There is a general consensus among both academics and practitioners, that NPV is the best investment decision rule, because it takes into account all of the cash flows of a project, its risk, and time value of money, as well as being a good measure of the economic value created by the project for a company's shareholders. Nevertheless, NPV is not perfect. One of the down sides of NPV$,$ is that it does not reflect the size of the project being considered. This means that when companies have limited resources, as they do in the real world $($i$.$e$.$ there is capital rationing$),$ and when they have multiple projects to choose from, again, as they do in the real world, they cannot rely solely on the NPV of individual projects. Please meet or otherwise communicate with your group to answer the following:

$1.$ Suppose a company has three independent projects to choose from, A$,$ B$,$ and C$,$ and all have positive NPVs$,$ i$.$e$.$ $$1,000,$ $$700,$ and $$400,$ for each project, respectively. Assume also that projects A$,$ B$,$ and C require initial investments of $$1,600,$ $$1,100,$ and $$500,$ and respectively. If the company has a total budget of $$1,600$ that it can allocate to capital projects, please answer the following:

iii. Would it be possible to use the Profitability Index $($PI$)$ method to give us the correct answer $($about which combination of projects to pick$)?$ Please find the PI for each standalone project, A$,$ B$,$ and C$,$ and check to see if we can use it to select the same set of projects as in part $($b$).($Hint: the PI of project X can also be computed from: $($NPV of X $+$ Initial Investment for X$)/($Initial Investment for X$).$