For the following questions provide well detailed answers.

Let X be a random variable with an exponential distribution, so that the probability density function is given by: fx(x) = de-dx (i) Determine the probability density function of the random variable Y, where Y= X. [3] (ii) Show that Y has a Weibull distribution, stating clearly the parameters of the distribution. [1] [Total 4]You are a member of a team responsible for the evaluation of investment proposals in a large multinational company that is quoted on a major stock exchange. The directors of one of the company's largest subsidiaries has proposed a major investment that would double that subsidiary's manufacturing capacity and would enable it to export to several new markets. The proposed investment would require the company to raise a great deal of money, either by borrowing or by the issue of equity. The amount involved is large enough to justify either a share issue or the sale of loan stock, but not a combination of the two. The proposal has been backed by a detailed analysis of the cash flows that are expected to arise from this expansion. The company has a policy of evaluating investment opportunities on the basis of the net present value (NPV) of estimated cash flows. (i) (a) Identify the factors that the company may use to determine the rate at which this proposal might be discounted; and (b) Explain which of these factors would be most relevant to this project. [6] (ii) Explain how the decision to raise finance using either loan stock or equity might affect the company's weighted average cost of capital (WACC). [8] (iii) It has been suggested that "political", or subjective, factors within companies are often more relevant to investment decisions than objective economic factors in deciding whether a project should proceed. Explain why this might be so. [6] [Total 20]