Mathematical Model and Correlation Analysis in Business Analytics

MODULE: BUSINESS
ANALYTIC

TABLE OF CONTENTS
INTRODUCTION...........................................................................................................................1
MAIN BODY...................................................................................................................................1
QUESTION- 1.................................................................................................................................1
a) Mathematical model................................................................................................................1
b) i) Calculation of the profit or loss............................................................................................2
ii) Five year projections...............................................................................................................2
c) Costing and the revenue behaviour..........................................................................................2
QUESTION- 2.................................................................................................................................3
a) Correlation coefficient of the advertising and sales in the company.......................................3
b) Scatter diagram of the data showing the relationship between the two variables...................4
c) Critical analysis of the impact of the advertising expenditure on the sales of the company...4
QUESTION- 3.................................................................................................................................5
a) Calculation of the break-even point and the margin of safety.................................................7
b) Reasons for the adoption of the original plan or amending it as per the Production and the
Marketing manager......................................................................................................................9
c) Other factors that should be considered by the management before committing the any
action for the business..................................................................................................................9
d) Benefits and limitation of the break-even model and its application in the marginal costing
and formulation of the business strategy...................................................................................10
CONCLUSION..............................................................................................................................11
REFERENCES..............................................................................................................................13

INTRODUCTION
In order to make the several decisions in the business has to use the various techniques
like the decision tree, break-even analysis, correlation coefficients etc. to study the relationship
of the various variables. It shows how one of the variables shall be impacting the other and
accordingly the business shall form the business strategy to obtain profitability and growth in the
market. The current project shall be analysing upon the different practical problems and seeking
their solutions to find out the results and what can be inferred by the management and
accordingly how will they perform the further business strategies in the business to perform
effectively. The report shall be containing the description of the mathematical model and the
correlation analysis of the two variables wherein the company shall be finding out the
relationship of the various variables that are functioning in the company and accordingly the
growth strategies shall be defined in the business. Apart from that it shall even highlight the
break-even analysis of the company showing the optimum level of the sales that the company
needs to execute so that the profitability of the company can be maximized for the company. It
shall also reflect the change in the break-even point with the change in the strategies of the
business and accordingly the profitability shall be altered in the business.
MAIN BODY
QUESTION- 1
a) Mathematical model
Particulars Figures
Annual output 200000
Fixed cost 80000
Variable cost (per unit) 0.65
Sales price (per unit) 3
The mathematical model of the company represents that the total costs of the company
that shall be involving both the fixed and the variable elements. The fixed cost is determined in
totality and the variable costs of the company are per unit of the output that is generated in the
routine operations of the business. It can be ascertained that the mathematical model of the
company is Profit / Loss= Sales – Variable costs – Fixed costs, this can be applied to calculate
the various elements of the cost and the profits in the business.
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b) i) Calculation of the profit or loss
Particulars Amount (in £)
Sales 600000
Less: Variable cost 130000
Less: Fixed cost 80000
Profit or loss 390000
Through the above information that is provided to the company it can be ascertained that
the company is producing the profitability of 390000 by selling the annual output of 200000
units at the selling price of 3 per unit. In this 0.65 per unit is attributable to the variable costs of
the product and the remaining costs are attributed to the fixed costs of the product.
ii) Five year projections
2021 2022 2023 2024 2025 2026
Annual output 200000 220000 242000 266200 292820
32210
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Variable cost (per
unit) 0.65 0.69 0.73 0.77 0.82 0.87
Sales price (per
unit) 3 3.15 3.31 3.47 3.65 3.83
Particulars 2022 2023 2024 2025 2026
Sales 693000 800415 924479 1067774 1233279
Less: Variable cost 151580 176742 206081 240291 280179
Less: Fixed cost 80000 80000 80000 80000 80000
Profit or loss 461420 543673 638398 747483 873099
The above table shows the future projections from the year 2022 to 2026 and these are
showing the increasing trend in the sales and the profitability of the company. From this it can be
assessed that the company shall be having the positive financial and the liquidity position of the
company that shall be leading to the growth prospects of the business (Kimmel, Weygandt and
Kieso, 2018). It can also be known that the company is capturing the market share in each of the
subsequent years as it is selling the higher number of the products.
c) Costing and the revenue behaviour
From the above projections it can be assessed that the in the company with the increase in
the costs of the company the revenues and the profitability of the company are also increasing
keeping the fixed element of the costs constant. The proportionate change are different as with
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