Question Three: (6 marks) (This question practices your ability to undertake and understand theory.) Consider the classical n-observation, K-regressor linear regression model: y = X + u ; u~N(0,In) where X is nonstochastic of full column rank. Suppose we specify prior, nonsample, information on as g exact linear restrictions R = r, where R is a (g K) nonstochastic, full row rank, matrix and r is a nonstochastic (g 1) vector. (1) (a) We estimate the classical model subject to the restrictions R = r; i.e., we use the restricted least squares estimator, BR, as the estimator of . Consider a corresponding estimator of : = (y - XBR)' (y - XR) n-K + g eReR n-K + g Use the following Theorems and Hints to prove that is an unbiased estimator of under the null hypothesis that R : = r. Problems on Decision Criteria for firm-level investment decisions Problem 1 The financial analyst team of XYZ Co. is trying to evaluate two independent projects and make investment decisions. The two projects have the following cash flows: Year 0 1 2 3 4 5 6 7 8 Project A -15,000 -10,000 | -5,000 3,000 8,000 10,000 10,000 10,000 10,000 Project B -5,000 -3,000 -2,000 1,000 3,000 3,000 3,000 4,000 4,000 XYZ Co. does not plan to raise additional financing for taking new projects. It has a debt-to- assets ratio of 20%. XYZ Co.'s cost of debt financing is 4%. In addition, XYZ Co. has a beta of 1.2. The market risk-free rate is 2% and the expected stock market return is 7%. Answer the following questions with the given information. Part A: What is the WACC of XYZ Co.? Do not consider the tax impact on WACC. Part B: What are the NPVs of Project A and Project B? Based on your calculation, should XYZ Co. take Project A or Project B or Both? Part C: What are the Profitability Indices of Project A and Project B? Based on your calculation, should XYZ Co. take Project A or Project B or Both? Part D: What are the IRRS of Project A and Project B? Based on your calculation, should XYZ Co. take Project A or Project B or Both? Part E: What are the Payback periods for Projects A and B. If the projects are independent, cash flows are spread evenly throughout the year, and the cut-off is 5.0 years, should you take on projects A and B? If instead we assume end of year cash flows for years 1-8, what does this do to your payback calculations and decisions? Part F: Suppose that Project A and Project B are mutually exclusive. Based on NPVs you calculated in Part B, which project should XYZ Co. take? Based on IRRS you calculated in Part C, which project should XYZ Co. take? Are they giving consistent suggestions? If they are not consistent, why such inconsistency exists? Part G: Suppose that Project A and Project B are mutually exclusive, and calculate the incremental IRR. Which project should XYZ Co. take? Is the incremental IRR giving consistent suggestion with NPV? Problem 2 ABC Co. is trying to evaluate an independent project with the following cash flows: Year 0 1 2 3 4 5 6 7 8 Project X -5,000 | -2,500| -2,500 5,000 -5,000 100,000 10,000 10,000 | -150,000 Use the Modified IRR to make a decision on Project C. Suppose that the discount rate is 20%.