You run a construction firm. You have just won a contract to construct a government office building. Constructing it will take two years

and require an investment of $$10$ million today and $$5$ million in one year. The government will pay you $$25$ million upon the building$$s completion.

Suppose the cash flows and their times of payment are certain, and the risk$-$free interest rate is $10\%.$

a$.$ What is the NPV of this opportunity?

b$.$ If the interest rate increases to $12\%,$ what is the change in NPV in $\%?$