联系我们： 手动添加方式: 微信>添加朋友>企业微信联系人>13262280223 或者 QQ: 1483266981

MATH2040/6131 Financial Mathematics
Practical Assignment
This assignment is worth 20% of the overall mark for the module.
Completed work should be submitted on Blackboard before 23:59 on Monday,
4 December 2023. The deadline is strict and penalties for late work will be applied
in accordance with the University’s late work policy.
To submit your report and Excel spreadsheet go to the Blackboard page of
MATH2040/6131, under the Class tests, Exam Papers and Courseworks tab there is
an assignment called Coursework submission-2023/2024. In your submission please
attach the following two files:
1. The report in a file called report-ID.pdf, where ID is your student ID number;
2. The Excel spreadsheet in a file called spreadsheet-ID.xls, where ID is your
student ID number.
Note that all your results must be presented in your written report
with the steps and justifications. Calculations should be done entirely in
Excel, without use of Macros/VBA. Therefore please avoid expressions such
as ”Please see the spreadsheet” in the report. There is a strict limit of 5 A4 pages
for the written report, which is easily sufficient to receive full credit. Font sizes of at
least 11pt must be used. Careful explanation and clear presentation are important.
All coursework must be carried out and written up independently (see University’s
Academic Integrity Guidance)
1. An investor is considering whether to invest an amount of ￡1 million in one
of the following projects.
(1) The project A requires the investment of the whole amount in properties.
– Income from rents at an annual rate of ￡60,000 per year for 4 years
after an initial period of 1 year in which no income will be received.
Rents are expected to increase thereafter at the start of each year at
a rate of 0.5% per annum compound. The income will be received
monthly in advance.
– Costs of ￡10,000 per annum in the first year, rising at a constant
rate of 0.5% per annum are expected to incur at the beginning of
each year.
– At the end of 20 years, the investor expects to be able to sell the
properties for ￡2 million after which there will be no revenue or
costs.
(2) The project B involves the investment of the whole amount in an investment fund which pays an income of ￡60,000 per annum annually in
advance and returns the whole invested sum at the end of 20 years.
(a) Calculate the net present values of both projects for i = 0.01. [6]
(b) Plot the net present values for both projects for i = 1%, 2%, .., 9%. [8]
(c) Calculate the internal rates of return for both projects. [6]
(d) Calculate the discounted payback period for project B at an effective rate
of interest of 1% per annum. [5]
(e) Without performing any calculations, explain whether the discounted
payback period at an effective rate of interest of 1% per annum of project
A is higher or lower than that from the second project. [5]
(f) Using your answers, discuss which project is the better project for the
investor. [10]
[40]
Present your work for (a)–(e) in an Excel sheet labelled Q1.
2. ￡80,000 is invested in a bank account which pays interest at the end of each
year. The interest rate is determined at the beginning of each year and remains
unchanged until the beginning of the next year and is determined as follow :
In the first year, the annual effective rate of interest will be 4%, 6% or
8% with equal probability.
In the second year, the annual effective rate of interest will be 7% with
probability 0.75 or 5% with probability 0.25.
In the third year, the annual effective rate of interest will be 6% with
probability 0.7 or 4% with probability 0.3.
The rate of interest applicable in any one year is independent of the rate
applicable in any other year.
(a) Calculate the mean and standard deviation of the accumulated value of
the investment after 3 years. [5]
(b) Using simulation, estimate the probability that the accumulated value
after 3 years is more than ￡95,000 and give the 95% confidence limits
for this probability. [In each case, use 5,000 simulations and use the
confidence interval for a proportion.] [15]
Present your work in an Excel sheet labelled Q2-a-b
Assuming now that ￡80,000 is invested at the start of each year.
(c) Estimate the mean, standard deviation of the accumulated amount at
the end of 3 years using 5,000 simulations of the accumulated value . [5]
(d) Estimate the probability that the accumulated value is less than ￡270,000
and give the 95% confidence limits for this probability. [In each case, use
5,000 simulations and use the confidence interval for a proportion.] [15]
Present your work in an Excel sheet labelled Q2-c-d [40]