Business Analytics: Mathematical Models, Correlation Coefficient, and Marketing Tactics

This report covers the development of mathematical models for calculating profits and five-year projections, calculation of correlation coefficient and scatter diagram for examining advertisement expenditure, and critical analysis of the impact of advertising expenditure on sales with recommendations for relevant marketing tactics.

BUSINESS ANALYTICS.

Table of Contents
INTRODUCTION...........................................................................................................................3
MAIN BODY...................................................................................................................................3
Question 1....................................................................................................................................3
(d) Critical analysis of costing and revenue behaviour in general, in relation to DC Ltd...........5
Question 2....................................................................................................................................7
(a) Calculation of correlation coefficient between advertising and sales of Nice Wear Ltd.......7
(b) Scattered diagram of the data and comment on the relationship between advertisement and
......................................................................................................................................................8
sales variable................................................................................................................................8
(c) Critical analysis of impact of advertising expenditure on sales and recommendation of
relevant marketing tactics............................................................................................................8
Question no. 3..................................................................................................................................9
1) Determine the following for Basu Plc.........................................................................................9
Conclusion ......................................................................................................................13

INTRODUCTION
The term business analytics is referred to processing all the historical data of the
company in order to evaluate the patterns and the roots that the company is following in its past
performance. Business analytics also helps company to take right decisions that will improve the
performance of the company (Maheshwari, Maheshwari and Maheshwari, 2021). Business
analysis also improves operational efficiency of the business. The report below will include the
mathematical models for calculating profits of the company and five-year projection. Moreover,
report will also include calculation of correlation coefficient scatter diagram for examining
advertisement expenditure that company is doing on its sales department. At last, the break even
analysis and projected sales has been show with benefits and the limitations of the break-even
analysis.
MAIN BODY
Question 1.
a) Development of mathematical model using the cost information
Total cost = 110000 + 490000
Total cost = £ 600000
Fixed cost = £ 110000
Variable cost = 700000 * 0.70
Variable cost = £ 490000
Unit variable cost = £ 0.70
Quantity produced = 700000 units
(b) Calculation of the profit and loss of DC Ltd assuming all the outputs are sold
Particulars. Amount.
Sales. (700000 * 3.50 ) 2450000
(-) variable cost (700000 * 0.70) 490000

contribution 1960000
(-) fixed costs 110000
Profit. 1850000
The net income earned by the company DC Ltd. If all the outputs of 700000 were sold is
£1850000.
c) Developing graph of five-year projection considering 5% increase in unit variable cost, 10%
increase in total output and 3% increase in unit sales price.
Particulars. 2023 2024 2025 2026 2027
Unit variable
cost.
0.70 * 105 %
= 0.73
0.73 * 105 %
= 0.77
0.77 * 105 %
= 0.81
0.81 * 105 %
= 0.85
0.85 * 105 %
= 0.89
Unit sales
price.
3.50 * 103 %
= 3.60
3.60 * 103 %
= 3.71
3.71 * 103 %
= 3.82
3.82 * 103 %
= 3.93
3.93 * 103 %
= 4.17
Total output. 700000 *
110% =
770000
770000 *
110% =
847000
847000 *
110% =
931700
931700 *
110% =
1024870
1024870 *
110% =
1127357
Particulars. 2023 2024 2025 2026 2027
Sales revenue 2772000 3142370 3559094 4027739 4701079
(-) variable
cost
562100 652190 754677 871140 1003348
Contribution 2209900 2490180 2804417 3156599 4597731
(-) fixed cost 110000 110000 110000 110000 110000
Net income /
loss
2099900 2380810 2694417 3046599 4487731

(d) Critical analysis of costing and revenue behaviour in general, in relation to DC Ltd.
Cost behaviour is basically the measure or the ways how the costs particularly behave at
a specific stage in an organization within a specific duration. The revenue behaviour also states
the ways through which the revenue or the sales of the company particularly increase or decrease
after the change in the overall production throughout the years. In this specific case the costs
fixed costs are obviously the same all through the duration as whatever the number that are
produced change the cost particularly remains the same. This is only the case of fixed cost in
particular. When it comes to variable costs these are the costs that specifically change as the
units that are being produced change. Which means if the number of units that are produced
increase the variable cost will also increase.
This will further change the overall cost of goods sold in total which will further increase
the sales price of the units that are being produced too. As per the question that has been asked,
the number of the units that are sold in the year 2022 are 700000 units. Every unit is sold on the
selling price of 3.50 euros per unit. In accordance to that the income statement is prepared and
the variable costs are also given or stated to be 0.70 euros per unit. As the number of units will
increase the variable cost and the overall sales revenue earned by the company will also increase
or change in particular. The fixed cost that is incurred in the overall procedure is constant

throughout all the years whose net income or loss is particularly estimated in the above tables in
accordance to the rate of change as per the question that is provided in particular. The statement
further states that as the variable cost to be incurred on the production or the procedure of
manufacturing is increased by 5 % each year, the total selling price will also increase by 3 % per
unit every year until the next five years whose income statement is prepared further after the
examination above.
The major understanding is that as the selling price of each product is increased by 3 %
the overall annual output will also increase by the 10 % in particular. As the overall output in the
beginning of the year 2023 is considered to be 770000 after its 10 % increase in accordance to
the production done in the year of 2022. Further, in the year 2024, again the overall annual
output of the products that are produced by the organization or the company in particular are
increased by 10 % each year. Like for the year 2025 further there is an increase of 10 % in the
value of the output of the year 2024 in particular. A net income of 1850000 euros is particularly
earned in the year 2022. Due to change in the overall variable cost which will further change the
total costs and further the selling price the profit is also impacted in a manner which is
considered to be very relevant.
This is mainly due to changes in the major factors that impact or affect the overall
evaluation as well as calculation of the profits or the revenues earned or the losses incurred by
the businesses in particular. But, there is a change in the overall annual outcome of the
organization too. This change is counted to be 10 %. Which means the number of products sold
by the company increase by each of the passing year. This basically does not hinder the profit
generation in a manner that is negative then. Which means the profit is increasing and the change
in the profits or the net income that is generated by the company will be positive if the working
of the company is in accordance to the plan they particularly have prepared.
The net income earned by the company is calculated to be 1850000 with a variable cost
of 490000 and a fixed cost of 110000. In the next year the profit that is generated is 2099900
with a variable cost of 562100 which basically means that if the variable cost have increased
with a rate of 5 % then the profits or the net income of the company has increased by the rate of
12 % per annum. And the similar rate is implied in the further years too. Every year as the
variable cost per unit is increased by 5 % and the selling price per unit is increased by 3 % the
overall income that is generated by the company DC Ltd. Is increased by the rate of 12 %. this is

majorly how the revenues or the overall income is behaving due to change in costs throughout
the years.
Question 2.
(a) Calculation of correlation coefficient between advertising and sales of Nice Wear Ltd.
Year. Advertising
expenditure
(X) (£000s)
Sales revenue
(Y) (£000s)
XY X^2 Y^2
2017 2 80 160 4 6400
2018 5 100 500 25 10000
2019 4 70 280 16 4900
2020 6 120 720 36 14400
2021 3 60 180 9 3600
Σ 20 430 1840 90 39300
Coefficient of correlation = (n * Σ XY – ΣX * ΣY) / √ [n * Σ X^2 (Σ X) ^ 2] [n * Σ Y ^2 – (ΣY)
^2]
5 * 1840 – 20 * 430 / √ [ 5 * 90 * (20) ^2 ] [ 5 * 39300 – (430 ^2]
(9200 – 8600) / √ 50 * 11600
600 / √ 580000
600 / 761.577
Coefficient of correlation = 0.79
As the table that has been prepared above and the solution that has been generated or
calculated in particular, it is stated that the coefficient of the correlation is 0. 79. Which basically
means that the percentage of the sales and the advertising expenditure of the company is related
to each other with a rate of 79 % in particular. And also the answer is attained in to be positive.
Which basically states that the advertising expenditure as well as the sales revenue have a
positive strong relation with each other. Therefore, when the advertising expenditure incurred by
the company will increase the sales revenue that is earned by the company will also increase

(THAKURI, 2022). The pace of increase will also be similar as they share a strong relationship
with each other. Then, at the time of decrease in the amount of the advertising expenditure the
sales revenue of the company will also decrease, due to their positive relation as well. This
means that the change in the advertising expenditure will bring change in the sales revenue as
well, because the sales revenue is the dependant aspect which is depending upon the independent
aspect of advertising expenditure in particular. This is how the major changes will occur in the
overall expenditure and the revenue that is being generated.
(b) Scattered diagram of the data and comment on the relationship between advertisement and
sales variable
After analysing the scatter diagram above it has been found that there is existed direct
relationship between the advertisement and the sale of the company (Deutsch and et.al., 2018).
The more company spends on its advertisement cost through various methods of selling, the
company will be going to earn more profit. Generally there are two types of relationship positive
and the negative and this diagram has cleared that here positive relationship exist between
dependent and the independent variables (Ndaliman, and Bala 2017)

(c) Critical analysis of impact of advertising expenditure on sales and recommendation of
relevant marketing tactics.
Advertisement simply means to promote products of the company by various marketing
techniques. The marketing helps to form brand image of the company, there exist direct
relationship between the expenses of advertisement and the revenues that company earn in the
market. Advertisement is done through both online and offline medium but today online medium
is becoming popular (Ishikar and et.al., 2020). With the raising online users companies are trying
to shift from regular traditional method of marketing to online sources. It creates drive in minds
of people to purchase products of the company no matter whether products are useful or not.
Companies have separate department names as the marketing department. Marketing department
of the company focuses on managing the affairs related to the marketing at the same time the
duty of marketing department is also to create hype of the products (Kapoor and Kapoor,
2020).
Recommendation of marketing tactics-
There are various marketing techniques that company can use in order to promote its product to
raise its revenue. The marketing techniques such as blogging, social media sites, advertisement
in newspaper through both online and offline mode of the marketing will help company to
perform better. The mode of marketing must be followed according to the company. Company
chooses its own method and also establishes channels that will make company to reach better.
The tactics are important in order to reach the higher level of success. Further, all techniques will
be beneficial for creating good brand image of the company. The marketing tactics will benefit
company for sure. It is highly recommended that the company should choose online method of
marketing rather than the offline as online marketing has been recently getting lot of attention as
youth is getting influenced by the things that are been selling on such marketing platforms. Other
than this company can also focus on creating the demands of the product through influencer
marketing which also has gain attention and hype in recent years. Both these tactics will be
befitting company. The marketing ultimately builds brand image and consumer base for the
company that in turn gives higher profits to the company (Ullal and Hawaldar, 2018).

Question no. 3
1) Determine the following for Basu Plc.
Selling price 600×640= 384000
Variable costs:
Labour 200 ×640 = 128000
Materials 40 ×640 = 25600
Selling 10 ×640 = 6400
Contribution 224000
Determine the following for Basu Plc.
Break even point in terms of number of programs sold.
Break even point= fixed cost/ contribution per unit
Fixed cost = 80000+60000 = 140000 = 140000/350= 400
Contribution per unit= 224000/640= 350
The break-even point of the company simply refers to the point when company is in condition of
no profit and no loss. Break-even point will be achieved by the Basu limited when company
sales 400 units. The 400 units is point where company will earn no profit but will recover all its
variable cost.
Margin of safety-=
Projected sales- break even Sales
640-400= 240
Margin of safety Is referred to all the sales that company does after its break even sales.
Basu limited will earn profit after achieving its break- even point of 400. Out of total sale of 640
units, company will attain margin of safety after 400 units that it 240 units in the scenario above
(Aryani 2022).

2) The company’s target profit for the year is £56000, Will the estimated sales volume be
sufficient to achieve this. By how much will profit from the estimated sales volume exceed or
fall short of the target profit.
Target profit= 560000
Fixed cost+ desired profit/ contribution per unit* selling price
56000+140000/ 350 = 560 units
To target profit of 56000, the company has to sale 560 units. The 560 units will be
recovering all the variable cost that has been done in order to make profits, further it will be
covering fixed cost and will give company profit for 56000.
4)Prepare a break even chart for Basu Ltd. showing clearly the Breakeven point and margin of
safety.
units
variable
cost
fixed
cost
total
cost revenues
600 150000 140000 290000 350000
500 125000 140000 265000 320000
400 100000 140000 240000 240000
350 87500 140000 227500 220000
300 75000 140000 215000 200000
250 62500 140000 202500 180000
From the analysis of break-even point it is clear that it helps company to understand and
evaluates company performs in the market (Kampf, Majerčák and Švagr, 2016). This break-even
analysis makes company profitable and at the same time it helps company to take better decision

for their organization. The most important advantage of finding break-even point is that it helps
to formulate right price for their products that in turn can higher margin of safety by reducing
risk in the market. The risk must be avoided to run company in long run and margin of safety
means profits after the break-even analysis brings that to the company.
5) Critically analyse the benefits and limitations of the break-even model.
The break- even point is the point where company the total cost and the total revenues of the
company are same (Sinambela and et.al., 2022). There is neither profit nor loss to the company.
The benefits of using the break- even model is as follows-
1. The first and most important benefit of using such analysis is to understand how many
units is needed to be sold in order to achieve require amount of profit. This also indicates
whether product is worth selling in market..
2. The next important benefit is that it helps company to form strategy for funding. The
funding channels are mostly keen towards the profits that the company will make in the
future.
3. It also helps company to reduce risk by guiding product line towards the required profit
of the company and also in order to make product successful in the market.
4. The proper pricing strategy can be formulated for ensuring the required amount of profit
from the market (Barletta, Despeisse and Johansson, 2018).
The limitation of break- even model is as follows-
1. Break- even analysis only work in the condition when there is clear difference between
all the fixed cost and the variable cost. However, to make such distinction is quite
difficult ((Ndaliman and Bala 2017).
2. The another problem related is that making assumption that the selling price remains
same in all the revenue line but this is not the case. It changes in different countries that is
not counted.
3. This has also been proven that it is insufficient in various sector such as the shipbuilding.

4. The quantity of capital used in the firm is also not taken into account while doing break-
even analysis.
5. Fixed cost is assumed to be constant at all the levels of activity which if further not true
every-time.
The break-even point has own limitations and the advantages that can be used by company in the
favour of company. For the given case above the break-even point was realized at 400 units but
companies made further units to gain margin of safety that can give company a compeitive
advantage.
CONClUSION
In this report in particular there are three major questions that are being discussed in a manner
that is suitable and the most appropriate calculations are being done. In the first question the net
income of the given data or the information is being calculated in particular and the budgeted
income of the next five years is calculated and the data regarding the changes that have occurred
in the variable costs, the fixed costs and the overall sales has been given in the report. In the next
question the coefficient of the correlation has been calculated and in accordance to that the
relationship between the overall advertising expenditure and the sales revenue has been
determined in the report above in particular. In the third question break even point has been
determined and the margin of safety is also determined in particular. The report gives an analysis
about all the things in a manner that is evaluative. Along with this report, also calculate
correlation coefficient, an scatter diagram of data, and also critical analysis impact of advertising
expenditure as well as company gain competitive advantage in designer clothing industry.
Moreover, the report also determine the break even point , marginal of safety of the company.
Furthermore, determine projected sales, and also critically analyse benefits as well as limitations
of the break even model.

References
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