Big Mike Co$.$ is evaluating a project requiring a capital expenditure of $$200,000.$ The project has an estimated life of $5$ years and no salvage value. The estimated net income and net cash flow from the project are as follows:

Year

Net Income

Net Cash Flow

$1$

$ $35,000$

$$65,000$

$2$

$25,000$

$55,000$

$3$

$20,000$

$50,000$

$4$

$15,000$

$45,000$

$5$

Total

$10,000$

$$105,000$

$40,000$

$$255,000$

$$

The company's minimum desired rate of return is $12\%.$ The factors for the present value of $$1$ at compound interest of $12\%$ for $1,2,3,4$ and $5$ years are $0\mathrm{.}893,0\mathrm{.}797,0\mathrm{.}712,,0\mathrm{.}636,$ and $0\mathrm{.}567$ respectively.

Determine $($a$)$ the average rate of return on investment and $($b$)$ the net present value.