I want to invest in a new company and so I want to calculate the free cash flow and hence the IRR of it

I use the typical formula in which EBIT *(1-T)+depreciation-change in working capital- capex = free cashflow

But in one of the cost item of this company, it is a management fee (assume it is $100) which is payable to me every year as the new shareholder of this company

and how should this management fee be accounted for? should it add back into the above free cashflow formula?

You are entitled to 2 different cash-flow streams:

Calculate the annual management fee (after personal income taxes) for the forecast period

Calculate the free cash flow as you described above minus financing cash flows (interest plus repayments). Remember that you need to calculate the Flow to Equity. This is the cash-flow (on a pro-rats basis) you are entitled to. You might also consider personal taxes here, i.e. taxes on dividends.

Sum up both cash-flow streams and calculate the IRR taking into consideration your initial investment.

really thank you for your reply, if i use the formula you suggest then the result I get will be the Equity IRR, in which I consider the effect of loan. However if I do really want to calculate the project IRR, is it reasonable to just add the management fee to the free cashflow. lets assume i will acquire 40% of the target company for $1000,

can i say the cash outflow is 1000, and every year after the acquisition the cash inflow is 40% of the FCFF + $100 management fee ?

But that NI of Investee already has after tax $100 Fee as expense.

Since you received only 40% of the after tax $100 through NI therefore you are short of remaining 60% of $100 which you need to add back to your share of Income = 40% of NI of Investee + 60% of $100