A project is expected to provide cash flows of $$10,650,$ $$11,600,$ $$14,700,$ and $$9,200$ over the next four years, respectively. At a required return of $9$ percent, the project has a profitability index of $1\mathrm{.}347.$ For this to be true, what is the project's cost at Time $0?$

Multiple Choice

$$27,767$

$$42,824$

$$50,381$

Insufficient information.

$$25,453$