The Bartram$-$Pulley Company $($BPC$)$ must decide between two mutually exclusive investment projects. Each project costs $$6,750$ and has an expected life of $3$ years. Annual net cash flows from each project begin $1$year after the initial investment is made and have the following probability distributions:

Project A

Project B

Probability

Net Cash Flows

Probability

Net Cash Flows

$0\mathrm{.}2$

$$6,000$

$0\mathrm{.}2$

$$0$

$0\mathrm{.}6$

$$6,750$

$0\mathrm{.}6$

$$6,750$

$0\mathrm{.}2$

$$7,500$

$0\mathrm{.}2$

$$18,000$

BPC has decided to evaluate the riskier project at a $12\%$ rate and the less risky project at a $10\%$ rate.

$1.$ What is the risk$-$adjusted NPV of each project?

$2.$ If it were known that Project B is negatively correlated with other cash flows of the firm whereas Project A is positively correlated, how would this affect the decision?

$3.$ If Project Bs cash flows were negatively correlated with gross domestic product $($GDP$),$ would that influence your assessment of its risk?

Please show formulas