Question $4$: Project Appraisal $[8$ Marks$]$ Jack Pty Ltd is a fishing company in the Eastern Cape. It is considering opening new offices in Durban. The NPV of the project is estimated at R$12$ million. The economy and the market are expected to be average over the next few years. Management believes that there is a fifty per cent $(50\%)$ chance that the economy will be average. The board of directors is worried about this uncertainty. As a result, a statistician was hired and has put forward the following scenarios: Economic scenario Probability of outcome NPV $($$$)$ Recession $0\mathrm{.}05-60$ million Below average $0\mathrm{.}20-35$ million Average $0\mathrm{.}5014$ million Above average $0\mathrm{.}2022$ million Boom $0\mathrm{.}0532$ million Required: a$)$ What is the expected NPV of the project? $(3$ Marks$)$ b$)$ Calculate the standard deviation of the NPV of the project. $(3$ Marks$)$ c$)$ Calculate the coefficient of variation of the NPV of project. $(2$ Marks