Quantitative Methods and Financial Maths Project, S1 2020, MAT10706

This project assignment analyzes quantitative methods and financial maths, focusing on revenue and cost functions of different products. The assignment examines break-even points, profit analysis, and the impact of fixed and variable costs. The first question involves comparing the profitability of three dog products, analyzing their revenue and cost functions to determine break-even points and the optimal number of units to sell. The second question explores the impact of GST removal on an airline's revenue, pricing, and quantity sold. The analysis includes the percentage of GST savings passed on to customers, and the assumptions made in this context. The project provides a detailed understanding of financial calculations and their implications in a business context, including the effects of taxation on profitability and pricing strategies. The solution also includes the student's analysis of how the company can maximize its profits by making changes in its pricing strategies. The student made a critical analysis of the problem and provided insights into the company's profitability.

Running head: QUANTITATIVE METHODS AND FINANCIAL MATHS
Quantitative Methods and Financial Maths
Name of the Student
Name of the University
Author Note

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QUANTITATIVE METHODS AND FINANCIAL MATHS
Table of Contents
Question 1....................................................................................................................................2
Question 2....................................................................................................................................5
Bibliography.................................................................................................................................7

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QUANTITATIVE METHODS AND FINANCIAL MATHS
Question 1
1. The total revenue function and the total cost functions of the three products are as
follows:
Particulars Dog 1 Dog 2 Dog 3
Selling Price of a dog 75 90 120
Revenue earned from a dog 75x 90x 120x
Where x is the number of dogs sold by the
business
Cost function of a dog (34.5+9)x
+625
(42+13)x
+625
(59+25)x
+625
Where x is the number of dogs sold and
625 is the fixed cost of
making a dog

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QUANTITATIVE METHODS AND FINANCIAL MATHS
10 15 20 25
0
200
400
600
800
1000
1200
1400
1600
1800
2000
Dog 1
Revenue Cost function
15 18 21 24
0
500
1000
1500
2000
2500
Dog 2
Revenue Cost function

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QUANTITATIVE METHODS AND FINANCIAL MATHS
15 16 17 18
1600
1700
1800
1900
2000
2100
2200
Dog 3
Revenue Cost function
2.
The intersection points between the costs and revenue
functions
20 18 17
for both the dogs are as follows
3.
Profit when the number of dogs sold is x 75x-
(43.5x)-625
90x-55x-
625
120x-
84x-625
Break-even point for each dog 20 31 39
4. From the above analysis, it is evident that the cost of production is highest in case of Dog 3.
The breakeven point for this product is also the highest due to this reason. Hence, in order to

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QUANTITATIVE METHODS AND FINANCIAL MATHS
make profits from Dog 3, the company needs to sell this product more. Similarly, the breakeven
for Dog 1 is very low as the costs of the product are very low. Other reasons for the differences
in the costs of the product include the variable expenditure incurred on the products. Apart from
these, the revenue functions and the cost functions of the products converge at 20 Units for Dog
1, 18 Units for Dog 2 and 17 Units for Dog 3. The profits are obtained after deducting the costs
from the revenue generated from the products. The fixed cost, however, remains constant for all
the products. These costs need to be recovered for the product to break even.
Question 2
Before GST removal After GST removal Difference
Equilibrium quantity 14 12 2
Equilibrium price 114 103 11
Percentage of GST
saving passed onto
customers
9.7% of savings is passed on
to customers from the GST
savings made by the entity.
Revenue airline
receives 1596
1239 256
Revenue airline
receives if it passes on
ALL of GST saving 1450 1125
325
7.
a) The removal of GST results in an increase in the profits available with the entity. Hence,
this would result in a decrease in its prices and also a reduction in the quantity sold by it. There is
also a decline in the revenue due to these price changes. Hence, it can be said that the business
will earn lower revenues due to the removal of GST. However, as the GST is changing, the
company needs to transfer all of its revenues to the external parties to ensure that they profit
from the same.

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QUANTITATIVE METHODS AND FINANCIAL MATHS
b) The company is passing on around 9.7% of the total savings made by it in the form of GST
savings. This is because of the differences in the price level of the entity due to the changes
occurring in the GST. If the company passed on all of its savings, then there would be a
significant reduction in the prices paid by the consumers and there would be a significant
increase in the consumer surplus.
c) The assumptions made in this regard are that the changes in the price levels is the surplus
passed on to the consumers. Hence, it is expected that the reduction in the price levels will
benefit the consumers. Some of the assumptions include the revenue of the entity being constant
at all times without any changes occurring due to the changes in the market conditions. It is also
assumed that the level of capacity of the airlines will remain constant at all times. Other
assumptions include the company passing on all of its savings which may or may not happen in
the real life world.

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QUANTITATIVE METHODS AND FINANCIAL MATHS
Bibliography
Narasimhan, C., 2016. Breakeven Analysis. TC, 2, p.R3.
Vadrale, K.S. and Katti, V.P., 2018. Break-Even Point Analysis of Public and Private Banking
Business. Wealth: International Journal of Money, Banking & Finance, 7(3).