Sales forecast: 6 corrected financial years

Welcome to this article whose sole purpose is to help you progress in the chapter of sales forecasting using corrected exercises from the Operational Management subject of the BTS MCO.

If you would like to first see or review the course on sales forecasting, I invite you to read my article Sales Forecasting: The 4 Methods to Master.

Lesson 6 corrected exercises on sales forecasting of this page mainly relate to the calculation of sales forecasts.

You will also find corrected exercises on the following concepts: the least squares method, the extreme points method and the double average method (Mayer method).

Here is the list of 6 sales forecasting exercises corrected:

1. Sales forecast Corrected financial years: Turnover – Least squares method
2. Sales forecast Corrected exercises: Extreme points method
3. Sales forecast Corrected financial years: Forecast turnover – Double average method
4. Sales forecast Corrected financial years: Turnover – Least squares method
5. Sales forecast Corrected exercises: Extreme points method
6. Sales forecast Corrected financial years: Turnover – Mayer method

 

Sales forecast Corrected financial years: Turnover – Least squares method

States

The Mionneur commercial unit manufactures and sells spare parts for trucks for road professionals.

Its manager, Madame Laroutière, would like to estimate her turnover for year N+1.

To do this, it provides you with the evolution of its turnover for the previous seven years.

 

Work to do

1. Determine the forecast turnover N+1 using the least squares method.

 

Proposed correction

1. Determine the forecast turnover N+1 using the least squares method.

In order to answer the question, it is necessary to create a preparatory table.

• xi corresponds to the rank of the period
• yi corresponds to turnover
• xi² : 1 squared, then 2 squared, then 3 squared and so on.
• xi yi corresponds to the product (multiplication) of xi and yi, therefore: 1 × 3 then 000 × 2, then 3 × 200 and so on.
• the last line is a “Total” line.

By creating this preparatory table, it is possible to find the elements of the equation that we need to make the forecast.

The desired equation is of the form:

It is therefore necessary to calculate the elements “a” and “b”.

Before calculating the element “a”, it is necessary to calculate the averages of “x” and “y”.

To calculate the averages, the following management formulas must be used:

Which gives in our exercise:

With “n” the number of variables in our base table.

et

Which gives in our exercise:

Now that we have the averages of x (4) and y (3), we can calculate the element "a" with the following formula:

We have all the numerical elements to write the formula for the element “a”:

therefore:

a = 183,93

regarding “b”, the formula is:

We admit that the averages verify the equation, we therefore replace “x” and “y” by their average:

Which gives with the numerical elements:

b = 3 – (521,43 × 183,93)

b = 2

We have found the value of “a” and the value of “b”, so we can now write the equation, of the form y = ax + b, which allows us to calculate any forecast turnover:

y = 183,93x + 2

 

Calculation of the forecast

We can finally forecast the turnover N+1, to do this we replace “x” with the rank number of the year sought.

From N-6 to N, there are 7 ranks, so N+1 is 8^th rank :

y = (183,93 × 8) + 2 = 4 257,15 €

The forecast turnover of the commercial unit is €4.

 

Sales forecast Corrected exercises: Extreme point methods

States

The Mouflet commercial unit makes and sells clothing for entertainment professionals.

Its manager, Madame Lepatron, wishes to evaluate its turnover for the next two years.

 

Work to do

1. Determine the forecast turnover N+1 and N+2 using the extreme points method.

 

Proposed correction

1. Determine the forecast turnover N+1 and N+2 using the extreme points method.

In order to answer the question, it is necessary to create a preparatory table.

In this method, only the first and last lines need to be taken into consideration. We therefore have two extreme points:

x1: 1 and y1: 3 and x000: 7 and y7: 7

We pose the system of equations with two unknowns:

This system can be solved in several ways: by substitution or by combination.

So we can do the second equation minus the first:

4 – 100 = 3a + b – (000a + b)

1 = 100a + b – 7a – b

1 = 100a + 6b

So :

a = 1 / 100

a = 183,33

We can now find “b” in the following way:

b = y1 – ax1

So we have :

b = 3 – (000 x 183,33)

b = 2

 

Calculation of the forecast

We can now make the required forecasts using the following equation:

y = 183,33x + 2

 

For N+1 you have to replace “x” with rank 8 because N had rank 7:

y = (183,33 x 8) + 2

y = 4

 

For N+2 we must replace “x” with rank 9 so we have:

y = (183,33 x 9) + 2

y = 4

The forecast turnover figures for years N+1 and N+2 are therefore €4 and €283,31.

 

Sales forecast Corrected financial years: Forecast turnover – Double average method

States

The Nal business unit manufactures and sells pipes for municipalities and departments.

His customers do not pay on time, the manager, Mr Leborgne, wishes to evaluate future turnover.

 

Work to do

1. Determine the forecast turnover N+1 and N+2 using the double average method.

 

Proposed correction

1. Determine the forecast turnover N+1 and N+2 using the double average method.

This method consists of splitting the statistical series into two sub-series then calculating the averages and finally solving a system of equations in which and are the unknowns.

We can thus split the series between N-4 and N-3:

Sub series 1:

Calculating the averages of “x” and “y”

 

 

et

 

 

 

Hence the following first equation:

Second sub-series:

Calculating the averages of “x” and “y”

 

 

et

 

 

 

Hence the following second equation:

We then solve the following system of equations:

 

 

 

So we have :

3 – 560 = 3a – 075a +b – b

485 = 4a

a = 485 ÷ a = 121,25

 

We then replace “a” by its value in one of the two equations:

3 = 560a + b for example

Which give :

3 = 560 × 6,5 + b

3 = 560 + b

b = 3 – 560

b = 2

We therefore obtain the following equation:

Calculating the sales forecast

This equation makes it possible to find the forecast turnover by replacing it with the rank of the year concerned.

Here N+1(rank 9) gives us:

y = (121,25 ×9) + 2

y = 3

The forecast turnover for year N+1 is €3.

 

Sales forecast Corrected financial years: Turnover – Least squares method

States

We give the following table:

 

Work to do

• Determine the forecast turnover N using the least squares method.

 

Proposed correction

In the topic of sales forecasting, “xi” represents time and “yi” represents turnover.

So we can use the following formulas:

We will now design a preparatory table in order to obtain the elements necessary for the application of the formulas:

1. a date cannot be used in formulas. It is therefore necessary to assign a rank number, starting from the oldest date, to each period.

We can now carry out the calculations:

Calculation of averages :

Calculation of element “a”:

Calculation of element “b”:

b = 4 – (692 × 536) = 3

We can therefore write the equation of the form which allows us to find any turnover figures:

y = 536x + 3

 

Calculating the sales forecast

By replacing x with the rank number corresponding to the period sought we have:

y = 536x + 3

y = (536 × 9) + 3

y = 6

The forecast turnover for year N is €6.

 

Sales forecast Corrected financial years: Turnover – Extreme points method

States

We give the following table:

 

Work to do

1. Determine the forecast turnover N using the extreme point method.

 

Proposed correction

In this corrected management exercise, it is first necessary to determine the extreme points which correspond to the oldest period and the most recent period.

Of course, “xi” corresponds to the periods by indicating a rank for each of them and “yi” corresponds to the turnover figures.

Thus, the preparatory table can be as follows:

Extreme points :

P1 has coordinates x1 = 1 and y1 = 3

P2 has coordinates x2 = 5 and y2 = 5

 

Then, we pose a system of equations with the parameters “a” and “b” to be determined which will allow us to find an equation of the form “y = ax + b”.

This will allow us to find any future turnover.

System of equations :

 

 

 

Solving the system of equations by the subtractive method :

We're going to do the second equation minus the first.

5 – 690 = 3a – a + b – b

2 = 190a

a = 2 ÷ 190

a = 547,50

 

We therefore find “a” = 547,50 and by replacing this value in one of the initial equations we can find the element “b”:

3 = a + b

3 = 500 + b

b = 3 – 500

b = 2

 

Thus we find the elements “a” and “b”. We can now write the equation which allows us to find any future turnover:

y = 547,50x + 2

 

Calculating the sales forecast

To find the forecast turnover N, you must replace it with the rank corresponding to period N: it is therefore rank 6.

y = (547,50 × 6) + 2

y = 6

Thus the forecast turnover N amounts to €6.

 

Sales forecast Corrected financial years: Turnover – Mayer method

States

We give the following table:

 

Work to do

1. Determine the forecast turnover N using the Mayer method.

 

Proposed correction

In this corrected exercise on sales forecasting, you must first divide the statistical series into two sub-series, then determine the averages for x and y, deduce an equation of the form y = ax+b then finally solve a system of equations by finding the parameters “a” and “b”.

First sub-series :

Calculation of averages:

Hence the following equation:

 

Second sub-series :

 

Calculation of averages:

Hence the following equation:

So we must solve the following system of equations:

Solving the system of equations by the subtractive method :

5 – 460 = 4a – 180a + – b

1 = 280a

a = 1 ÷ 280

a = 512

 

To find “b”, simply replace “a” in one of the two basic equations with the value found.

4 = (180 × 2) + b

4 = 180 + b

b = 4 – 180

b = 3

So we can write the equation which allows us to find any future turnover:

y = 512x + 3

 

Calculating the sales forecast

To find the requested forecast, you must replace it with the rank of the requested period, i.e. rank 6:

y = (512 × 6) + 3

y = 6

So the forecast turnover N is €6.