Suppose a firm has existing projects with an expected cash flow of $$90$M and

Volatility $(\backslash$sigma $)$ of $$20$M$.$ The firm is evaluating whether it should invest in the following

new project:

$-$ Initial cost is $$50$M

$-$ Expected payoff is $$60$ M in one year; Volatility $(\backslash$sigma $)$ of the payoff is $$45$M

$-$ The correlation of this project with existing firm projects is $40\%$

$-$ The new project$$s Beta $(\backslash$beta $)=1\mathrm{.}2$

$-$ The risk$-$free rate is $5\mathrm{.}5\%,$ and the market risk premium is $3\mathrm{.}5\%.$

$-$ The marginal cost of having a cash flow at risk $($CaR$)$ of a given level is $10\%$

$-$ Use CaR$(5\%)$

a$.$ What is the NPV of the new project?

b$.$ How does risk get accounted for in the NPV rule?

c$.$ How does risk influence the value of the project? Calculate the economic value of the

project.

d$.$ How much does risk matter $($hint: what is true cost of capital relative to that used in b$)?$

e$.$ Why does the CaR have a cost? And where does the cost of risk come from?