Blue Bay Ltd$.$ has made an initial investment of R $500000$ in a new project. The firm$$s cost of capital is $12\%.$ The investment is expected to generate the following cash inflows over the next five years:

Year $1$: R $50000$

Year $2$: R $60000$

Year $3$: R $150000$

Year $4$: R $140000$

Year $5$: R $500000$

The profitability index $($PI$)$ is $...$ ; therefore, the investment should $...$

a$.$

$1\mathrm{.}14$; be undertaken.

b$.$

$1\mathrm{.}14$; not be undertaken.

c$.$

$1\mathrm{.}29$; not be undertaken.

d$.$

$1\mathrm{.}29$; be undertaken.