Hiram Finnegan Int. (HFI) is a high-tech company in designing computer software. Due to high market demand for its products, the company is going to expand its business by considering three projects. The three projects all have the same maturity of three years. The first project is called â€œAlphaâ€ that needs an initial investment of Â£20 million. Alpha is able to generate a cash flow of Â£70 million at the end of the first year, the second cash flow of Â£10 million at the end of the second year, and the last cash flow of Â£10 million at the of the third year. The second project is called â€œBetaâ€ that needs an initial investment of Â£10 million. Beta is forecasted to have a cash flow of Â£15 million at the end of the first year, the second cash flow of Â£40 million at the end of the second year, and the final cash flow of Â£10 million at the end of the third year. The third project is called â€œGammaâ€ that needs an initial investment of Â£10 million now and a further investment of Â£5 million at the end of the first year. Gamma will have a cash flow of Â£60 million at the end of the second year and the final cash flow of Â£10 million at the end of the third year. Assume the annual discount rate is 12%.

(i) Calculate net present values (NPV) and the profitability index (PI) for Alpha, Beta and Gamma. Assume that the three projects are independent of each other, which project(s) should be accepted in terms of NPV and PI?

(ii) Calculate payback periods for Alpha and Beta. Consider Alpha and Beta. If these two projects are mutually exclusive -i.e. HFI can only accept either Alpha or Beta, should you use NPV or payback method to evaluate the two projects and what are the differences between the two methods?

(iii) Assume that HFI only has a Â£20 million budget, which project(s) should HFI invest in? Please justify your answer.