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January 2023 Assessment: R-project

ST226

Actuarial Investigations: Financial

Throughout the paper consider the prospect of investing in a small business over a 50-year period. At the end of the 50-year period any upfront costs cannot be recovered. The business is expected to generate revenue immediately, and its upfront costs and monthly cash flow are summarised below.

Note: remember that marks will be awarded for the clarity of your R code, as well as for the accuracy of your written answers.

Question 1

Write a function in R which takes as inputs an effective yearly interest rate, a time horizon in years, an upfront cost, per-period costs, per-period revenue, and the number of periods in a year (e.g. 12 for months, 4 for quarters) and returns the Net Present Value (NPV) of an investment.

Use your function to calculate the NPV for the proposed investment assuming an effective in- terest rate of 5% per year. [25 marks]

Question 2

Using the function you wrote in Question 1 produce a plot of the NPV against different values of the effective interest rate ranging from 0% to 20% per year. Interpret your plot. [25 marks]

Question 3

Explain in detail how you would calculate the internal rate of return for the proposed investment. Implement your method in R and report the output. [30 marks]