Linda Clark received $$286,000$ from her mother$$s estate. She placed the funds into the hands of a broker, who purchased the following securities on Linda$$s behalf:

a$.$ Common stock was purchased at a cost of $$156,000.$ The stock paid no dividends, but it was sold for $$280,000$ at the end of three years.

b$.$ Preferred stock was purchased at its par value of $$48,000.$ The stock paid a $8\%$ dividend $($based on par value$)$ each year for three years. At the end of three years, the stock was sold for $$20,000.$

c$.$ Bonds were purchased at a cost of $$82,000.$ The bonds paid annual interest of $$3,500.$ After three years, the bonds were sold for $$87,000.$

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 stated that the investments had earned more than a $14\%$ return, and he gave Linda the following computations to support his statement:

Common stock:

Gain on sale $($$$280,000$ $$156,000)$ $ $124,000$

Preferred stock:

Dividends paid $(8\%\backslash$times $$48,000\backslash$times $3$ years$)11,520$

Loss on sale $($$$20,000$ $$48,000)(28,000)$

Bonds:

Interest paid $($$$3,500\backslash$times $3$ years$)10,500$

Gain on sale $($$$87,000$ $$82,000)5,000$

Net gain on all investments $ $123,020$

$($$$123,020-$: $3$ years$)-$: $$286,000=14\mathrm{.}34\%$

Click here to view Exhibit $12$B$-1$ and Exhibit $12$B$-2,$ to determine the appropriate discount factor$($s$)$ using tables.

Required:

$1-$a$.$ Using a $14\%$ discount rate, compute the net present value of each of the three investments.

$1-$b$.$ On which investment$($s$)$ did Linda earn a $14\%$ rate of return?

$2.$ Considering all three investments together, did Linda earn a $14\%$ rate of return?

$3.$ Linda wants to use the $$387,000$ proceeds $($$$280,000+$ $$20,000+$ $$87,000=$ $$387,000)$ from sale of the securities to open a retail store under a $7-$year franchise contract. What minimum annual net cash inflow must the store generate for Linda to earn a $12\%$ return over the $7-$year period?