$3.(14$ points$)$ Consider a public$-$private partnership under the following conditions:

The government is committed to support a community development project with a subsidy of $$10$ mil., but only after the private developer has demonstrated a certain level of commitment and competence in the implementation of the project. The government will thus release the funds from the subsidy only after $2$ years of successful operation and government monitoring $$ that is$,$ at the beginning of $2027.$

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The projected private cash flows from the operations are:

Year $2025$ capital expenditures of $$22$ mil.

Years $2026,2027,2028,2029,2030,2031$:

$-$ costs: workers$$ salaries of $$4\mathrm{.}1$ mil. per year each year

$-$ revenue: $$7$ mil. per year each year$$

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Assume for simplicity that all costs and revenues are realized at the beginning of each year. The current date is beginning of $2025.$ All cash flows are net of inflation. Assume the opportunity cost of capital for the private investor is at $9\mathrm{.}5\%$ per year.

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a$)$ Calculate the Net Present Value $($NPV$)$ of this project. Will the private developer undertake this project or not?

b$)$ Would it influence the private developer$$s decision if the government subsidy was released right away at the beginning of $2025($instead of $2027)?$ Explain.

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Remember to show your calculations in a separate excel