Linda Clark received $$221,000$ from her mother$$s estate. She placed the funds into the hands of a broker, who purchased the following securities on Linda$$s behalf:

Common stock was purchased at a cost of $$110,000.$ The stock paid no dividends and was sold for $$190,000$ at the end of three years.

Preferred stock was purchased at its par value of $$42,000.$ The stock paid a $4\%$ dividend $($based on par value$)$ each year for three years. At the end of three years, the stock was sold for $$28,000.$

Bonds were purchased at a cost of $$69,000.$ The bonds paid annual interest of $$3,000.$ After three years, the bonds were sold for $$74,000.$

The securities were all sold at the end of three years so that Linda would have funds available to open a new business venture. The broker said the investments earned more than a $12\%$ return, and he gave Linda the following computations to support his statement:

Common stock:$$Gain on sale $($$$190,000$ $$110,000)$$ $80,000$Preferred stock:$$Dividends paid $(4\%$ $$42,0003$ years$)5,040$Loss on sale $($$$28,000$ $$42,000)(14,000)$Bonds:$$Interest paid $($$$3,0003$ years$)9,000$Gain on sale $($$$74,000$ $$69,000)5,000$Net gain on all investments$ $85,040$

$1-$a$.$ Using a $12\%$ discount rate, compute the net present value of each of the three investments.

$1-$b$.$ On which investment$($s$)$ did Linda earn a $12\%$ rate of return?

$2.$ Considering all three investments together, did Linda earn a $12\%$ rate of return?

$3.$ Linda wants to use the $$292,000$ proceeds $($$$190,000+$ $$28,000+$ $$74,000=$ $$292,000)$ from sale of the securities to open a retail store under a $12-$year franchise contract. What minimum annual net cash inflow must the store generate for Linda to earn a $9\%$ return over the $12-$year period?