An investment is expected to produce the following annual year$-$end cash flows:

Year $1$ $ $5,000\mathrm{.}00$

Year $2$ $ $1,052\mathrm{.}00$

Year $3$ $ $\mathrm{.}00$

Year $4$ $ $5,100\mathrm{.}00$

Year $5$ $ $6,100\mathrm{.}00$

Year $6$ $ $910\mathrm{.}82$

The investment will cost $$13,200$ today.

Required:

a$.$ Will this investment be profitable?

b$.$ What will be the IRR $($compounded annually$)$ on this investment?

c$.$ Show how much of each year$$s cash flow is recovery of the $$13,200$ investment and how much of the cash flow is return on investment. $($Hint: See Exhibit $3-13$ and Concept Box $3\mathrm{.}2.)$