FIN4006 Business Maths Assignment: Algebra, Forecasting Techniques

This document presents a detailed solution to a Business Maths assignment, addressing various aspects of algebra and its application in financial decision-making. The assignment covers topics such as solving algebraic equations, calculating markup and margin, understanding simple and compound interest, and applying forecasting techniques like moving averages. It also includes probability calculations, expected value analysis, payback period, net present value (NPV), and internal rate of return (IRR) for investment decisions. Furthermore, the solution provides correlation analysis between complaints and sales/orders, along with a discussion on the weaknesses of correlation analysis. Desklib provides a platform to explore similar solved assignments and access AI-powered study tools for students.

Business Maths

Table of Contents
QUESTION 1:.................................................................................................................................2
QUESTION 2:.................................................................................................................................3
QUESTION 3..................................................................................................................................5
QUESTION 4..................................................................................................................................7
QUESTION 5..................................................................................................................................9
b) Briefly discuss the weaknesses of correlation analysis:.......................................................12
REFERENCES..............................................................................................................................13
1

QUESTION 1:
Answer each question part, showing your step-by-step workings to reach the conclusion.
[(x+11)/2] + [(x+8)/3] = 190, find x.
Sol- [(x+11)/2] + [(x+8)/3] = 190
⇒ 3×(x+11) + 2×(x+8) = 190×6
⇒ 3x+33+2x+16 = 1140
⇒ 5x+49 = 1140
⇒ 5x = 1091
⇒ x= 218.2
[(2y+7)/3] + [(y+5)/4] = 150, find y to 1 decimal point.
Sol- [(2y+7)/3] + [(y+5)/4] = 150
⇒ 4×(2y+7) +3×(y+5) = 150×12
⇒ 8y+28+3y+15 = 1800
⇒ 11y+43 = 1800
⇒ 11y = 1757
⇒ y = 159.7
[(3z+5)/2] + [(z-9)/4] = 900, find z to nearest whole number.
Sol- [(3z+5)/2] + [(z-9)/4] = 900
⇒ 2×(3z+5) + (z-9) = 900
⇒ 6z+10+z-9 = 900
⇒ 7z+1 = 900
⇒ 7z = 899
⇒ z = 128.43
⸫ z ≈ 128
(x/3) + (6/3) = (x/9) + (1/9), find x and present answer as a fraction.
Sol- (x/3) + (6/3) = (x/9) + (1/9)
⇒ (x/3) + 2 = (x/9) + (1/9)
2

⇒ (x/3) - (x/9) = (1/9) - 2
⇒ (3x-x)/9 = (1-18)/9
⇒ 2x = -17 ( Denominator gets cancelled from both the⸪
sides)
x = -17/2⸫
(2v+20)/4 = (v-6)/6, find v.
Sol- (2v+20)/4 = (v-6)/6
⇒ 6×(2v+20) = 4×(v-6)
⇒ 12v+120 = 4v-24
⇒ 8v = -144
v = -18⸫
QUESTION 2:
A)
Use basic principles of Algebra and apply mathematical skills to finance decisions.
Definitions and business uses of calculating mark-up and margin? Please use
academic sources.
GBP
Sales Revenue 168,500
Purchases 128,500
Gross Profit 40,000
Selling Expenses 20,500
Admin Cost 7,500
Operating Profit 12,000
Sol- Mark-up can be defined as the total profit earned on selling a specific service or
commodity. It is calculated by keeping the cost price of the article as base for the
calculations.
Some of the business uses of calculating mark-up are stated below-
Utilizing mark-up gives businesses and individuals an opportunity to make profit. The
larger the gap between cost price and marked price, the more profit a sale is expected to
yield.
3

With an excellent mark-up strategy, businesses can sell their products at competitive
prices which, in turn, helps in maximizing sales. Mark-up pricing strategy is the go-to strategy
for businesses to price products in an efficient and fast manner.
Margin is defined as the difference between expenses and revenue generated by offering a
particular product or service. In other words, the sales of a product or service minus the costs of
products and good sold gives margin as the outcome.
Some of the business uses of calculating margin are-
Profit margin is generally calculated to get an idea of profitability that is expected for a certain
period of time. In order to remain fiscally healthy, businesses must pay close attention to
margins, specifically, profit margins.
Margins help in getting an overview of how a particular business is performing. By studying
margin calculations closely, businesses will be able to point out areas where they are struggling
and improvement is needed.
B)
Calculate mark-up (in percentage to nearest whole number).
Sol- Mark-up = selling price - cost
= Sales Revenue - (Purchases + Selling Expenses +
Admin Cost)
= 168,500 – (128,500 +20,500+7,500)
= £12,000
C)
Calculate the margin as a % to 2 decimal places.
Sol- Margin percentage = a% = (Gross profit/ Revenue) × 100
= (40,000/168,500) × 100
= 23.74
E)
Define the following and provide respective examples using academic sources.
Simple interest, Compound interest, Trade discount.
4

Sol- Simple Interest- It is a method to calculate the interest that is charged on a principal
amount or loan. The interest rate for SI is only applied on the principal amount and not on
periodic interest payments.
For example, John borrowed £50,000 for 3 years at the rate of 3.5% per annum. The
simple interest in this case will be calculated as-
SI = (Principal amount × rate × time)/100
= (50,000×3.5×3)/100
= £5250
Compound Interest- Compound interest is defined as the interest charged on a principal
amount plus the additional accumulated interest.
For example, John borrowed a sum of £50,000 for 3 years at the rate of 3.5% per annum
compounded annually. The compound interest in this case will be calculated as-
CI = Principal× [1+ (r/100)] ^t – Principal where, r = rate, t = time
= 50,000 × [1+(3.5)/100] ^3 – 50,000
= 50,000×1.11-50,000
= £5500
QUESTION 3
a)
Month Houses Sold 3 – Point Moving
Average
Jan 38100
Feb 36900 38066.66
March 39200 38966.66
Apr 40800 39766.66
May 39300 39600
June 38700 39133.33
July 39400 41233.33
Aug 45600 43833.33
Sep 46500 46066.66
5

Oct 46100 42400
Nov 43900 45500
Dec 37200 42400
Three point moving averages
(38100 + 36900 + 39200) / 3 = 114200 / 3 = 38066.66
(36900 + 39200 + 40800) / 3 = 116900 / 3 = 38966.66
(39200 + 40800 + 39300) / 3 = 119300 / 3 = 39766.66
(40800 + 39300 + 38700) / 3 = 118800 / 3 = 39600
(39300 + 38700 + 39400) / 3 = 117400 / 3 = 39133.33
(38700 + 39400 + 45600) / 3 = 123700 / 3 = 41233.33
(39400 + 45600 + 46500) / 3 = 131500 / 3 = 43833.33
(45600 + 46500 + 46100) / 3 = 138200 / 3 = 46066.66
(46500 + 46100 + 43900) / 3 = 136500 / 3 = 45500
(46100 + 43900 + 37200) / 3 = 127200 / 3 = 42400
b)
(1 / 9) x - 19000 = 0
1 / 9 x = 19000
X = 19000 * 9
X = $ 171,000
c)
Probability of coming 1st = 1/20
Probability of coming 2nd = 1/10
Probability of coming 3rd = 1/4
Probability of wining = 1/20 + 1/10 + 1/4
= (1 + 2 + 5) / 20
= 8 / 20 = 2 / 5
Yes, it is worth entering the race.
d) Expected Value = 0.35 (-30000) + 0.40 (0) + 0.25 (55000)
6

= -10500 + 0 + 13750
= $ 3250
The project should be proceeded.
e) Expected Value = 0.75 * 135,000 – 0.25 * 88000
= 101250 – 22000
= $ 79250
The plan should be executed because the expected value of return is $ 79250, which is positive.
QUESTION 4
a)
PAYBACK PERIOD Cash Inflows
PRODUCT A cumulative
PRODUCT
B
cumulativ
e
Initial investment 450000 450000
1 72000 72000 36000 36000
2 72000 144000 76000 112000
3 132000 276000 156000 268000
4 252000 408000 190000 458000
PRODUCT A 174000 0.69047619 3.7yrs
PRODUCT B 182000 0.957894737 3.9yrs
b)
NPV Cash Inflows Initial investment 450000
Year PRODUCT A NPV rate @5% PV
£
1 72000 0.893 64285.714
7

2 72000 0.797 57397.959
3 132000 0.712 93954.993
4 252000 0.636 160150.556
Total discounted cash inflows Total PV 375789.222
Less: Initial investment 450000
NPV 74210.778
NPV Cash Inflows Initial investment 450000
Year PRODUCT B NPV rate @5% PV
£
1 36000 0.952 34285.714
2 76000 0.907 68934.240
3 156000 0.864 134758.665
4 190000 0.823 156313.470
Total discounted cash inflows Total PV 394292.090
Less: Initial investment 450000
NPV 55707.910
From the above results it can be said that the net present value of Product A is more
viable for investment for the company as it has higher net present value in comparison to the
Product B. NPV is the current value of the future stream of payment from the company for the
project or investment.
c) From the above findings it can be said that the product A needs to be taken as it is able to gain
the returns faster than product B. This means that the business is going to be in profit by
investing in product A in comparison to that of the product B. The focus of the organization has
to be on the ways in which they are going to be able to gather the success that is required.
Investing in products that gets the business with quicker returns is going to help the organization
be more sustainabile.
d)
IRR
Year
PRODUCT
A Cumulative
Cumulativ
e
-450000 4% -450000 18% -450000
8

1 72000
0.96153846
2
69230.7692
3
0.8528
7
61406.618
4
2 72000
0.92455621
3
66568.0473
4
0.8581
1
61783.646
9
3 132000
0.88899635
9
117347.519
3
0.8631
7
113938.65
5
4 252000
0.85480419
1
215410.656
1
0.8680
7
218753.74
6
IRR 5% 1% 0%
e)
Advantages and disadvantages of IRR are,
Advantages Disadvantages
It helps in finding the time value of money
that is considered to be very essential for the
management of the capital budgeting
methods.
It is said to ignore the size of the project that
helps in the gathering of resources that is
required for the management of the
operations.
It is very simple for the development is can be
easy to use and understood for the
practitioners.
The future costs of the projects are ignored
for this capital budgeting tool this makes it
inaccurate.
Advantages and disadvantages of Payback period are
Advantages Disadvantages
The formula of the payback period is very
easy and simple and can be easy to calculate.
It does not considered the time value of the
money and is said to less applicable in the
practicality.
It allows to evaluate the project very quickly
hence is considered to be very effective in the
management of the operations.
It also fails to consider the inflow of the cash
after the payback period.
9

QUESTION 5
a)
Correlation between complaints and sales
S.N
x (No.
Customer
Complaints)
Y
(Sales
£ks) XY X^2 Y^2
1 184 800 147200 33856 640000
2 144 880 126720 20736 774400
3 56 1120 62720 3136 1254400
4 56 1360 76160 3136 1849600
5 48 1280 61440 2304 1638400
6 40 2720 108800 1600 7398400
7 56 18040 1010240 3136 325441600
8 48 1280 61440 2304 1638400
9 56 960 53760 3136 921600
10 56 960 53760 3136 921600
11 72 880 63360 5184 774400
12 160 1200 192000 25600 1440000
Total 976 31480 2017600 107264 344692800
Formula= n(Σxy)- (Σx)(Σy)/ √n [(Σ x2)-(Σ x)2][ n [(Σ y2)-(Σ y)2]
r 12(2017600)-(976)(31480)/√[12(107264)-952576][12(344692800)-
990990400]
12(2017600-30724480)/ √12(107264)-952576][12(344692800)-
990990400]
(24211200-30724480)/ √[1287168-952576][4136313600-990990400]
(24211200-30724480)/ √(334592)(3145323200)
10

(24211200-30724480)/32440714.85
-6513280/32440714.85
r -0.20
Correlation between complaints and orders
S.N
x (No.
Customer
Complaints) Y (Orders) XY X^2 Y^2
1 184 8 1472 33856 64
2 144 12 1728 20736 144
3 56 10.4 582.4 3136 108.16
4 56 12 672 3136 144
5 48 11.2 537.6 2304 125.44
6 40 16 640 1600 256
7 56 16 896 3136 256
8 48 12 576 2304 144
9 56 9.6 537.6 3136 92.16
10 56 8.8 492.8 3136 77.44
11 72 8 576 5184 64
12 160 12 1920 25600 144
11