$1.$ Determine the average rate of return for a project that is estimated to yield total income of $$720,000$ over $10$ years, has a cost of $$1,100,000,$ and has a $$100,000$ residual value.

$2.$ A project has estimated annual net cash flows of $$60,000.$ It is estimated to cost $$510,000.$ Determine the cash payback period. Round to one decimal place.

$3.$ A project has estimated annual net cash flows of $$225,000$ for $8$ years and is estimated to cost $$800,000.$ Assume a minimum acceptable rate of return of $6\%.$

Using the present value of an annuity table appearing in Exhibit $5$ of this chapter, determine $($a$)$ the net present value of the project and $($b$)$ the present value index, rounded to two decimal places.

$4.$ A project is estimated to cost $$402,360$ and provide annual net cash flows of $$120,000$ for $5$ years. Determine the internal rate of return for this project, using the present value of an annuity table appearing in Exhibit $5$ of this chapter.

$5.$ Project $1$ requires an original investment of $$375,000.$ The project will yield cash flows of $$90,000$ per year for $8$ years. Project $2$ has a computed net present value of $$50,000$ over a $6-$year life. Project $1$ could be sold at the end of $6$ years for a price of $$40,000.($a$)$ Using the present value tables in Exhibits $2$ and $5,$ determine the net present value of Project $1$ over a $6-$year life, with residual value, assuming a minimum rate of return of $10\%.($b$)$ Which project provides the greatest net present value?