$.$ American Biodyne $($AB$)$ is considering expanding into a new line of business. The expansion will require an investment of $$500,000$ in new equipment. This equipment which will cost another $$200,000$ to install, will be depreciated on a straight$-$line basis over an $8-$year period to an estimated salvage value of zero. If the expansion project is accepted, working capital will increase by $$100,000$ immediately. Revenues for the first $3$ years are forecasted at $$600,000$ per year and at $$800,000$ in years $4-8.$ Operating costs exclusive of depreciation are expected to be $$310,000$ per year for $3$ years and increase to $$400,000$ per year for the following $5$ years. AB has a marginal tax rate of $40\%$ and its required rate of return for the project under consideration is $20\%.$ If AB assumes that the new equipment will have an actual market value of $$50,000$ at the end of the $8$th year, should the expansion be undertaken? Compute the NPV$.$ Compute the IRR. Compute the payback period. Show your work.