Introduction to Mathematics and Statistics for Business Finance

This assignment delves into the application of mathematical and statistical concepts within a business context. It begins with a Linear Programming Problem (LPP) analysis, examining resource allocation. The assignment then progresses to financial calculations, including mortgage payments and the impact of interest rate changes. A significant portion is dedicated to investment appraisal methods, comparing payback period, average rate of return (ARR), net present value (NPV), and internal rate of return (IRR) to evaluate investment options. Statistical analysis is also employed, summarizing data and calculating confidence intervals to assess the significance of various values. The assignment covers a range of financial and statistical techniques to provide a comprehensive overview of business finance.

INTRODUCTION TO MATHEMATICS AND STATISTICS
FOR BUSINESS

TABLE OF CONTENTS
Question 1....................................................................................................................................................................................................3
1 LPP.......................................................................................................................................................................................................3
Question 2....................................................................................................................................................................................................4
1 Monthly payment of John.....................................................................................................................................................................4
2 Impact on John monthly payment due to increase in rate by BOE up to 4%.......................................................................................4
3 Time taken by John to make payment..................................................................................................................................................5
Question 3....................................................................................................................................................................................................7
(a)Discuss and compare a different investment appraisal methods and their merits as well as demerits...............................................9
(b and c) Selection of project and recommendation..............................................................................................................................10
(d) Evaluation of option c......................................................................................................................................................................10
Question 4..................................................................................................................................................................................................11
(a)Summary of data...............................................................................................................................................................................11
(b) Significant difference of values from 150........................................................................................................................................12
© Significant difference at value of 6000000........................................................................................................................................12
(d) Value at 98% confidence interval....................................................................................................................................................13

Question 1
1 LPP
Cell Name Cell Value Formula Status Slack
$C$23 Aluminum Basic 0 $C$23<=$C$27
Not
Binding 4000
$C$24 Other Metals Basic 0 $C$24<=$C$27
Not
Binding 4000
$C$25 Other Materials Basic 0 $C$25<=$C$27
Not
Binding 4000
$C$26 Labor Basic 0 $C$26<=$C$27
Not
Binding 4000
$D$23 Aluminum Medium 0 $D$23<=$D$27
Not
Binding 3500
$D$24 Other Metals Medium 0 $D$24<=$D$27
Not
Binding 3500
$D$25 Other Materials Medium 0 $D$25<=$D$27
Not
Binding 3500
$D$26 Labor Medium 0 $D$26<=$D$27
Not
Binding 3500
$E$23 Aluminum High 0 $E$23<=$E$27
Not
Binding 2000
$E$24 Other Metals High 0 $E$24<=$E$27
Not
Binding 2000
$E$25 Other Materials High 0 $E$25<=$E$27
Not
Binding 2000
$E$26 Labor High 0 $E$26<=$E$27
Not
Binding 2000
All products must be equally produced by the firm to make effective use of resources.

Question 2
1 Monthly payment of John
Table 1Monthly payment of installment
5th March 2009 0.50%
Mortgage rate 0.0042
Value of house 650000
75% value 487500
Mortgage year 25
Maximum limit for
payment 3200
n 300
Monthly payment of
installment 3796.049
Interpretation
Monthly payment of installment is £3796 and it exceed the maximum limit that is set by John according to the level up to
which he can afford to take debt. It can be said that John needs to pay mentioned amount to the lender.
2 Impact on John monthly payment due to increase in rate by BOE up to 4%
Table 2Impact on monthly payments with change in interest rate
1 2 3 4 5 6 7 8 9
5th March 2009 1.00% 2.00% 3.00% 4.00% 5.00% 6.00% 7.00% 8.00% 9.00%
Mortgage rate 0.0008 0.0017 0.0025 0.0033 0.0042 0.0050 0.0058 0.0067 0.0075
Value of house 650001 650002 650003 650004 650005 650006 650007 650008 650009
75% value 487500.8 487501.5 487502.3 487503 487503.8 487504.5 487505.3 487506 487506.8
Mortgage year 25 25 25 25 25 25 25 25 25

Maximum limit for
payment 3200 3200 3200 3200 3200 3200 3200 3200 3200
n 300 300 300 300 300 300 300 300 300
Monthly payment 2449.675 2755.062 3082.388 3430.961 3799.864 4187.998 4594.114 5016.867 5454.852
Table 3Quarterly payment of installment
1 2 3 4 5 6 7 8 9
816.5582 918.3539 1027.463 1143.654 1266.621 1395.999 1531.371 1672.289 1818.284
Interpretation
It can be seen from the table that with elevation in interest rate monthly payment amount increased. It can be observed that
John can make payment up to £3200 per month and accordingly one must take loan at interest rate up to 3% per annum. After 3%
John cannot take debt at more interest rate because its payment capacity allow it to make payment up to mentioned percentage.
3 Time taken by John to make payment
Years
Yearly payment
capacity
Cumulative
value Loan amount net amount
1 38400
2 38400 76800 650000 -573200
3 38400 115200 650000 -534800
4 38400 153600 650000 -496400
5 38400 192000 650000 -458000
6 38400 230400 650000 -419600
7 38400 268800 650000 -381200
8 38400 307200 650000 -342800

9 38400 345600 650000 -304400
10 38400 384000 650000 -266000
11 38400 422400 650000 -227600
12 38400 460800 650000 -189200
13 38400 499200 650000 -150800
14 38400 537600 650000 -112400
15 38400 576000 650000 -74000
16 38400 614400 650000 -35600
17 38400 652800 650000 2800
18 38400 691200 650000 41200
19 38400 729600 650000 79600
20 38400 768000 650000 118000
21 38400 806400 650000 156400
22 38400 844800 650000 194800
23 38400 883200 650000 233200
24 38400 921600 650000 271600
25 38400 960000 650000 310000
Interpretation
Time taken by John to make payment is 192 months because in the 16 years entire payment will be made by same which
means that 192 months (16*12) will be taken to pay entire debt amount.

Question 3
Table 4Calcualtion of payback period
Year
Option
A
Option
B
Option
c
Initial investment -1000 -7000 -1000
1 1000 0 300 -6700 1000 0
2 1500 2500 1500 -5200 1500 2500
3 1750 3250 3000 -2200 1750 3250
4 500 2250 3000 800 500 2250
5 3000 3800 250 750
6 3000 6800 750 1000
7 2700 9500 1250 2000
8 2000 11500 1250 2500
9 1500 13000 1250 2500
10 1000 14000 1250 2500
Table 5Calcualtion of ARR
Year
Option
A
Option
B
Option
c
Initial investment 1000 7000 1000
1 1000 300 1000
2 1500 1500 1500
3 1750 3000 1750
4 500 3000 500
5 0 3000 250

6 0 3000 750
7 0 2700 1250
8 0 2000 1250
9 0 1500 1250
10 0 1000 1250
Average 475 2100 1075
Total investment 1000 7000 7001
ARR 48% 30% 15%
Table 6Calculation of NPV
Year Option A Option B Option c
Initial investment 1000 7000 1000
1 1000 0.892857 892.8571 300 0.892857 267.8571 1000 0.892857 892.8571
2 1500 0.797194 1195.791 1500 0.797194 1195.791 1500 0.797194 1195.791
3 1750 0.71178 1245.615 3000 0.71178 2135.341 1750 0.71178 1245.615
4 500 0.635518 317.759 3000 0.635518 1906.554 500 0.635518 317.759
5 3000 0.567427 1702.281 250 0.567427 141.8567
6 3000 0.506631 1519.893 750 0.506631 379.9733
7 2700 0.452349 1221.343 1250 0.452349 565.4365
8 2000 0.403883 807.7665 1250 0.403883 504.854
9 1500 0.36061 540.915 1250 0.36061 450.7625
10 1000 0.321973 321.9732 1250 0.321973 402.4665
Total 3652.022 11619.71 6097.372

Average 913.0056 1161.971 609.7372
NPV 91% 17% 61%
Table 7Calcualtion of IRR
Year
Option
A
Option
B
Option
c
Initial investment -1000 -7000 -1000
1 1000 300 1000
2 1500 1500 1500
3 1750 3000 1750
4 500 3000 500
5 0 3000 250
6 0 3000 750
7 0 2700 1250
8 0 2000 1250
9 0 1500 1250
10 0 1000 1250
IRR 114% 4% 114%
(a)Discuss and compare a different investment appraisal methods and their merits as well as demerits
Some of different investment appraisal methods are as follows. Payback period: This is the method that is used to identify the duration which will be taken by the project to cover investment
value. Main merit of the payback period method is that calculation process is very simple. Demerit of the mentioned method is
that discount rate is not employed in calculation process. It can be said that there are both positive and negative sides of
mentioned method.

 Average rate of return: This method reflect the mean percentage that can be gained on the project. Positive point of ARR is
that average performance of proposal can be estimated by this method. Negative point is that present value of cash flows is not
computed. On comparison of both methods it can be said that both methods evaluate the project in different manner and
importance of both cannot be undermined. Net present value: Net present value indicate the value of project which is residual value after excluding initial investment
from the sum of present value of cash flows. Main merit of the NPV method is that concept of present value is used in same.
Negative point is that procedure followed for calculation is tough. NPV in comparison to ARR is considered better because by
using same project can be evaluated in better way. Internal rate of return: It is the method which indicate the real return that can be gained on the project. Its main positive point
is that it reflect the actual gain that can be made on the project. Limitation is that like NPV calculation is tough. In comparison
to payback period and ARR IRR is better method because it indicate the accurate picture of the project in terms of return.
(b and c) Selection of project and recommendation
On the basis of payback period option 1 is selected because it is indicating that project will cover investment in first year. Option
1 cover investment amount in one year in comparison to other one. This reflects that same is viable for the firm.
(d) Evaluation of option c
Investment can be made in the option C because from same for 10 years cash inflows can be generated by making same amount
of investment that is made in option A.

Question 4
(a)Summary of data
Table 8Calculation of descriptive statistics
Profit (£000s) Sales (£000s) Size (000s sq. ft.) Lines
Mean 43.53 Mean 554.995 Mean 2.655 Mean 141.45
Standard Error 5.603260799 Standard Error
46.9767963
3 Standard Error 0.309454103 Standard Error 8.615003742
Median 40.95 Median 574.1 Median 2.8 Median 146.5
Mode 40.8 Mode #N/A Mode 3.2 Mode 164
Standard
Deviation 25.05854408
Standard
Deviation
210.086619
9
Standard
Deviation 1.383920822
Standard
Deviation 38.52746799
Sample Variance 627.9306316 Sample Variance
44136.3878
7 Sample Variance 1.915236842 Sample Variance 1484.365789
Kurtosis
-
1.082036384 Kurtosis -0.31532157 Kurtosis
-
1.034702564 Kurtosis
-
0.463137853
Skewness 0.344628318 Skewness -0.36339445 Skewness
-
0.032622662 Skewness
-
0.446476803
Range 82.4 Range 753.4 Range 4.7 Range 131
Minimum 8.6 Minimum 147.5 Minimum 0.3 Minimum 69
Maximum 91 Maximum 900.9 Maximum 5 Maximum 200
Sum 870.6 Sum 11099.9 Sum 53.1 Sum 2829
Count 20 Count 20 Count 20 Count 20
Interpretation
Results indicate that on average basis firm is earning profit of 43.53 million in its business and sales of 554 million is made in
the business. Average size of the premises from where product sold is 2.655 and on average basis 141 product lines are sold in the
market from single store. Most of times profit of 40.8 is made by the firm in its business. In most of premises size is 3.2 and for lines

mode value is 164 which means that most of stores are selling 164 variety of product to the customers. Standard deviation is very high
in case of sales relative to lines and this means that sales value as well as products variety sold by firm are changing at moderate pace.
It can be said that sales made by different channel of distribution is different from each other.
(b) Significant difference of values from 150
Table 9Calculation of One way ANNOVA
SUMMARY
Groups Count Sum Average Variance
Column 1 20 2829 141.45 1484.366
Column 2 20 3000 150 0
ANOVA
Source of
Variation SS df MS F P-value F crit
Between Groups 731.025 1 731.025 0.984966 0.327254 4.098172
Within Groups 28202.95 38 742.1829
Total 28933.98 39
Interpretation
Value of level of significance is 0.32>0.05 and this reflects that there is no significant difference between mean value of the
variable. It be said that sales made by different channels vary significantly from standard value which is 150.
© Significant difference at value of 6000000
Table 10Calculation of ANNOVA
SUMMARY