Finance Test: Capital Investment, Data Analysis, and Sampling

This finance test solution covers several key areas of financial analysis and business statistics. Section A focuses on capital budgeting techniques, specifically the Net Present Value (NPV) method, providing calculations and advice to management based on the results. It also explores factors influencing investment decisions such as interest and inflation rates. Section A also includes a detailed explanation of various sampling methods, including simple random, systematic, stratified, cluster, and quota sampling, along with their respective advantages and disadvantages. The distinction between probability and non-probability sampling is also clarified. Section B delves into data analysis and presentation. It includes the calculation of mean, median, mode, and range for a given dataset, along with a discussion of the limitations of using the average for certain data types. The test further explores the most useful methods of data presentation, such as pie charts and bar graphs, with examples. Finally, the solution outlines mathematical tools for appraising capital investment decisions, including the Payback Period, Accounting Rate of Return, Net Present Value, and Internal Rate of Return (IRR) methods, with detailed calculations for IRR in two different projects.

Finance Test

Contents
Section A......................................................................................................................................................3
Section B......................................................................................................................................................4

Section A
Question 1
(a) NPV method:
Year
Cash
inflow
cash
outflo
w cash flow
PV
factor
discounted cash
flow
1 51000 55000 -4000
0.87719
3 -3508.77193
2 62000 56000 6000
0.76946
8 4616.805171
3 96000 61000 35000
0.67497
2 23624.00307
4 120000 60000 60000 0.59208 35524.81664
5 130000 61000 69000
0.51936
9 35836.43784
6 145000 68000 77000
0.45558
7 35080.16417
131173.455
NPV: Discounted cash flow-investment
= 131173.45-110000
= 21173.45
(b) Advice to management:
The above computed value of NPV is positive which is of 21173.45 and this will generate higher
return in upcoming time period.
© Factors affecting investment decisions:

Interest rate- The investment is either funded by existing savings or by loans. Investment thus
depends heavily on bond yields. Higher interest rate borrowing more costly. Rising interest rates
can provide a greater return from of the fact that the bank keeps money. Investing has a larger
economic cost with rising interest rates, as repayment of income is lost.
Inflation rate-The inflation rates can impact price in the long term. High and unpredictable
inflation tends to cause additional insecurity and confusion and to raise concerns about future
investment costs. If inflate is high and unpredictable, companies might also fear excessive
inflation would result in economic instability and future recession at the eventual expense of
their investment. States with a lengthy period of low and steady inflation generally have higher
investment rates.
Question 2
a.
1. Simple random sampling: In this method, a randomly collection of sample is done within
given population.
2. Systematic sampling: In this method, systematic algorithm is set by data collector or it is
simply a pattern based on which researcher collects sample.
3. Stratified Sampling: In this sampling method, population is classified into different segments
especially based on age, taste, religion and so on. This classification is known as strata. After that
sample is collected from each strata separately.
4. Clustered sampling: When population is too big, that it is difficult to cover entire population
simply through simple random sampling, cluster is formed by collecting data from each area of
the selected population.
5. Quota sampling: In this method, certain rules and regulations are set by researcher based on
which he collects data from population.
b.
Types of Sampling Advantages Disadvantages

Simple Random Sampling Ensures that the sample is
representative.
It is time consuming and
exhausting.
Systematic Sampling It ensures a high level of
representativeness and
eliminates the requirement for
a random number table.
Random sampling is less
random than stratified random
sampling.
Stratified Random Sampling Ensures that all strata or levels
of the population are
adequately represented.
It is time consuming and
exhausting.
Cluster Sampling Simple and practical It's possible that unit members
differ from one another,
reducing the efficacy of
approaches.
Quota Sampling Assures that all strata of the
population are represented in
some way.
The degree of generalizability
is in doubt.
c.
Probability sampling is a sampling strategy in which all population members have an equal
chance of being chosen as a representative sample. Nonprobability sampling is a sampling
strategy in which it is impossible to predict which individual from the population will be chosen
as a sample.
Section B
Question 3
(a) Histogram
(b) Calculation
Mean: Sum of data/number of values

Student
number
Data
in %

1 43
2 45
3 46
4 46
5 48
6 51
7 51
8 51
9 53
10 53
11 55
12 56
13 57
14 61
15 62
16 62
17 62
18 66
19 66
20 68
21 71
22 74
23 74
24 77
25 77
26 87
27 87
28 87
29 91
30 95
1922

Mean: 1922/30
= 64.06
Median: {N/2th item+ N/2th item + 1}2
N= 30
M= (30/2th item + 30/2th item + 1)/2
(15th item+ 16th item)/2
= 62+62
= 62
Mode: 51 is mode as it has higher frequency.
Range: Higher-lower value
= 95-43
= 52
(c)
Limitation:
The average cannot be computed as the number could be totaled for categorical variables.
The mean is impacted by extremes and since that contains every item in the range.
Question 4
I) Most useful method of data presentation
The most useful methods of data presentation include data representation. The data
representation includes; pie chart, bar graph, column graph, line graph, histogram and other

statistical diagrams. These graphs and charts show the status of data information quickly to the
users. As a result, management can take quick decisions based on it.
II) Chart
a) Pie chart
Biology
10%
Engineering
12%
Business
19%
History
48%
Information Technology
9%
Literature
1%
Number of students
b) Bar chart
Biology
Engineering
Business
History
Information
Technology
Literature
0 5000 10000 15000 20000 25000 30000 35000 40000
Number of students
Number of students
Question 5

(I) Mathematical tools to appraise capital investment decisions.
Payback Period Method- The payback time is normally in years, and cash flows from a capital
budgeting are equal to the sales revenue. The technique acknowledges the recuperation of
original investments in a business. The cash flow from the project is equal to the cash flow of the
project during the payback period.
Accounting Rate of Return Method-The required rate of return is also referred as 'return on the
investment' as the typical accounting approach used to evaluate the projected profit growth in an
investment by stating the net financial relationship between net profit of that investment.
Net Present Value Method- The Company is aimed at building goods and services via the use of
present and future assets. In order to generate wealth, the current value of all expected cash flow
must be higher. Present values value is achieved by discount, by a set percentage for the total
average cost of the company, the cash outflows and the influxes due to a given investment.
Internal Rate of Return Method-The IRR is a percentage valuation method used in capital
expenditure assessments that equals project costs and future cash inflows. The rate of return is
the same as that of the starting expense for the current value of forecast future cash flows. The
IRR is measured as the measure at which the current net worth is nil.
Calculation of IRR
Project A
Ye
ar
cash
inflow
cash
outflow
cash
flow
PV factor at
15%
discounted
cash flow
PV at
20%
discounted
cash flow
1 50000 30000 20000
0.86956521
7 17391.30435
0.8333
33 16666.67
2 62000 50000 12000
0.75614366
7 9073.724008
0.6944
44 8333.333
3 70000 55000 15000
0.65751623
2 9862.743486
0.5787
04 8680.556
4 82000 50000 32000 0.57175324 18296.10386 0.4822 15432.1

6 53
54623.8757 49112.65
NPV at R1: 54623.87-50000
= 4623.87
NPV at R2: 49112.65-50000
= -887.35
IRR: 15+4623.87/-5511.22*5
= 15-4.19
= 10.80%
Project B
Ye
ar
cash
inflow
cash
outflow
cash
flow
PV factor at
20%
discounted
cash flow
PV at
25%
discounted
cash flow
1 50000 32000 18000
0.83333333
3 15000 0.8 14400
2 62000 40000 22000
0.69444444
4 15277.78 0.64 14080
3 66000 45000 21000
0.57870370
4 12152.78 0.512 10752
4 77000 51000 26000
0.48225308
6 12538.58 0.4096 10649.6
0.40187757
2 54969.14
0.3276
8 49881.6
109938.27 99763.2

NPV at R1: 109938.27-50000
= 59938.27
NPV at R2: 99763.2-50000
= 49763.2
IRR: 20+59938.27/10175.07*5
= 20+29.45
= 49.45%