A firm considers an investment of \($28,000,000\) (purchase price) in new equipment to replace old equipment that has a book value of \($12,000,000\) (market value of

\($20,000,000).\) If the firm replaces the old equipment with the new equipment, it expects to save \($17,500,000\) in pretax cash flow (net savings) savings the first year and an additional 12 percent (more than the previous year) per year for each of the following three years

(total of four years). The old equipment has a four-year remaining life, being written off on a straight-line depreciation basis with no expected salvage value. The new equipment will be depreciated under the MACRS system (which uses a double-declining balance approach, the half-year convention in year 1, and the option to switch to straight-line when it is beneficial) using a three-year life. In addition, it is assumed that replacement of the old equipment with the new equipment would require an increase in working capital of \($5,000,000,\) which would not be recovered until the end of the four-year investment. If the relevant tax rates is 40 percent, find:

a. The net investment (time 0 cash flow).

b. The after-tax cash flow for each period.

c. The internal rate of return, the net present value, and the profitability index.