$12-12$ PROJECT RISK ANALYSIS The Butler$-$Perkins Company $($BPC$)$ must decide

between two mutually exclusive projects. Each project has an initial after$-$tax cash

outflow of $$6,750$ and has an expected life of $3$ years. Annual project after$-$tax cash

flows begin $1$ year after the initial investment and are subject to the following

probability distributions:

BPC has decided to evaluate the riskier project at $12\%$ and the less$-$risky project at

$10\%.$

a$.$ What is each project's expected annual after$-$tax cash flow? Project B$\text{'}$s

standard deviation $,({}_B)$ is $$5,798,$ and its coefficient of variation

$(C{V}_B)$ is $0\mathrm{.}76.$ What are the values of ${}_A$ and $C{V}_A?$

b$.$ Based on the risk$-$adjusted NPVs$,$ which project should BPC choose?

c$.$ If you knew that Project B$\text{'}$s cash flows were negatively correlated with the

firm's other cash flows, but Project A$\text{'}$s cash flows were positively correlated,

how might this affect the decision? If Project B$\text{'}$s cash flows were negatively

correlated with gross domestic product $($GDP$),$ while A$\text{'}$s cash flows were

positively correlated, would that influence your risk assessment?