 1: calculate the seasonal components

Step 2: deseasonalize the data by removing the seasonal component from the actual values. Then you calculate the trend the deseasonalised figures.

Step 3: here you deduct the trend figures from the deseasonalised figures in order to leave the errors.

Step 4: you calculate the mean average deviation in order to judge whether the model is reasonable or to select the best from different models. Then you calculate the seasonal components for the addictive model.

Let us consider the data below.

Table 2: QUANTITY OF PRODUCT SOLD OVER THE LAST 13 YEARS 3 MOTHLY PERIOD

 Date quantity sold 000 Jan – May 19 x 6 239 apr – Jun 201 Jul – sep 182 Oct – Dec 297 Jan – Mar 19 x 7 324 apr – Jun 278 Jul – sep 257 Oct – Dec 384 Jan – Mar 19 x 8 401 apr – Jun 360 Jul – sep 335 Oct – Dec 462 Jan – Mar 19 x 9 481

Let us now assume that we want to analyze the data if we can find historical pattern so as we use it to forecast the quantity sold in the subsequent three monthly periods. The figures are plotted as shown below. From the diagram, we can deduce that the sales in the winter seasons 1 and 4 are consistently higher than those in the summer seasons 2 and 3. However, the seasonal components appear to be fairly constant over the three years. The trend shows that sales increase overall from around 230 in 19×6 to 390 however, the seasonal fluctuations have not increased. The method can be used effectively in forecasting financial statements.

## 3.8 Multiple Linear Regressions

This is another advanced quantitative method for forecasting financial statements. Let as assume there are more than one factor which influence the dependent variable, for instance, if we are interested in predicting the cost per week for the production department we have to consider other factors such as production hours worked, raw materials used and the number of items produced and the maintenance hours worked. For us to come up with a dependable forecast, we have to consider all the above mentioned variables. The linear model for the multiple regressions will be as follows.

Y=α + β1x12 x2 + β3x3 + ….βnxn +€

The main problem with the use of the multiple linear regression in forecasting is that  it is likely to lead to very complex calculations. However, to make the work easier, certain computer packages can be used hence making the work simple. Leave a Reply