Anita Vasquez received $$160,000$ from her mother$$s estate. She placed the funds in the hands of broker, who purchased the following securities on Vasquez$$s behalf.

a$.$ Common shares were purchased at cost of $$80,000.$ The shares paid no dividends, but they were sold for $$180,000$ at the end of four years.

b$.$ Preferred shares were purchased at their par value of $$30,000.$ The shares paid $6\%$ dividend $($based on par value$)$ each year for four years. At the end of four years, the shares sold for $$24,000.$

c$.$ Bond were purchased at a cost of $$50,000.$ The bonds paid $$3,000$ in interest every six months. After four years, the bonds were sold for $$58,500.($Note: In discounting a cash flow that occurs semi$-$annually, the procedure is to halve the discount rate and double the number of periods. Use the same procedure in discounting the proceeds from the sale$).$

The securities were all sold at the end of four years so that Vasquez would have funds available to start a new business venture. The broker stated that the investments had earned more than a $20\%$ return annually, and he gave Vasquez the following computation to support his statement:

c$.$ Bond were purchased at a cost of $$50,000.$ The bonds paid $$3,000$ in interest every six months. After four years, the bonds were sold for $$58,500.($Note: In discounting a cash flow that occurs semi$-$annually, the procedure is to halve the discount rate and double the number of periods. Use the same procedure in discounting the proceeds from the sale$).$

The securities were all sold at the end of four years so that Vasquez would have funds available to start a new business venture. The broker stated that the investments had earned more than a $20\%$ return annually, and he gave Vasquez the following computation to support his statement:

Common shares:

Gain on sale $($$$180,000-$$$80,000)..................................$ $$100,000$

Preferred shares:

Dividends paid $(6\%$ x $$30,000$x $4$ years$).......................7,200$

Loss on sale $($$$24,000-$ $$30,000)...................................(6,000)$

Bonds:

Interest paid $($$$3,000$x $8$ periods$)....................................24,000$

Gain on sale $(58,500-$ $$50,000)......................................8,500$

Net gain on all investments......................................................... $133,700$

Required:

Ignore income taxes.

$1.$ Using a $20\%$ discount rate, compute the net present value of each of the three investments. On which investment$($s$)$ did Anita earn a $20\%$ rate of return? $($Round computations to the nearest whole dollar.$)$

$2.$ Considering all three investments together, did Anita earn a $20\%$ rate of return? Explain.

$3.$ Anita wants to use the $ $262,500$ in proceeds $($$$180,000+$ $$24,000+$ $$58,500=$ $$262,500)$ from sale of the securities to open a fast$-$food franchise under a $10-$year contract. What net annual cash inflow must the store generate for Anita to a $16\%$ return over the $10-$year period? Anita will not receive back her original investment at the end of the contract. $($Round computations to the nearest whole dollar$)$