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MATH2040/6131 Financial Mathematics
发布时间：2023-12-02
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MATH2040/6131 Financial Mathematics
Practical Assignment
This assignment is worth 20% of the overall mark for the module.
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 in- vestment 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]
