Question 3 You are an intern for the corporate finance office of SCF, Inc. and have been tasked to evaluate the following potential investment projects: Project A: Initial cash outflow of $96 million followed by cash inflows of $23 million per year for the next 10 years. Project B: Initial cash outflow of $22 million followed by cash inflows for the next 10 years, starting at $5 million next year and growing at an annual rate of 3%. Project C: Initial cash outflow of $20 million followed by cash inflows of $3 million per year forever. Project D: Initial cash outflow of $10 million followed by cash inflows grow at 3% per year indefinitely, starting from $2 million next year. The window of opportunity to invest in these projects is closing and SCF, Inc. currently only has $100 million available for new projects. Also, the return required on these projects is 10%. Your supervisor is a strong advocate of the Profitability Index (PI) as an investment analysis tool because he argues that the PI indicates a projects bang for the buck and is the most relevant information for decision-making in this context as investment funds are limited. (a) Given SCF, Inc.s resource constraints, using the PI would lead the firm to undertake which project or combination of projects? (11 marks) (b) Do you agree with your supervisor that the PI is the best rule on which to base your investment decision under the firms current circumstances? Discuss and substantiate your answer numerically. (9 marks) (c) Consider a one-period project with conventional cash flows of C0 and C1 at the beginning and end of the period respectively. Denote the return required on this project as WACC. (i) Express the projects internal rate of return (IRR) in terms of its cash flows. (3 marks) (ii) Express the projects PI in terms of its cash flows and required return. (2 marks) (iii) Using your answers to parts (c)(i) and (c)(ii), express the projects PI in terms of its IRR. (3 marks) (iv) Establish whether the relation between a projects PI and IRR in part (c)(iii) for a one-period project holds for Project D, a multi-period project. (5 marks)