Problem $1$:

Consider an investment that requires an outlay of $$5$ million initially, with expected cash flows of $$1$ million, $$0,$ and $$5$ million, respectively, for the following $3$ years.

a$)$ What is the NPV of this investment if the discount rate is $5\%?$

b$)$ What is the NPV of this investment if the discount rate is $8\%?$