$($A$)$ Sunny Company is investigating four different opportunities. Information on the four projects under study is as follows:

Project $1234$

Investment required $$480,000$ $$360,000$ $$270,000$ $$450,000$

Present value of cash$$ inflows $567,270433,400336,140522,970$

Net present value $$87,270$ $$73,400$ $$66,140$ $$72,970$

Life of project $6$ years $12$ years $6$ years $3$ years

The company$$s required rate of return is $10\%$; therefore a $10\%$ discount rate has been used in the present value computations above. Limited funds are available for investment, so the company cannot accept all of the available projects.

Required:

a$)$ Compute the profitability index for each investment project.

b$)$ Rank the four projects according to preference, in terms of:

$($i$)$ Net present value, $($ii$)$ Profitability index.

$($B$)$ Snow Company is considering the purchase of a new piece of equipment for laying sod. Relevant information concerning the equipment follows:$$

Cost of Equipment $$180,000\mathrm{.}00$

Annual Cost saving from new equipement $$37,500\mathrm{.}00$

Expected Annual Net Income $12$ year

Expacted Annual Income $$15,000\mathrm{.}00$

Compute the annual rate of return on the equipment