im gonna give you short answers to your questions, hope that would be enough to get you going!
1) working capital tells you what would be left if a company took all of its short term resources, and used them to pay off its short term liabilities. the more working capital a firm has on hand, the lesser financial strain it experiences.
current assets - current liabilities = working capital.
equity - non current assets + non current liabilities = working capital.
2) We should undertake the financial appraisal of capital investment because it helps us to come to a cunclusion about the end-result of the investment (return that can be earned, resale value after a few years etc.) and choose the appropriate capital investment based on our requirements and capital outlay and capital investment decisions of the firm. financial appraisal comprehensively uses TIME VALUE OF MONEY method to appraise a plethora of investment oppurtunities. capital budgeting usually involves very higly complex decisions without financial appraisal. these are a few capital budgeting techniques used for appraisal - payback period (discounted, normal), net present value method, internal rate of return method etc.
3) Discounting methods are better than Non- Discounting methods because discounting metods involve using time value of money method that gives you the actual value of a rupee after some X years. now, 1 rupee earned at the end of each year for 4 years will definitely get you 4 rupees after 4 years from now but the value of those 4 rupees will be down. you may not be able to buy something for 4 rupees after 4 years that u can buy now. so, the value of money receivable after some time is lesser at that time. this is where discouting rate comes into play. if, discounting rate is 10%, value of a rupee receivable after a year would be, 1/(100+10)% = 0.909 = 90 paise. and after two years, it is .909/110% = 0.826 rupees. so, discounting lets you be prudent and assess the actual value of amount you might receive after N years so you dont over-rate your return on investment.
Project financing refers to funding of greenfield projects whereas financing a project can be of any project including greenfield or brownfield project.
The biggest difference is that in project financing a new asset needs to be constructed thus this sort of financing carries maximum of completion risk and repayment carries the operational risks whereas funding of brown field project only has operational risks. Completion risk is not applicable therein.
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