# Statistical methods in Finance

PART 1   This part should be approximately 2200 words.   Part 1-A   Task of the Assessment   This task relates to another one of the underlying principal functions of finance that is allocating funds to appropriate projects which are value enhancing. In this assignment we look at this issue from the companys perspective and thus this involves analysing a problem that faces corporate treasurers. First, the appropriate weighted average cost of capital for the project needs to be determined, which depends on the capital structure of the firm and the risk of the project amongst other factors. Secondly, capital budgeting needs to be implemented to decide whether the project should be implemented as well an assessment of the risks and benefits from undertaking the project via sensitivity analysis and critical evaluation of the methods implemented. The task should take the form of a report with a conclusion that summarises your key recommendations to managers.   Assignment Instructions   Choose any two companies in different business sectors (e.g. different GICS sub-industries) that have a primary listing on in the UK on the London Stock Exchange (either the Main Market or the Alternative Investment Market (AIM)). Company accounts need to be in British Pounds. Each company must have:  Company market capitalization between £10,000,000 and £5,000,000,000  Total debt of more than £500,000  Total debt divided by total firm value between 5% and 95%  Been trading on the Stock Exchange for a minimum of two years with financial data available   Neither company should be in the financial sector; name them respectively Company A and Company B. Company A wishes to diversify its activities, and has identified a project with 5- year maturity in the business sector of Company B. It decides to use Company B as a comparison company for calculating the appropriate Weighted Average Cost of Capital (WACC) with which to undertake the NPV evaluation of this project.   Please note that for simplicity your best estimate of the WACC should be based on: Gearing ratio calculated as total debt divided by total firm value (total debt plus total equity). A risk-free rate of 1.1% and a market equity premium of 5.8%.   1)    Provide a best estimate for the WACC that Company A should apply to the new project. Discuss precisely how this WACC value is calculated. This should incorporate information from part 1), follow the guidance above and include additional information as appropriate.               Part 1-B   In order for Company A to undertake this project, it is necessary to purchase a new piece of machinery immediately at a cost of £2,000,000. It is anticipated that this will have a resale value of £200,000 at the end of year 5. For tax purposes, capital allowances are calculated on a straight-line basis.   The firm is already committed to spending £50,000 on developing this new product over the next year and will spend an additional £25,000 on adapting the product to market requirements if the project goes ahead. There is a fee of £15,000 to undertake the project evaluation.   It has been estimated that sales will be 50,000 items of the new product in year 1. You expect items to sell at £20 per item in nominal terms. The nominal variable costs of production will be £10 per item in year 1. The project will lead to an increase in the firms fixed costs of £200,000 but the toy division will be allocated with £300,000 of fixed costs. The project is expected to increase dividend payments by £75,000.   Assume that this project a negligible amount of working capital will be held. Assume that sales will grow from year 1 to year 3 at 30% per annum but will decline by 10% in year 4 and year 5. The firm is expected to sell the machinery at the end of year 5 rather than continue production into year 6. Inflation is expected to be 5% per annum and will impact all revenues and costs.   2) Estimate the NPV of the project that Company A will undertake. Conduct sensitivity analysis on key inputs into the NPV decision making process. Justify clearly which variables are crucial for determining whether the project should be implemented or not. Provide a final recommendation to management on the viability of the project.     PART 2   1.What stylised features of financial data cannot be explained using linear time series models? [10 marks]   2. Which of these stylised features could be modelled using a GARCH (1,1) process? [10 marks]   3. Why, in recent empirical research, have researchers preferred GARCH (1,1) models to pure ARCH(p)? [10 marks]   4. Describe two extensions to the original GARCH model. What additional characteristics of financial data might they be able to capture? [20 marks]     b) Suppose that a research wanted to test the null hypothesis that ??1 + ?? = 1 in this equation. Explain how this might be achieved within the maximum likelihood framework. [10 marks]   c) Suppose now that the researcher had estimated the above GARCH model for a series of returns on a stock index and obtained the following parameter estimates: ???= 0.0023, ???0 = 0.0172, ??? = 4 0.9811, ???1 = 0.1251. If the research has data available up to and including time T, write down a set of equations in  2 ??????  their lagged values, which could be employed to produce one-, two- and three-step-ahead forecasts for the conditional variance of ??t. [15 marks]   d) Suppose the coefficients estimate of for this model is 0.98 instead. By reconsidering the forecast expressions, you derived in part C) explain that would happen to the forecasts in this case. [15 marks]

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