Copperbelt University
Directorate of Distance Education and Open Learning
Term Project II
Anthony Singogo
SIN: 22900601
Master’s in business administration (General)
GBS 541: Quantitative Methods
Dr. Danielle Babb
2023-08-1
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Financing Decision
Table of Contents
Literature review ….………….……………………….…….……2
Research question ……………………………………...……….3
Methodology ………………………………………….…….…….3
Analysis of the dat.…………………………………….….…..….3
Outcome ……………………………………….……….……....…5
Summary…………………………………….……………….…... 6
References……………………………….….……………….…….7
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Financing Decision
LITERATURE REVIEW
This section outlines the literature reviewed by the researcher in relation to the
study at hand. The review involved online publications, Journal articles and books to
help the researcher amass data from the body of knowledge and present ideas worth
researching research findings.
Zambia perspective
Every employer wish to foster the welfare of its workers during and after the tenure
of employment service and in achieving this some organization get affiliated to
institutions like Nkwazi cooperative so that individual workers who may wish to
voluntarily join and serve part of their resources with a cooperative are free to do so,
other organizations design training programs to impart their members a culture of
serving that would sustain them beyond employment life these include invitations to
stock brokers to make presentations to members of staff on how to invest in shares e.tc.
The rate of borrowing over the years has been over 16 percent and relatively high for
ordinary citizen to afford loans acquisition and repayments, this pushes people to join
cooperatives and village banking were cheaper and affordable loans are accessed with
reasonable repayment period that could have been agreed my members themselves. It
may not be easy to acquire a loan from the bank as terms and conditions may demand
a surety in form of the title deed for the land or a car and others may not have those
requirements hence making it difficult borrow and invest into businesses of their choice.
It is for this reason why some cooperatives have continued to record an increase in
membership (8% increase in 2020 and 5% increase in 2022) even amid COVID-19
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Financing Decision
because they are investing for future use and posterity generation (annual report, 2022
p19).
Research questions
1. How do we minimize the total dollars needed to meet the gratuity plan’s six-year
obligation?
2. What are decision variables from the data given?
3. What is the total investment required to meet the gratuity plan’s six-year
obligation?
Methodology
This chapter covered what is called research methodology. Dawson C (2009) defined
research methodology as: “Philosophy or the general principle which guides your
research. It is the overall approach to studying your topic and includes issues you need
to think about such as the constraints, dilemmas and ethical choices within your
research.’’ Hypothetical data set relating to Nkwazi Cooperative Savings and Credit
Society was generated using quantitative methods and results interpreted.
Analysis (meaning) of the data
According to Anderson, D. R., et al. 2015, p375, decision variables are defined
as follows:
F= total dollars required to meet the retirement plan’s six -year obligation
B_1 = units of bond 1 purchased at the beginning of year 1
B_2 = units of bond 2 purchased at the beginning of year 1
B_3 = units of bond 3 purchased at the beginning of year 1
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Financing Decision
S_i = amount placed in savings at the beginning of year i for i= 1,…,6
The objective function is to minimize the total dollars needed to meet the retirement
plan’s six -year obligation, or
Min F
An essential feature of this type of financial planning problem is that a constraint must
be formulated for each planning horizon. Each constraint takes its form.
funds available at
Funds invested in bonds
the beginning of the year - and placed in savings
Cash obligation for
=
the current year
The funds available at the beginning of the year 1 are given by F. With the current price
of $1150 for bond 1 and investments expressed in thousands of dollars, the total
investment for B_1 units of bond 1 would be 1.15B_1, for bond 2 would be 1.2B_2 and
bond 3 would be 1.3B_3.
The investment in savings for year 1 is S_1. Using this outlook and the first-year
obligation of 85, we generate constraints for years 1:
F- 1.15B_1 – 1.2B_2 -1.3B_3 -S_1 =85
The investments in bonds take place only in this first year, and the bond will be held
until maturity.
The funds available at the beginning of year 2 include the return on investment of 5.5
00% on the par value of bond 1, 8.875% par value of bond 2 and 11.75% on the par
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Financing Decision
value of bond 3 and 3% on savings. The new amount to be invested in savings for year
2 is S_2 with an obligation of 75, the constraint from year 2 to 6 are:
0.055B_1 + 0.08875B_2 + 0.1175B_3 + 1.03S_1 – S_2 =75
Year 2
1.055B_1 + 0.08875B_2 + 0.1175B_3 + 1.03S_2 – S_3 = 50 Year 3
1.08875B_2 + 0.1175B_3 + 1.03S_3 - S_4 = 60
Year 4
0.1175B_3 + 1.03S_4 – S_5 = 55
Year 5
1.1175B_3 + 1.03S_5 – S_6 =45
Year 6
Note that the constraint for year 3 shows that funds available from bond 1 are
1.055B_1. The coefficient of 1.055 means the bond 1 matures at the end of year 2. The
par value plus the interest from bond 1 during year 2 is available at the beginning of
year 3. Same with bond 2 matures in year 3 and is available at the beginning of year 4.
We have no bond maturing in year 4, hence at the beginning of year 5 nothing to show
but bond 3 matures at the end of year 5 and is available at the beginning of year 6
(Anderson, D. R., et al. 2015, p375).
Outcomes
For year 2, the return on investment is added to the funds available, and the new
amount is used to calculate savings for year 2.
For year 3 to year 6, the coefficient in front of B_1, B_2, or B_3 indicates the funds
available from the respective bond that matured in the previous year.
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Financing Decision
To optimize this scenario, you would typically set an objective function that you want to
maximize or minimize. This objective function could be related to the total return on
investment, total savings, or some other financial goal.
With the constraints and objective function defined, you can use an optimization solver
like Lingo or Excel Solver to find the optimal values for B_1, B_2, B_3, S_1, S_2, S_3,
S_4, S_5 and S_6 that satisfy the constraints and optimize the objective function. The
solver will automatically adjust the variable cells (B_1, B_2, B_3, S_1, S_2, S_3, S_4,
S_5 and S_6) to achieve the best possible outcome according to the given constraints
and the objective function (Anderson, D. R., et al. 2015, p375).
Summary
After generating the sensitivity report based on excel solver, with the objective function
of F, the total investment plan required to meet the six-year plan obligation is obtained
and the current price of each of the bonds of 1150, 1200 and 1300 can be multiplied by
the unit purchased to obtain the investment amount required to meet the obligations.
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Financing Decision
References
Anderson, D. R., et al. (2015). Quantitative methods for business. Boston, MA:
Cengage.
ISBN-13: 978-1-285-86631-4
Nkwazi Annual report 2022. Retrieved from
https://www.nkwazicoop.com/storage/app/media/resources/annual-reports/annualreport-2022.pdf
CEIC Data, 2023
https://www.ceicdata.com/en/indicator/zambia/bank-lending-rate
World Bank, 2023
https://pubdocs.worldbank.org/en/248071492188177315/mpo-zmb.pdf