Answer all the following parts of the question on capital budgeting.

The Luxury Cards & Stationery (LCS) is considering investing in a new postcard manufacturing machine that has an estimated life of three years. The cost of the machine is 30,000 and the machine will be depreciated straight line over its three-year life to a residual value of 0.

The postcard manufacturing machine will result in sales of 2,000 postcards in Year 1. Sales are estimated to grow by 10% per year each year through Year 3. There will be no sales in Year 4. The price per postcard that the LCS will charge its customers is 18 each and is to remain constant. The postcards have a cost per unit to manufacture of 9 each and it will remian constant.

In Year 0, installation of the machine and the resulting increase in manufacturing capacity will require an increase in various net working capital by 3,300. From Year 1 to Year 3, it is estimated that the LCS needs to hold 2% of its annual sales in cash, 4% of its annual sales in accounts receivable, 9% of its annual sales in inventory, and 5% of its annual sales in accounts payable. In Year 4, the balance in net working capital will be fully recovered. The firm is in the 35% tax bracket. Assume that all cash flows occur at the end of a year.

a. Using the information described above, calculate the changes in net working capital for each of the relevant years for the LCSs new project. Briefly explain each step of your calculation.

b. Using the information described above, calculate the free cash flow that will be generated by the project for each relevant year. Briefly explain each step of your calculation.

c. Suppose that the LCS has a debt-to-equity ratio of 2/3. The cost of debt of the LCS is 9%. The LCS has a stock beta of 1.5. The market risk premium is 8% and the risk-free interest rate is 4%. Assume that the new project has the same risk as does the company in general. Using the information described above, calculate the net present value (NPV) of the LCSs new project. Would you recommend investing in the project?