$1.$ What is the NPV of the mall project? The project would require an initial investment in equipment of $$600,000$ and would last for either $3$ years or $4$ years $($the date when the project ends will not be known until it happens and that will be when the equipment stops working in either $3$ years from today or $4$ years from today$).$ The first annual operating cash flow of $$238,000$ is expected in $1$ year, and annual operating cash flows of $$238,000$ per year are expected each year until the project ends in either $3$ years or $4$ years. In $1$ year, the project is expected to have an after$-$tax terminal value of $$377,000.$ The cost of capital for this project is $6\mathrm{.}82$ percent.

$2.$ Tripp Industries is considering buying a new recycling system. The new recycling system would be purchased today for $$70,000.$ It would be depreciated straight$-$line to $$10,000$ over $2$ years. In $2$ years, the recycling system would be sold and the after$-$tax cash flow from capital spending in year $2$ would be $$30,000.$ The system is expected to reduce costs by $$74,000$ in year $1$ and by $$18,000$ in year $2.$ If the tax rate is $50\%$ and the cost of capital is $12\mathrm{.}7\%,$ what is the net present value of the new recycling system project?