Company X is evaluating the following project. The initial investment in physical assets (to be made at the end of year 0) costs 100m. The assets are expected to last four years and none of their value is expected to be recovered in year 4. Revenues are expected to be 80m in years 1-4. Total costs in each year are expected to be half of revenues. Assume that all cash flows occur at the end of the relevant year. An inventory of 10m has to be kept at the end of year 0 and an additional 10m needs to be added to the inventory at the end of year 1. All goods in the inventory will be sold at the end of year 4.

a. Assume no taxes. Determine the NPV of the project under a 10% discount rate.

b. Assume that the company faces a corporate tax rate of 30%. Using the straight line depreciation method, determine the NPV of the project under a 10% discount rate.

c. Assume that the company's debt to equity ratio is equal to 1, the company's equity has a beta equal to 2, the market risk premium is 6% and the risk-free rate is 1%. The yield to maturity of the company's bonds is 10% and the corporate tax rate is as in b). Determine the appropriate discount rate for the project. Could the company reduce its cost of capital by increasing its leverage? Give reasons for your answer.

Write out each step in detail, please!