Cupcake Corp. is considering an investment of $40 million in plant and machinery. This is expected to produce sales of $23 million in year 1, $26 million in year 2, and $30 million in year 3. Subsequent sales are expected to increase by 10% each year for the remaining 2 years. The plant and machinery will be scrapped after 5 years with a salvage value of $10 million. The property and machinery belong to the 3 year recovery period class for depreciation purposes (MACRS). Cost of goods sold (COGS) is expected to be $8 million in year 1, $14 million in year 2, and to increase at 9% each year for the remaining 3 years. Fixed operating expenses are $1,000,000 per year. Year-end net working capital (NWC) is given below. The corporate tax rate is 40%. k = 000s 0 1 2 3 4 5 NWC 500k 700k 800k 800k 500k 0 Calculate the free cash flows for time 0 through time 5. Calculate the (NPV) for a 12% cost of capital. Find the (IRR). Calculate the sensitivity of the investment to a change in the cost of capital (it could be as low as 8% or as high as 16%). Should Cupcake make the investment? Why or why not? note: They initially invest $500,000 in NWC. At the end of the first year, NWC increases to 600,000 so the firm has increased its investment in NWC by $100,000. This process continues over the project